Design, Development and Test of a Refractometer

UNIVERSITÀ DEGLI STUDI DI SIENA

Facoltà di Ingegneria

Dipartimento di Ingegneria dell'Informazione

Design, Development and Test of a Refractometer Based on Optical Fiber Gratings: Physical and Biochemical Applications Francesco Chiavaioli Ph.D Thesis in Information Engineering

Supervisors Prof. Valerio Vignoli Prof. Massimo Brenci

Examination Commitee Prof. Elena Biagi Prof. Sabina Merlo Prof. Marco Mugnaini

Thesis reviewer Dr. Cosimo Trono

Siena January 20, 2012

To my mother Nadia and my father Elvio

iii

Epigraph A life without research is not worthy of being lived for man Platone

Apologia di Socrate (cap. 28)

The beauty does not spring up from wealth, but by virtue. Research leads to truth Socrate

Who are we and what are we looking for? The answer will be revealed through research

v

Contents

Acknowledgements

xxiii

Glossary

xxv

Abstract

xxvii

1 Introduction

1

1.1

Motivation and approaches

. . . . . . . . . . . . . . . . . . . .

1

1.2

Application to sensor based on optical ber grating . . . . . . .

3

1.3

Contributions and outline

. . . . . . . . . . . . . . . . . . . . .

5

1.4

Istruzioni per la stampa

. . . . . . . . . . . . . . . . . . . . . .

7

I Theory, manufacturing and applications of optical ber gratings 2 General concepts about optical ber gratings

9 11

2.1

Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11

2.2

Diraction gratings . . . . . . . . . . . . . . . . . . . . . . . . .

16

2.3

Towards optical ber gratings . . . . . . . . . . . . . . . . . . .

20

2.3.1

21

Graphical method

. . . . . . . . . . . . . . . . . . . . .

3 Theory of optical ber gratings 3.1

Basics about theoretical perspectives of OFGs . . . . . . . . . . vii

27 27

Contents

3.2

Study of OFGs by means of the coupled mode theory (CMT)

.

29

3.2.1

Optical characteristics of FBGs . . . . . . . . . . . . . .

58

3.2.2

Optical characteristics of LPGs . . . . . . . . . . . . . .

63

3.2.3

Hybrid coupled mode theory

65

. . . . . . . . . . . . . . .

3.3

Study of OFGs by means of the transfer matrix method (TMM)

68

3.4

Study of OFGs by means of the nite element method (FEM) .

79

4 Manufacturing of optical ber gratings

83

4.1

Basics about gratings manufacturing . . . . . . . . . . . . . . .

83

4.2

Fiber Bragg gratings . . . . . . . . . . . . . . . . . . . . . . . .

86

4.3

4.2.1

Internal writing technique . . . . . . . . . . . . . . . . .

88

4.2.2

Two-beam interferometer techniques

. . . . . . . . . . .

91

4.2.3

Phase mask techniques . . . . . . . . . . . . . . . . . . .

96

Long period gratings . . . . . . . . . . . . . . . . . . . . . . . . 100 4.3.1

Photochemical or UV methods

4.3.2

Non-photochemical or non-UV methods

. . . . . . . . . . . . . . 103 . . . . . . . . . 113

5 Optical ber gratings for physical and biochemical sensing 139 5.1

5.2

5.3

5.4

Theory of optical ber gratings for physical sensing . . . . . . . 139 5.1.1

Fiber Bragg gratings . . . . . . . . . . . . . . . . . . . . 140

5.1.2

Long period gratings . . . . . . . . . . . . . . . . . . . . 146

Applications of optical ber gratings for physical sensing . . . . 165 5.2.1


5.2.2


Theory of optical ber gratings for biochemical sensing . . . . . 175 5.3.1


5.3.2


Applications of optical ber gratings for biochemical sensing . . 191 5.4.1


5.4.2


II Flow cell for refractive index measurements: design, development and test

199

6 Experimental setup for refractive index measurements

201

viii

Contents

6.1

Basic concepts about the refractive index measurements

. . . . 201

6.2

Methodology of the proposed refractive index sensor

6.3

Thermo-stabilized ow cell . . . . . . . . . . . . . . . . . . . . . 205

6.4

Manufacturing of the gratings . . . . . . . . . . . . . . . . . . . 209

6.5

Interrogation system and data processing

6.6

Fluidics system and chemicals . . . . . . . . . . . . . . . . . . . 233

. . . . . . 203

. . . . . . . . . . . . 230

7 Compensated refractive index measurement for mixtures 7.1

7.2

235

Characterization of the sensor's cross-sensitivities . . . . . . . . 235 7.1.1

Strain characterization . . . . . . . . . . . . . . . . . . . 235

7.1.2

Temperature characterization . . . . . . . . . . . . . . . 235

7.1.3

Long-term stability of the sensor

. . . . . . . . . . . . . 235

Refractive index measurement . . . . . . . . . . . . . . . . . . . 235

8 Preliminary biochemical measurement on antibody-antigen bioassay 237 8.1

An overview about antibody-antigen bioassay

8.2

Materials and methods . . . . . . . . . . . . . . . . . . . . . . . 237

8.3

. . . . . . . . . . 237

8.2.1

Reagents

. . . . . . . . . . . . . . . . . . . . . . . . . . 237

8.2.2

Chemical treatment of the sensor and immunoassay . . . 237

Biochemical measurement on an antibody-antigen bioassay . . . 238

III Conclusions

239

9 Conclusions

241

9.1

Summary and contributions . . . . . . . . . . . . . . . . . . . . 241

9.2

Tracks for future works . . . . . . . . . . . . . . . . . . . . . . . 241

Bibliography

243

Index

267

Publications List

273

ix

List of Figures

2.1

Optical ber sensors classication:

extrinsic OFS on the left

and intrinsic OFS on the right . . . . . . . . . . . . . . . . . . . 2.2

Optical ber gratings: physical depiction (a) and refractive index prole of the ber core (b)

2.3

. . . . . . . . . . . . . . . . . .

. . . . . . . .

14

Long period grating: depiction of light coupling and propagation with the distinctive spectra (Λ not in scale)

2.5

13

Fiber Bragg grating: depiction of light coupling and propagation with the distinctive spectra (Λ not in scale)

2.4

12

Diraction grating:

. . . . . . . .

15

an example of reection grating (a) and

transmission grating (b)

. . . . . . . . . . . . . . . . . . . . . .

17

2.6

Diraction eect of a grating using wavefronts . . . . . . . . . .

18

2.7

Diraction of a light wave by a grating . . . . . . . . . . . . . .

20

2.8

Fiber Bragg grating: illustration of coupling between the fundamental core mode and its respective counter-propagating core mode by means of the ray-optic depiction (a) and its

2.9

β -plot

(b)

22

Long period grating: illustration of coupling between the fundamental core mode and the rst forward-propagating cladding mode by means of the ray-optic depiction (a) and its

3.1

β -plot

(b)

Step-index single mode ber: geometry (a) and refractive index distribution (b) . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2

24

28

Local intensity of light as a function of radial position for the rst four

l=1

cladding modes (p xi

= 1, 2, 3, 4)

. . . . . . . . . .

37

3.3

Normalized coupling constant for

l = 1

cladding modes in a

step-index single-mode ber. The black circles are odd cladding modes, whereas the white circles are even cladding modes 3.4

. . .

42

Phase-matching conditions in a ber Bragg grating (FBG) with a period

Λ.

The counter-propagating coupling can occur be-

tween (top to bottom, longest to shortest wavelength) oppositely traveling core modes, the core mode and a cladding mode and the core mode and radiation modes 3.5

. . . . . . . . . . . . .

45

Phase-matching conditions in a long period grating (LPG) with a period

Λ.

The forward-propagating coupling can occur be-

tween (top to bottom, longest to shortest wavelength) the core mode and a cladding mode and the core mode and radiation modes 3.6

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47

Experimentally measured transmission spectrum of a typical ber Bragg grating in a step-index SMF. The deepest peak on the right represents the core-mode core-mode counter-propagating coupling, whereas the other peaks represent the core-mode claddingmode counter-propagating couplings

3.7

. . . . . . . . . . . . . . .

49

Experimentally measured transmission spectrum of a LPG in a step-index SMF with

Λ = 410µm.

The six peaks represent the

coupling between the fundamental core mode and the rst six odd cladding modes 3.8

. . . . . . . . . . . . . . . . . . . . . . . .

50

LPG phase-matching conditions of cladding modes for a stepindex SMF. Low-order cladding modes are on the right, whereas high-order cladding modes are on the left

3.9

. . . . . . . . . . . .

LPG phase-matching conditions of low-order (p

= 1, 3, ...19)

cladding modes for a Boron-Germanium co-doped ber . . . . . 3.10 LPG phase-matching conditions of high-order (p

54

55

= 21, 23, ...39)

cladding modes for a Boron-Germanium co-doped ber . . . . . 3.11 LPG phase-matching conditions of very-high-order (p

56

= 41, 43, ...59)

cladding modes for a Boron-Germanium co-doped ber . . . . .

57

3.12 FBG reection spectrum as a function of normalized resonance wavelength in uniform gratings with

κ bL=8

κ bL=2

(dashed line) and

(solid line) . . . . . . . . . . . . . . . . . . . . . . . . .

59

3.13 FBG reection spectra: 10 mm-long gratings with dierent values of induced-index change stant induced-index change

∆ ncore (a) and gratings of a con−3 RIU with of ∆ ncore = 5 × 10

dierent lengths and resonance wavelengths (b) . . . . . . . . .

61

3.14 Measured (dots) and theoretically calculated (solid line) reection spectrum for a 1 mm-long uniform FBG with

κ b L = 1.64

.

62

κ b L = 0.39 . . . S (z) due to an exposure

66

. . . . . . . . . . . . . . . . . . . . . . . .

74

3.15 Measured (dots) and theoretically calculated (solid line) transmission spectrum for a 50 mm-long LPG with 3.16 Longitudinal refractive index variation function of width

W

3.17 Azimuthal refractive index variation

P (r, φ)

divided into ring

sectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.18 Sketch of periodic grating structure of total length and period 4.1

Λ

75

L = NΛ

with input and output unperturbed regions

. . .

81

Common types of ber gratings classied by the variation of the induced-index change along the ber axis: (a) uniform, (b) Gaussian-apodized, (c) raised-cosine-apodized, (d) chirped, (e) discrete phase-shift and (f ) superstructure . . . . . . . . . . . .

85

4.2

Blazed ber Bragg grating: physical depiction . . . . . . . . . .

87

4.3

Chirped ber Bragg grating: physical depiction . . . . . . . . .

87

4.4

Schematic of the original experimental setup used for writing ber Bragg gratings within the optical bers [1] . . . . . . . . .

4.5

Time evolution of reectivity of a 1 m-long Ge-doped-core optical ber (NA = 0.1 and core diameter = 2.5

µm).

Insets (a) and

(b) show typical FBG reection and transmission, respectively . 4.6

89

90

Schematic of the original experimental setup used for writing ber Bragg gratings in optical bers by means of transverse holographic method [2] . . . . . . . . . . . . . . . . . . . . . . .

4.7

Sketch of the experimental setup used for writing ber Bragg gratings by means of transverse holographic method [3] . . . . .

4.8

93

Sketch of the experimental setup used for writing ber Bragg gratings by means of source-tunable interferometer method [3] .

4.9

92

95

Sketch of the phase mask used for writing ber Bragg gratings by means of phase mask technique

. . . . . . . . . . . . . . . .

97

4.10 Schematic of modied phase mask technique used for writing ber Bragg gratings

. . . . . . . . . . . . . . . . . . . . . . . .

99

4.11 Absorption spectrum of 3.5 mol% Ge-doped fused silica [4] compared with that of pure fused silica . . . . . . . . . . . . . . . . 101 4.12 Schematic of photoexcitation pathways for dierent LPG writing techniques in standard optical ber: the conventional singlephoton (5 eV) and three multi-photon approaches [4] . . . . . . 102 4.13 Experimental setup for writing LPGs by means of an amplitude mask . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 4.14 Time evolution of a LPG with period of intervals [5]

Λ=

474

µm

at 1-min

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

4.15 Transmission spectrum of a 4cm-long LPG with a period of 200

µm

written in 10 mol% Ge-doped ber [6] . . . . . . . . . . . . 108

4.16 Dependence of induced refractive index on near-UV power density [6] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 4.17 Schematic of experimental setup for point-to-point LPGs manufacturing with high-intensity femtosecond UV and near-UV laser pulses [4]

. . . . . . . . . . . . . . . . . . . . . . . . . . . 110

4.18 Photograph of the LPG section written by means of pointto-point technique based on high-intensity femtosecond laser pulses at a wavelength of 352 nm [4]

. . . . . . . . . . . . . . . 113

4.19 Experimental setup for LPGs manufacturing by means of a point-to-point non-UV technique based on a IR laser source [7]. ND, neutral density. CCD, charge-coupled device . . . . . . . . 115 4.20 Transmission spectrum of a 29.9 mm-long LPG with a period

Λ=

460

µm

[7] . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

4.21 Transmission spectrum of LPG written in non-H2 -loaded and H2 -loaded dispersion-shifted bers [8] . . . . . . . . . . . . . . . 119 4.22 Fabrication apparatus for writing LPGs by point-to-point CO2 laser exposure [9] . . . . . . . . . . . . . . . . . . . . . . . . . . 120 4.23 Fabrication apparatus for writing LPGs by electrical discharges produced by a commercial splicer . . . . . . . . . . . . . . . . . 122 4.24 Transmission spectra of three dierent LPGs with the same period of 540

µm

[10] . . . . . . . . . . . . . . . . . . . . . . . . 124

4.25 The inuence of dierent axial tension (GB , GS and GSS ) on grating inscription [10] . . . . . . . . . . . . . . . . . . . . . . . 125 4.26 Photograph of the arc discharge showing its asymmetry [11] . . 126 4.27 Photograph of the asymmetric deformation of a silica capillary (56

µm

/ 125

µm)

submitted to an arc discharge [11] . . . . . . 127

4.28 Photograph made by the transmission optical microscope Nikon Optiphot of an electric arc-induced LPG written in a standard step-index SMF-28 optical ber . . . . . . . . . . . . . . . . . . 129 4.29 Schematic of ion implantation technique with a metal amplitude mask [12]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

4.30 Photograph (a) and sketch (b) of the cross-section of the He-ion implanted optical ber. Sketch (c) of the cross-section of the optical ber etched with hydrouoric acid [12] . . . . . . . . . . 132 4.31 Transmission spectrum of the He-ion implanted etched optical ber [12] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 4.32 Side view of a mechanically induced long period grating with period

Λ

[13]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

4.33 An example of periodically grooved plate used to induce LPGs mechanically

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

4.34 Transmission spectra of a grating with period

Λ =

712

µm

measured for an applied pressure increasing from p1 to p5 [13] . 136

5.1

Typical FBG characterization in axial strain of a standard Corning SMF-28 optical ber . . . . . . . . . . . . . . . . . . . . . . 143

5.2

Typical FBG characterization in temperature of a standard Corning SMF-28 optical ber

5.3

. . . . . . . . . . . . . . . . . . . 146

Dierence in group RI between the fundamental core mode and each of the rst 30 cladding modes (from

p = 1 to p = 59, only a

few are numbered) as a function of LPG resonance wavelength, calculated for BGe co-doped optical ber. points of the curves with the

∆ ng = 0

The intersection

axis correspond to the

turn around points. In the shaded region,

|e γ| > 5

. . . . . . . . 151

5.4

Shift in the resonance wavelengths of four attenuation bands, A−D, as a function of applied strain for a LPG. The dashed line is the strain-induced wavelength shift for a FBG fabricated at 1550 nm for comparison [14]

5.5

. . . . . . . . . . . . . . . . . . 155

Shift in the resonance wavelengths of four attenuation bands, A−D, as a function of temperature for a LPG. The dashed line is the temperature-induced wavelength shift for a FBG fabricated at 1550 nm for comparison [14] . . . . . . . . . . . . . . . 158

5.6

Experimental shift of the resonance wavelength in four attenuation bands (from curve A to curve D) of a long period grating as a function of the surrounding refractive index [14]

5.7

. . . . . . 161

Plot of the shift of the resonance wavelength (a) and the minimum transmission value of the related attenuation band (b) as a function of the refractive index of the medium surrounding a long period grating with a period 400 borongermanium co-doped optical ber [15]

5.8

µm

written in a

. . . . . . . . . . 163

Schematic of an optical add/drop multiplexer based on a ber Bragg grating . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

5.9

Schematic of an optical wavelength division multiplexing system based on a ber Bragg grating . . . . . . . . . . . . . . . . 167

5.10 Schematic of an optical dispersion compensation system based on a chirped ber Bragg grating . . . . . . . . . . . . . . . . . . 168 5.11 Eect of gain-attening (lled circles) using LPGs on the gain of erbium doped ber ampliers (solid curve) [5]

. . . . . . . . 170

5.12 Principle of operation of the liquid level sensor based on an LPG: (a) schematic of the LPG and (b) transmission spectrum of the expected split in the LPG attenuation band [16] . . . . . 171 5.13 Basic congurations of modied ber Bragg grating to be used as surrounding refractive index sensor: tilted ber Bragg grating (a) and etched ber Bragg grating (b) [17] . . . . . . . . . . 177 5.14 Schematic of a thin-lm coated LPG structure (a) and the corresponding refractive index prole (b) [18] . . . . . . . . . . . . 180

5.15 Experimental shift of the resonance wavelengths of the 9 (lled circles) and

p =

p =

11 (lled squares) cladding modes,

plotted as a function of the overlay thickness [19]

. . . . . . . . 183

5.16 Eective refractive index of cladding modes as a function of the overlay thickness [20] . . . . . . . . . . . . . . . . . . . . . . . . 185 5.17 Shift of the resonance wavelength as a function of the overlay thickness for dierent value of the refractive index of overlay material: lled triangles 2 RIU, lled rhombuses 1.7 RIU and lled squares 1.57 RIU [21]

. . . . . . . . . . . . . . . . . . . . 186

5.18 Optimum overlay thickness for the

p=

15 cladding mode as a

function of the overlay refractive index [22] 5.19 Shift of the resonance wavelength in the

. . . . . . . . . . . 188

p = 5 cladding mode as

a function of the overlay thickness for dierent overlay refractive index when the coated LPG is placed in air (nsur 5.20 LPG transmission spectra of the

= 1)

[20] . . . 189

p = 9 cladding mode for three

dierent surrounding refractive indices without the overlay (a) and with an overlay characterized by a thickness of 159 nm and a refractive index of 1.67 RIU [20] . . . . . . . . . . . . . . . . . 190 5.21 Schematic representation of a biosensor.

The dierent bio-

recognition elements and transducers are depicted in the gure [23]

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

5.22 Schematic representation of (A) hybrid sensor and (B) implanted hybrid sensor [24] . . . . . . . . . . . . . . . . . . . . . . . . . . 193 5.23 (A) Fiber optic SPR probe; (B) schematic representation of the system setup; (C) overview of the immunoassay strategies on the ber optic SPR biosensor; (D) the spectrum dips in PBS buer after 10 min incubation of the SPR ber in: a negative control sample (blue dip), a sample containing the antigen (red dip), a sample containing the antigen subsequently labeled with antibody linked nanobeads (black dip) [25] . . . . . . . . . . . . 195 6.1

Sketch of the manufactured ow cell: longitudinal cross−section (a) and top view (b) [26] . . . . . . . . . . . . . . . . . . . . . . 205

6.2

A picture of the developed ow cell [26]

6.3

A side-view picture of the ow cell

. . . . . . . . . . . . . 206

. . . . . . . . . . . . . . . . 208

6.4

Stabilization eect on the LPG resonance wavelength by means of the Peltier cells . . . . . . . . . . . . . . . . . . . . . . . . . . 209

6.5

Refractive index prole of B-Ge co-doped step-index singlemode Fibercore PS1250/1500 ber

6.6

. . . . . . . . . . . . . . . . 211

Schematic of the manufacturing setup for FBGs. SLD, superluminescent light diode . . . . . . . . . . . . . . . . . . . . . . . 212

6.7

Photograph of our manufacturing setup for FBGs . . . . . . . . 214

6.8

Detail of the ber clamping points and the ber positioning mechanism of our manufacturing setup for FBGs

6.9

. . . . . . . . 216

Schematic of a typical monochromator placed inside an optical spectrum analyzer for the spectral analysis of an optical signal . 217

6.10 Detail of the ber clamping points and the ber positioning mechanism of our manufacturing setup for LPGs

. . . . . . . . 219

6.11 Detail of the schematic of the manufacturing setup for LPGs . . 220 6.12 Photograph taken with transmission optic microscope Nikon Optiphot of a LPG written by means of the point-to-point technique with KrF excimer laser

. . . . . . . . . . . . . . . . . . . 221

6.13 Transmission spectra of the manufactured LPG at dierent scans.

Each curve is labeled with a dierent color (see the

label in the graph)

. . . . . . . . . . . . . . . . . . . . . . . . . 222

6.14 Transmission spectra of the manufactured LPG at dierent steps. Each curve is labeled with a dierent color (see the label in the graph)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 224

6.15 Comparison between the two distinct manufacturing approaches. The red curve refers to the rst approach (many scans-few shots), whereas the blue curve refers to the second approach (one scan-many shots)

. . . . . . . . . . . . . . . . . . . . . . . 226

6.16 Transmission spectrum of the ber with the FBG loss peak on the left and the LPG loss peak on the right.

The green-

highlighted distance between the two resonance bands is about 33 nm

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228

6.17 Theoretical prediction of the LPG optical parameters . . . . . . 229 6.18 Front panel of the developed NI CVI program for the real time monitoring of the attenuation bands of the two gratings

. . . . 232

6.19 Comprehensive block diagram of the refractive index measurements

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234

List of Tables

4.1

Comparison between the experimental data on LPG inscription eciency in a hydrogen-loaded Corning SMF-28 ber for pointto-point technique at dierent source wavelengths (LPGs of the same period, 300

µm,

and of the same length, 2 cm). . . . . . . 112

5.1

Comparison between the experimental data on FBG strain sen-

5.2

Comparison between the experimental data on FBG tempera-

sitivity at dierent wavelengths. . . . . . . . . . . . . . . . . . . 142

ture sensitivity at dierent wavelengths. 6.1

. . . . . . . . . . . . . 145

Used initial values of the tting parameters of the two gratings. 231

xxi

Acknowledgements

If I have seen farther than others, it is because I was standing on the shoulders of giants. Albert Einstein

At the end of my work, there are many People to thank for helping me during these three years of PhD. First of all, I wish to thank my supervisors, Prof. Valerio Vignoli and Prof. Massimo Brenci, for creating this opportunity to study exciting and fascinating research elds in optical ber sensor. I am very thankful for the guidance, advices and encouragements they provided since the beginning of my PhD. Cosimo (+reviewer) Francesco e Ambra Ada e Marco Franco e Simone ev:Tre bariste siena e Tre girls cnr It was a pleasure to work at the Laboratory of Telematics and Telecommunications and I'd like to thank all the colleagues of the Visual Information Processing and Protection group, for the interesting discussions and, above all, for their friendship... I am very grateful to the members of my thesis committee, Prof. Elena Biagi, Prof. Sabina Merlo and Prof. Marco Mugnaini, for accepting to be part of the committee. ...I would also like to express my gratitude to the reviewers of the thesis, Prof. Patrick Le Callet and Prof. Pedro Comesana Alfaro, for their valuable comments and suggestions... xxiii

Last but most important, I wish to thank my mother Nadia and my father Elvio for their everlasting love and support. From my heart, I love you! Francesco Chiavaioli Siena 13/01/12

Glossary

AFM

Atomic-Force Microscope

Extrinsic Optical Fiber

Sensor

BRE

Biological Recognition Element

CGN CW

EOFS

Colloidal Gold Nanoparticle

Continuous Wave

FBG

Fiber Bragg Grating

FEM

Finite Element Method

FOB

Fiber Optic Biosensor

FWHM

CMT

Coupled Mode Theory

DNA

DeoxyriboNucleic acid

GO

DNP

DiNitroPhenol

GODC

DBR

Distributed Bragg Reector

DSC ERI

Dual Shaped Core Eective Refractive Index

EMI

ElectroMagnetic Interference

ESA

Electrostatic Self-Assembly

EFBG

Etched Fiber Bragg Grating

Full Width at Half Maxi-

mum Geometrical Optics Germanium-Oxygen-Decient

Center

HRI

High Refractive Index

IR

InfraRed

IC

Interferometric Conguration

IOFS

Intrinsic Optical Fiber

Sensor

LB xxv

Langmuir-Blodgett

LED

Light Emitting Diode

PVC

LOD

Limit of Detection

RFI

LP

Linearly Polarized

LSPCF

Localized Surface Plasmon

Coupled Fluorescence

LPG

Long Period Grating

NMR NA

Nuclear Magnetic Resonance

Numerical Aperture

OFS

Optical Fiber Sensor

RI

PolyVinyl Chloride Radio Frequency Interference

Refractive Index

RIU

Refractive Index Unit

SLD

SuperLuminescent Diode

SPR

Surface Plasmon Resonance

SRI

Surrounding Refractive Index

sPS

Syndiotactic PolyStyrene

OFG

Optical Fiber Grating

TEC

ORS

Optical Resonating Structure

TFBG

OSA

Optical Spectrum Analyzer

TIR

ppm

Parts Per Million

TMM

Transfer Matrix Method

TIBC

Transparent Inux Boundary

PML

Perfectly Matched Layer

PRBC

Condition

PMC PCF

Phase-Matching Condition Photonic Crystal Fiber

Tilted Fiber Bragg Grating

Total Internal Reection

Perfectly Reecting Bound-

ary

Thermo-Electric Cooler

Condition

TAP UV

Turn Around Point

UltraViolet

VOC

Volatile Organic Compound

Abstract

The important thing is not to stop questioning. Curiosity has its own reason for existing. Albert Einstein

An optical ber sensing system based on a hybrid cascaded long period grating (LPG) and ber Bragg grating (FBG) conguration and a thermo-stabilized ow cell for refractometric measurements is proposed. The system makes it possible to measure, and thus cancel the LPG cross−sensitivities to strain, temperature and ber bending by means of an ad-hoc developed methodology. The experimental results show that the proposed system provides satisfactory performances as far as the refractive index sensitivity and resolution are concerned. The maximum sensor sensitivity and resolution are 3120 nm RIU−1 and 2 x 10−5 RIU, respectively. The whole system, including its ow cell and the gratings manufacturing, is extensively described, along with the acquisition and processing of data. The stability of the sensor has also been tested for several hours. Finally, the proposed system has been tested for preliminary measurements in the eld of chemical/biochemical sensing. xxvii

Chapter 1

Introduction Nothing comes from nothing.

1.1 Motivation and approaches

T

he growing need for devices able to carry out fast, reliable and

in situ

measurements in the eld of physical, chemical and biological sensing is

encouraging researchers to look for new technologies. There is much interest with regards to the refractive index (RI) measurements of liquids, which have been used for many years in the eld of both the physical sensing and biochemical one. In the former, the optical properties of solutions, mixtures and, in general, any liquid can be achieved by means of RI measurements [2729]. In the latter, instead, a chance for quantitative measurements of analytes in biological uids can be oered by RI measurements together with the deposition of chemical/biochemical recognition layers on suitable substrates, eg optical ber. Chemical/biochemical interactions with these layers lead to changes in the RI of the layer itself which can be detected by means of optical methods and which depend on the concentration of the interacting analyte [30,31]. This approach is known as label-free approach, in contrast with the methodology that makes use of luminescent markers chemically bound to recognition layers. Within the label-free approach, surface plasmon resonance (SPR) is unquestionably the most exploited optical approach [32], also because of the

1

presence of SPR-based devices on the market (eg Biacore system) .

Other

1 Biacore systems are used for label-free interaction analysis in real time and allow to char-

acterize molecules in terms of specicity of their interactions, kinetics and anity. A more detailed description is available on this website http://www.biacore.com/lifesciences/ index.html

1. Introduction

2

well-known and fascinating technology platforms are based on the use of interferometric congurations (ICs) [33], made both on optical bers and planar waveguides, and optical resonating structures (ORSs) [34, 35], which can be comparable with SPR in terms of resolution [31].

Within the optical ap-

proach, optical ber gratings (OFGs) have been recently proposed as tools for chemical and biochemical sensing [36]. These sensors have high sensitivity to the RI of the medium surrounding the ber cladding, in addition to all the other benets oered by optical ber sensors (OFSs). The main advantages coming from the use of OFGs-based sensor are as follows [37]: they are compact, lightweight and minimally invasive which are key features for use in the biomedical eld. They can be also used in extreme conditions and hence in the industrial eld thanks to their strength and toughness. Other distinctive features are the eective multiplexing capability on a single ber network and the easy integration into a wide variety of structures as the signal modulation is spectrally encoded.

It is also important to stress the fact that the

optical modulation of the signal is a wavelength modulation and this implies that the read-out will not aected by changes in optical power due to either ber bending and/or source uctuations. Moreover, they are immune to both electromagnetic interference (EMI) and radio frequency interference (RFI) as there are no electrical currents owing at the sensing point. In addiction, there is the expectation that they should be able to be produced at relatively low or competitive cost, often using a range of the technologies that have been borrowed from research in the optical communications eld. Last but not least, they show multifunctional sensing capabilities, ie strain, temperature, ber bending, surrounding refractive index (SRI), pressure, chemical and biological samples.

This latter feature can be either positive or negative.

In

fact, if we want to measure only the eects caused by the measurand of interest, we must bear in mind to design a methodology for eliminating the sensor cross-sensitivities. This key point will be discussed in part II of the present work.

For all the reasons just given, a number of refractometric measurement systems that make use of OFGs have been proposed in the literature relating to physical and biochemical sensing [27, 3843]. As mentioned above, this kind of sensors show great sensitivity not only to the SRI, but also at the same time to

1.2. Application to sensor based on optical ber grating

3

temperature, strain and ber bending. Therefore a number of techniques have been proposed in the past in order to get rid of the uctuations coming from these causes [14, 43, 44]. The inuence of the cross-sensitivities can be essential when the refractometric measurement is carried out with the investigated sample owing within a microuidic system, as generally occurs whenever the RI measurement is carried out for chemical/biochemical sensing. Very recently, another interesting optical system for refractive index measurements has been reported, which is based on one−dimensional photonic crystals [45] that are made by electrochemical micromachining of the silicon. Finally, it is worth pointing out a general concept, which, nevertheless, is extremely important, when RI measurements are used for physical sensing, we are talking about bulk or volume measurements because the interaction takes place all around the ber and hence in the volume of the liquid. When RI measurements are used for biochemical sensing, instead, we are talking about layer or surface measurements because the interaction takes place in the layer/surface that has been deposited on the optical ber.

1.2 Application to sensor based on optical ber grating

A

s mentioned in section 1.1, the change of RI induced by a chemical/ biochemical interaction or by physical interaction with a dierent liquid

surrounding the ber is the working principle used in the elds of biochemical and physical sensing. Starting from these considerations, there are two classes of OFGs-based sensors depending on the region where the interaction takes place. In the case of non-coated OFGs, the eect takes into account all the volume around the ber and the transmission spectrum of the ber is modied by the considered interaction (ie volume measurements). On the other hand, if we consider OFGs on which a layer is deposited onto the grating portion, the interaction takes place within this layer or on its surface (ie surface measurements). In this case, only a portion of the optical radiation traveling along the ber, which comes out of the ber through the grating, interacts with the external environment, depending on the optical properties (ie thickness and refractive index) of the deposited layer. There are a lot of application elds in

1. Introduction

4

which the OFGs-based sensors can be eectively used. In this section, a brief overview is given. Therefore it is obvious that, considering also the relative simplicity, the rst types of sensors were based on volume measurements. One of the rst examples of OFGs-based sensor is related to the determination of calcium chloride, sodium chloride and ethylene glycol in solution [28].

Since then,

many other OFGs-based sensors have been described for the measurement of isopropyl alcohol [46], glycerine [47], sucrose [48, 49], ethanol and glucose [49], cane sugar [50], antifreeze [27], xylene [29] and chloride ion [51, 52].

It is

worth observing that this approach presents the diculty of measuring any changes in RI that occur in the volume surrounding the ber, and hence the measurement will be highly aected by interferences coming from other substances dierent from the investigated one. Therefore the use of non-coated OFGs is restricted only to pure solutions. In the last years, instead, most OFGs-based sensors are using a technological platform, which is based on coated OFGs and then carries out surface measurements. In fact, the use of a layer capable of capturing the substance under test is essential for the development of a real sensor, which can be put on the market.

In the literature, we can nd a lot of exam-

ples of OFGs coated with polymers or sol-gel matrix for chemical sensing: sol-gel derived SnO2 thin lm for ethanol vapor detection [53], poly(acrylic acid)/poly(allylamine hydrochloride) polymeric thin lm for pH detection [54], syndiotactic polystyrene in the nanoporous crystalline

δ

form for chlo-

roform detection [55], palladium/palladium-argentum thin layer for H2 detection [56, 57], perovskite-type nanocrystalline thin lm for low level H2 detection [58] and polydimethylsiloxane/ polymethyl-octylsiloxane co-polymers for detection of vapors of volatile organic compounds (VOCs) [59]. In all these cases, generally, the selectivity is only partial, since the deposited layer is not totally selective to a single analyte, but it adsorbs more than one species. Very recently, considering also the growing need in the biomedical eld, many technological platforms based on coated OFGs have been developed for biochemical sensing. For this type of sensors, a biological recognition element (BRE) able to bind with the analyte can be used and, in this case, high selectivities can be also reached depending on the anity between the BRE

1.3. Contributions and outline

5

and the investigated analyte. One of the rst demonstrations that OFGs can be eectively used as biosensors was given by Wang et al. [60, 61] using the biotin-streptavidin system, which serves as bioconjugate pair.

OFGs-based

sensors are also used for the label-free detection of bacteria using physically adsorbed bacteriophages [62], for the measurement of DNA hybridization [63, 64] and for antibody-antigen interaction [6568]. Finally, the SRI sensitivity of OFGs can be also enhanced by means of colloidal gold nanoparticles (CGNs) deposited onto the grating portion. Using this methodology, two new classes of biosensors have been reported in the literature: the former is used for real-time and label-free monitoring of both the formation of DNA monolayer in aqueous environment and complementary DNA binding [69], the latter, instead, is used in order to create an antibody-antigen binding model for dinitrophenol (DNP) [70].

1.3 Contributions and outline

T

he present dissertation can be seen as a rst step towards the realization and characterization of a thermo-stabilized ow cell of relatively low vol-

ume for compensated RI measurements [26]. For this purpose, a hybrid conguration of OFGs is used. This hybrid conguration consists of two dierent in-line OFGs, the former is a long period grating (LPG), which is able to sense changes in SRI, while the latter is a ber Bragg grating (FBG), which is used for compensating the eects on the sensor response due to possible changes in strain and temperature induced on the ber. Specically, we focus our attention on the integration of a microuidic system with an OFGs-based sensor conguration which allow us to stabilize the whole system both mechanically and thermally, and hence to measure accurately any RI changes occurring on the ber surface. It is worth highlighting that the mechanical and thermal stabilization of both the ow cell and sensor is a crucial aspect when very low RI change occurs as is the case in bioassay or, more in general, in the biochemical eld.

In this case, a high sensitiv-

ity/resolution or a low limit of detection (LOD) is necessary in order to sense biological interactions with better metrological performance than other existing optical methods, and this can be only achieved by means of an eective

1. Introduction

6

mechanical and thermal stabilization of the whole system, when OFGs are used as sensing element. The issue of the development of a thermo-stabilized ow cell for accurate RI measurements to be used in biochemical eld too was an open problem that has now been solved. This work is organized as follows.

The part I provides a comprehensive

description of the theory of OFGs and a comparison between dierent theoretical approaches to the issue of OFGs. This part includes also a brief look at the most used fabrication technology of OFGs. The theory and the most interesting applications based on OFGs for both physical and biochemical sensing are presented in part I too.

In the part II, the design and characterization

of the thermo-stabilized ow cell with the OFGs-based sensor placed inside for accurate RI measurements are fully described and discussed.

Finally, a

summary and conclusions are given in the part III. The main contributions of this PhD thesis can be summarized as follows:

The integration of a thermo- and mechano-stabilized microuidic system with an OFGs-based sensor conguration for accurate RI measurements is presented. The experimental results show that the proposed system provides good performances as far as the RI sensitivity and resolution are concerned. The maximum sensor sensitivity and resolution are 3120

−1 (Refractive Index Unit) and 2 x 10−5 RIU, respectively. It

nm RIU

is worth noting that the maximum resolution is one order lower than a commercial refractometer.

The long-term stability of the whole system was demonstrated with a

−1 . This kind of measurement is essential

calculated drift of about 1 pm h

for our ultimate goal, which is that of applying this system to the eld of biochemical sensing, where several hour-long measurements can be necessary especially during the calibration procedure.

The methodology for measuring and thus for cancelling the sensor crosssensitivities to strain, temperature and ber bending is presented. The ber bending is negligible because the optical ber is glued to the ow cell using an UV optical exible adhesive which also guarantees a safe sealing of the ow cell.

Therefore the methodology lies in using both

a FBG written on the same ber in series with the LPG and an accu-

1.4. Istruzioni per la stampa

7

rate temperature measurement system which make it possible to introduce feedback signals in order to eliminate the interferences coming from strain and temperature changes.

Referring to the proposed methodology, it has proved crucial to consider and hence experimentally evaluate the inuence of the liquid RI on the sensor temperature sensitivity.

This is to be ascribed to the thermo-

optic eect acting on the dierent liquids. We will show in subsection

?? how this eect is negligible for liquids whose RI is around the RI of

distilled water (ie 1.333 RIU) while it becomes the dominant eect for liquids whose RI is around the RI of the ber cladding (ie 1.456 RIU). Considering this eect, we obtained the temperature sensitivity for all the test solutions and hence we were able to accurately measure the RI of any liquid in the sensor range by means of our methodology.

1.4 Istruzioni per la stampa Questo MASSIMO NON C'ENTRA NULLA!!!

Il documento deve essere stampato su fogli B5, fronte e retro;

Per le copertine usare il template fornito (le .pub) realizzato con Microsoft Oce Publisher;

Per la costola del libro indicare AUTORE, TITOLO, ANNO (scritti dall'alto verso il basso, in modo che quando il libro è posto in orizzontale le scritte non risultino rovesciate).

Part I

Theory, manufacturing and applications of optical ber gratings

Chapter 2

General concepts about optical ber gratings The secret to creativity is knowing how to hide your sources. Albert Einstein

2.1 Fundamentals

A

s above-mentioned in section 1.1, the use of optical bers for sensing purposes has many advantages over other technological platforms. Op-

tical bers were rstly used in the past for telecommunication purposes as transmission medium of signals. Concerning this, there were two milestones in the history of optical bers that have made possible their use in the eld of sensing: the former was on May 16, 1960, when Theodore H. Maiman operated the rst functioning laser at Hughes Research Laboratories, Malibu, California, while the latter was the discovery of the crucial attenuation limit of 20

−1 that was rst achieved in 1970, by researchers Robert D. Maurer,

dB km

Donald Keck, Peter C. Schultz and Frank Zimar working for American glass maker Corning Glass Works, now Corning Incorporated. They also demon-

−1 attenuation by doping silica glass (SiO ) 2 −1 with titanium. A few years later they produced a ber with only 4 dB km

strated a ber with 17 dB km

attenuation using germanium dioxide (GeO2 ) as the core dopant. The early 1970s saw some of the rst experiments on optical bers being used not only for telecommunications but also for sensing purposes. Henceforth, the term

optical ber sensor

(OFS) was coined to describe a type of sensor (physical,

chemical, biological) that takes advantages of the optical ber properties. OFSs can be classied into two dierent groups depending on the use of optical bers (see gure 2.1). In fact, when perturbations act on the optical ber and it in turn changes some characteristics of light propagation inside the ber itself, we are dealing with an intrinsic OFS (IOFS). In this kind of

2. General concepts about optical ber gratings

12

sensors, hence, the optical ber acts both as light guiding element and sensing one. When, instead, the optical ber is simply used to carry the light to and from an external optical device where the sensing mechanism takes place, we are dealing with an extrinsic OFS (EOFS). In this case, the optical ber acts only as light guiding element [71].

Figure 2.1: Optical ber sensors classication: extrinsic OFS on the left and intrinsic OFS on the right

Among the OFSs, those based on

optical ber gratings (OFGs) are a special

class, which have witnessed a considerable increase in the sensing eld during the last years. An OFG is a periodic (or aperiodic in the case of chirped gratings, see chapter 3) modulation of the core refractive index (ncore ) of a single mode ber (SMF) and/or the its geometry. As can be seen in gure 2.2(a), the induced modulation of the ber core refractive index (∆ncore ) is depicted by means of gray circles inside the ber, which are distant a period (Λ). In gure 2.2(b) an example of RI prole is reported in which the modulation is made by means of a typical square wave prole of the ber core RI along the ber axis (z). Both the amplitude and the period of this modulation constitute the key physical parameters to manufacture an OFG with the desired optical characteristics. How these parameters inuence the light coupling and propagation inside the ber will be accurately explained in the rst part of

2.1. Fundamentals

13

chapter 4.

Figure 2.2: Optical ber gratings: physical depiction (a) and refractive index prole of the ber core (b) OFGs are classied into two groups according to the grating period (Λ), that is to say the distance between the grating fringes, the length of which sets out a specic mechanism of light coupling and propagation inside a SMF. From a historical point of view, the rst type of in-ber OFG was demonstrated by Ken Hill in 1978 [72] and they are known as short period gratings or better

ber Bragg gratings (FBGs), which are characterized by a grating period

in the order of magnitude of hundreds of nanometers (nm) that gives rise to coupling between the fundamental core mode and its respective counterpropagating mode. For this reason, FBGs are also called

reection gratings .

Considering a single mode ber, the light is traveling along the ber core. When the light encounters the grating plane and hence sees a discontinuity of refractive indices, assuming to approximate the light propagation according to geometrical optics (GO) and remembering Snell's law, there will always be a reected ray and a diracted one at each interface. The diracted rays travel across the ber and constitute the fundamental mode remaining in phase with each other, while the reected rays, in the event of constructive interference

14


with each other, produce the coupling with a mode that travels inside the ber core in the opposite direction compared to the fundamental mode.

Figure 2.3: Fiber Bragg grating: depiction of light coupling and propagation with the distinctive spectra (Λ not in scale)

In gure 2.3 we can see the spectral characteristics of a typical FBG in both transmission mode and reection one.

Λ is the grating pitch and the red arrows

depict both the place and the direction of the coupling. In fact, considering to have a broadband source in input to the optical ber, whose spectrum is at for simplicity over the considered wavelength range, the reectance spectrum is characterized by a reectance peak. The respective transmission spectrum is characterized by a transmission dip.

Both the reectance peak and the

transmission dip are centered at a specic wavelength that veries the phasematching condition (PMC) and hence the coupling between the two modes. In the case of FBGs, this particular PMC is known as rst order Bragg condition, the details of which will be provided in the section 2.3.

2.1. Fundamentals

15

Later, in 1996, Vengsarkar et al. presented a new class, ie the second one, of OFG known as

long period gratings

(LPGs) [73], which are characterized

instead by a grating period in the order of magnitude of hundreds of micrometers (µm) that gives rise to coupling between the fundamental core mode and a discrete set of forward-propagating cladding modes. LPGs are also called

transmission gratings .

For this reason,

Therefore, in the case of LPGs,

the reected rays, in the event of constructive interference with each other, produce the coupling with some modes that travel inside the ber cladding in the same direction of the fundamental mode due to a greater grating period.

Figure 2.4: Long period grating: depiction of light coupling and propagation with the distinctive spectra (Λ not in scale)

In gure 2.4 we can see only the transmission spectrum of a typical LPG. As mentioned above,

Λ is again the grating pitch (greater compared to FBGs) and

the red arrows depict again both the place and the direction of the coupling. As can be seen from this gure, the coupling in this type of gratings occurs only in the ber cladding owning to a grating pitch three orders of magnitude larger than the operating wavelength.

This coupling happens between the

guided fundamental mode to forward-propagating evanescent wave cladding modes, which generates in the transmission spectrum of the ber a series of attenuation bands centered at discrete wavelengths that verify the PMCs of each coupled mode. These modes decay rapidly as they propagate along the ber axis owing to both the scattering losses at the cladding/plastic acrylate


16

coating interface and bends in the ber. It is obvious in this case that, taking place a coupling between co-propagating modes, no kind of reection occurs; for this reason the reectance spectrum is not reported in gure 2.4. So for LPGs, we simply refer to the phase-matching condition in which the coupled modes are specied by means of a subscript (m) in the condition. Even for LPGs, the details of PMC will be also provided in the section 2.3. An optical ber grating can be studied by means of two dierent approaches: one is more rigorous and comprehensive, and is based on the theory of lightwave propagation in dielectric waveguides [74] and hence on Maxwell's equations, while the other is more intuitive and simple, and is based on the well-known theory of diraction gratings. The former will be extensively explained in the chapter 3, the latter instead will be discussed in the next section.

2.2 Diraction gratings

A

diraction grating is a cascade of reecting (or transmitting) elements separated by a distance comparable to the wavelength of light under

study. A complete historical description of diraction gratings can be nd in

Diraction Grating Handbook

[75]. Typical examples of diraction gratings,

thought of as a cascade of diracting elements, are a pattern of transparent slits (or apertures) in an opaque screen or a collection of reecting grooves on a substrate. In either case, the foremost physical characteristic of a diraction grating is the spatial modulation of the refractive index. In accordance with the diraction theory, an electromagnetic wave incident on a grating has its electric eld amplitude, or phase, or both, modied predictably due to the periodic change in RI in the region near the grating surface. When monochromatic light of wavelength

λ

is incident on a grating surface, it is diracted

into discrete directions each of which can be seen as a very small, slit-shaped source of diracted light. Therefore the light diracted by each slit (or groove) interacts to form a set of diracted wavefronts. The interesting feature of a grating is the fact that there exists only a set of discrete angles along which,

2.2. Diraction gratings

17

for a given spacing (d) between slits (or grooves), the diracted light from each slit (or facet) is in phase with the light diracted from any other slit (or facet), leading to constructive interference.

Figure 2.5: Diraction grating: an example of reection grating (a) and transmission grating (b)


18

An example of diraction grating is shown in gure 2.5 [75]. The picture (a) shows a reection grating, while the picture (b) shows a transmission grating. In both pictures, the input light ray strikes the grating surface at an angle

d

α,

while the diracted rays come out from the grating surface (where

denotes again the grating pitch) along at set of angles (θm ). All the angles

are taken with respect to the grating normal, which is depicted as the dashed line perpendicular to the grating surface, and they are measured from the grating normal to the ray by means of arrows. The sign convention for these angles depends on whether the light is diracted on the same side (hence plus sign) or on the opposite side of the grating as the incident light (hence minus sign). The signs are reported at the top of the same gure close to the grating normal. Figure 2.6 shows in a dierent manner the eects of a diraction grating using the wavefronts, ie surfaces of constant phase [75].

Figure 2.6: Diraction eect of a grating using wavefronts The geometrical path dierence between two parallel rays of light from ad-

2.2. Diraction gratings

19

jacent slits (or grooves) is

d sin α + d sin θ, as highlighted with the gray arrows.

The principle of constructive interference states that, when two parallel rays, in phase between each other at a particular time and space as shown with the gray line A, strike the grating surface with a grating pitch of length

d,

they

preserve the same phase information, at a particular time and space as shown in the same gure with the gray line B, if the path dierence between the two rays is equal to the wavelength of incident light

λ

or some integer multiple

thereof. The constructive interference among rays occurs only for some discrete angles

θm ,

while the destructive interference will have for all the other

angles. Considering all these reasonings, the

grating equation

can be written as

follows:

mλ = d (sin α + sin θm ) where the integer

m is the diraction

order .

(2.1)

The grating equation governs the

angular locations of the principal intensity maxima when light of wavelength

λ is diracted from a grating of slit (or groove) spacing d. that, for a particular wavelength λ, all values of m for

It is worth noticing which

|mλ/d| < 2

correspond to propagating diraction orders rather than evanescent ones. The simplest case,

m = 0,

leads to the law of reection, ie

Generally several integers

m

θ = −α.

satisfy the equation (2.1) and they are the so

called diraction orders. Referring to gures 2.5 and 2.6, the rst diraction order (θ−1

= θ)

is just reported, not only for the sake of simplicity but also

because most of the energy is related to the rst diraction order (m

= ±1).

As seen from equation (2.1) and gure 2.5, the distinction between positive and negative diraction orders can be made according to this:

  θ > −α θ < −α  θ = −α This sign convention for

m

(m > 0), orders (m < 0), reection (m = 0)

for positive orders for negative for specular states that

m>0

(2.2)

if the diracted ray lies to the

left (the counter-clockwise side) of the zero order

(m = 0)

and

m> π , the sidelobes

change of power between two modes occurs when over, for strongly overcoupled gratings where become signicantly more pronounced.

01−1p

But since the sidelobes are usually

undesiderable, most LPGs are designed to have

κ01−1p core-clad L ≤ π/2

while the

strongest gratings are designed to have the maximum coupling strength and hence, to verify the condition given in equation (3.79). As for FBGs, the other characteristic parameter of optical ber gratings is the bandwidth of the coupled cladding mode under consideration. Also in this case, we consider the FWHM as grating bandwidth, which is still evaluated when

σ b = 0.

The most used expression in the literature, which is still used

in order to calculate the FWHM of a LPG, is that of determined by Erdogan as [86]

3.2. Study of OFGs by means of the coupled mode theory (CMT) ∆ λLPG res (p) =

where the subscript and the term

∆ ne p

p

λLPG res (p)

2 s

∆ ne p L

1 +

4 κ01−1p core-clad L π

65

(3.80)

indicates the number of the coupled cladding mode

represents the dierential ERI, namely the dierence in

eective refractive indices between the fundamental core mode and the

p−th

cladding mode. Thus the equation above highlights the bandwidth dependence of both the coupling constant of the cladding mode under consideration and the dierential ERI, and the optical parameters of the grating too. Broadly speaking for each cladding mode, looking at equation (3.80), the bandwidth decreases as the length of the grating increases (as for FBGs). In addition, the bandwidth of each cladding mode depends strongly on the dierential ERI and hence, on the ERI of the

p−th

cladding mode (unlike for FBGs obviously).

In this case as well, to compare the theory and an experimental measurement [76], gure 3.15 shows the measured (dots) and theoretically calculated (solid line) transmission spectrum of a 50 mm-long weak LPG, which couples the LP01 core mode to the lowest-order cladding mode. This LPG is characterized by a design wavelength of about 1545 nm and an induced-index change of

∆ ncore = 4.2 × 10−3

κ b L = 0.39. This value of the coupling optimum value of π/2, leads to a low value of

RIU, thus yielding

factor, which is far from the

transmission about the resonance dip depicted in gure 3.15. Typical values of the FWHM about LPGs ranges from 10 nm to 25 nm.

3.2.3 Hybrid coupled mode theory Broadly speaking, it is then usually straightforward to write a reasonable onset for the optical eld by superimposing the respective basis elds with coecient functions that are slowly varying along the direction of propagation. By following this approach, one obtains equations for the amplitudes of the basis elds and their solutions. Approaches of this kind are usually addressed by the above-mentioned CMT. The question is that only in special situations, typically for longitudinally homogeneous media (ie waveguides, optical bers), the CMT equations permit analytical solutions. This means that they lead to explicit analytical expressions that describe the light propagation. For other

3. Theory of optical ber gratings

66

Figure 3.15: Measured (dots) and theoretically calculated (solid line) transmission spectrum for a 50 mm-long LPG with

κ b L = 0.39

congurations, no less interesting, one obtains coupled systems of dierential equations of higher dimension or systems with nonconstant coecients that can only be treated by numerical analysis.

Then, the solutions consist of

numerical representations of the CMT coecient functions that still permit to inspect the amplitude evolutions of the couplings under consideration. Hammer [98] proved that a unied formalism covers co- and contradirectional propagation, where applicable. coordinate is not required.

Moreover, a common propagation

Starting from these assumptions, once a physi-

cally plausible eld template has been xed for a given structure, no further heuristics is required to arrive at the desired approximate solutions for the optical eld by means of the frequency-domain Maxwell equations.

In de-

tail, given the geometry and RI prole of a dielectric structure, the rst step

3.2. Study of OFGs by means of the coupled mode theory (CMT)

67

is that of xing a reasonable onset for the electromagnetic elds. Typically, the expressions incorporate the guided modes that are supported locally by the structure. These are multiplied by amplitude functions, which depend on the propagation coordinate, that is most convenient for the respective mode. Then, what remains is to determine the strength of the interactions, namely to determine the amplitude functions. At this point, it is necessary to use a numerical approach which allows us to discretized the amplitude functions by

2

linear 1-D nite elements (FE). Hence a Galerkin procedure

permits to estab-

lish a dense but small size system of linear equations for the FE coecients, which is nally solved numerically. It is interesting to note that the methodology proposed by Hammer can be also applied to 2-D structures. Moreover, it is worthy of highlighting that the range of applicability of CMT approaches need not be restricted to structures with low RI contrast. In fact, the example in reference [98] covers structures with moderate to high RI contrast, but with only relatively weak or only localized mutual perturbations of the interacting basis modes, such that the optical elds can be well described by the CMT templates by requiring the restricted functional to become stationary. If this last condition is conrmed, then the arguments of the functional of six electromagnetic-eld components satisfy the Maxwell equations in the domain of interest, together with suitable boundary conditions. These boundary conditions can be various.

In fact, Hammer [98] dealt with transparent inux

boundary conditions (TIBCs) and his methodology is known in the literature as

hybrid coupled mode theory .

On the other hand, Song et al [99] recently dealt with an optical ber structure which is enclosed by a perfectly matched layer (PML) terminated by a perfectly reecting boundary conditions (PRBCs) and their methodology is known in the literature as

complex coupled mode theory .

As widely explained

in this section, in most practical applications, only limited number of modes (usually two) close to PMC play signicant roles in the interaction of the modal elds. Consequently, a substantially reduced formulation of the CMT is used and simple analytical solutions are found.

For nonguided radiation

elds, instead, the conventional two-mode CMT becomes cumbersome due to continuous spectrum of the radiation modes. To overcome this problem, leaky

2 For mode details see the website http://en.wikipedia.org/wiki/Galerkin_method


68

modes are introduced to approximate the nonguided radiation modes [100]. The use of leaky modes in the conventional two-mode CMT suers from problems such as mode orthogonality and normalization in the real domain.

In

this context the Song's work gets in with the combination of the PML and PRBCs, which creates an open and reectionless environment in a close and nite computation domain. Such a structure yields a set of complex orthogonal modes that can be readily normalized in terms of power and hence can be solved rigorously by standard analytical and numerical algorithms, such as the nite dierence (FD) method [101]. With properly chosen modal parameters, the guided modes of the original structure are not aected, whereas the nonguided radiation modes are represented by discrete quasi-leaky modes conned in the cladding as well as the PML modes concentrated in the PML. At this point, a well-dened coupled mode formulations can be derived based on the eld expansion in terms of the complex modes. Song et al [99] showed that this theoretical approach can also be applied to optical bers of circular symmetry eciently.

3.3 Study of OFGs by means of the transfer matrix method (TMM)

I

t is obvious that the methodologies briey explained in section 3.2.3 represent comprehensive ways to solve strictly the electromagnetic problem

about circular dielectric structures, ie optical bers in which a RI perturbation was equally induced along the core of the ber. It is equally true that all the methods described in this dissertation are based on the CMT of hybrid HE1 p modes, or rather approximated LP1 p modes without azimuthal eld variation in step-index single-mode bers. For this type of structures (ie three-layer ber) in which the grating is written only in the core of the ber, the expressions of electromagnetic elds in both the core and the cladding regions are given in closed form. These assumptions are true in the case of UV-photowritten gratings, which represents the rst discovered methodology for the manufacturing of gratings. Lately, there was a number of publications focusing on LPGs made via alternative fabrication methods, such as CO2 laser inscription, ion implantation,

3.3. Study of OFGs by means of the transfer matrix method (TMM)

69

electric-arc discharge, mechanical gratings. All these fabrication methods will be extensively described in chapter 4 together with the dierences between them. However, there is evident that the RI distribution of gratings produced by these techniques is not uniform in cross section. The rst experiments made by Davis et al [102] showed a power exchange between the fundamental guided core mode and a too great number of higher-order cladding modes, or rather the transmission spectrum of the ber showed too many loss peaks.

This

phenomenon proves that the RI perturbation in those LPGs has azimuthal dependence and extends beyond the core region.

Anemogiannis et al [103]

rstly reported a numerical method to simulate nontilted OFGs which have an azimuthal and/or radial varying RI distribution and may extend to the ber cladding-air interface.

Therefore the optical ber under consideration

can also have an arbitrary RI prole, thus this methods is a general one. The Anemogiannis's methodology starts its analysis with the consideration that high-order LP modes have a two-folded degeneracy due to the sine and cosine dependence of the elds. Let us consider the LP modes of a cylindrical dielectric waveguide having an arbitrary RI prole.

Although the RI dierence between the cladding

and the environment is not negligible, the LP approximation is still valid for low-order modes having arbitrary azimuthal order

l.

According with the LP

mode formulation described in section 3.2 and borrowed by reference [80], the LPlp mode of order radius

rj−1 < r < rj

p

and within a cylindrical dielectric layer

and refractive index

propagating along the

z

nj ,

ko = 2π/λ, λ

having

axis given by

( ) cos (lφ) Et,lp(j) (r, φ, z) = e(− i βlp z ) sin (lφ) ( Clp(j) Jl rγlp(j) + Dlp(j) Yl rγlp(j) × Clp(j) Il rγlp(j) + Dlp(j) Kl rγlp(j) where

j

has the transverse electric eld

when

βlp < ko nj

when

βlp > ko nj

(3.81)

rβ lp is the longi 2 is = ko2 n2j − βlp

is the operating freespace wavelength,

tudinal propagation constant of the LPlp mode, the magnitude of transverse wavenumber,

φ

γlp(j)

is the azimuthal angle (see also


70

gure 3.1),

Clp(j)

and

Dlp(j)

are the arbitrary eld expansion coecients deter-

mined by the boundary conditions within the cylindrical layer and

Yl rγlp(j)

l (l ≥ 0) of Kl rγlp(j) are

are the Bessel functions of order

second kind, respectively, while Bessel functions of order

l

Il rγlp(j)

and

j , Jl rγlp(j)

the rst and the modied

of the rst and second kind, respectively. Note that

the equation (3.81) represents the general expression of the transverse electric eld, which have been explicitly written in the case of rst (l

= 1)

azimuthal

order for both the core and cladding regions (see equations (3.10), (3.11) and (3.29)-(3.31)).

At this point, we need to calculate the propagation constant

βlp .

To do

this, in the general case of optical bers having arbitrary RI prole in which all the azimuthal orders have to take into account, a particular optical approach must be used in order to simplify the electromagnetic problem and hence to nd the propagation constant of LP modes. This optical approach is known in the literature as

transfer matrix method

(TMM) and the rst who

applied this method to optical bers was Morishita [104]. Later, Anemogiannis et al [103] presented a more compact form of TMM than Morishita which makes allowances for faster calculations of

βlp .

Broadly speaking, the TMM is

a method used in optics and acoustics to describe the propagation of electromagnetic or acoustic waves through a layered medium, such as anti-reective coatings and dielectric mirrors.

In fact, the reection of light from a single

interface between two media is described by the Fresnel equations. However, when there are multiple interfaces, such as in optical bers with an arbitrary RI distribution, the reections, which are partially transmitted and then partially reected, can interfere destructively or constructively depending on the exact path length. The overall reection of a layered structure is the sum of an innite number of reections, which turns out to be cumbersome to calculate. Having just said that, the TMM is based on the fact that, according to Maxwell's equations, there are simple continuity conditions for the electric eld across interfaces from one medium to the next. If the eld is known at the beginning of a layer, the eld at the end of the layer can be derived from a simple matrix operation. Thus the layered structure can be represented as a system matrix, which is the product of the individual layer matrices. Finally, the method involves converting the system matrix back into reection and


71

transmission coecients, or rather into propagation constants in our case. In this thesis we report a brief description of this methodology. Our analysis start by rewriting the equation (3.81) in a more compact form as

Et,lp(j) (r, φ, z) = e(− i βlp z ) Ψlp(j) (r, φ) = e(− i βlp z ) Φl (φ) Rlp(j) (r) where the term

Ψlp(j) (r, φ)

(3.82)

is the amplitude connected with the transverse

electric eld which can be divided into two distinct terms:

the rst

Φl (φ)

is the azimuthal component of the eld, whereas the second

Rlp(j) (r)

is the

radial component of the eld in layer

j.

This last term can be compactly

expressed as

Rlp(j) (r) = Clp(j) Cl rγlp(j) + Dlp(j) Dl rγlp(j) By considering the component of the radial eld in layer continuity condition of the tangential electric elds,

R

j

and by applying the

and

dR/dr

quantities

must be continuous along the interface of two consecutive cylindrical layers. Therefore, at radius

r = rj

and at the interface between layers

j

and

j + 1,

it

is necessary to satisfy the following conditions:

Rlp(j) (rj ) = Rlp(j+1) (rj ) =⇒ Clp(j) Cl rj γlp(j) + Dlp(j) Dl rj γlp(j) = Clp(j+1) Cl rj γlp(j+1) + Dlp(j+1) Dl rj γlp(j+1)

(3.83)

and

dRlp(j+1) (rj ) dRlp(j) (rj ) = dr drh

i 0 0 =⇒ γlp(j) Clp(j) Cl rj γlp(j) + Dlp(j) Dl rj γlp(j) h i 0 0 = γlp(j+1) Clp(j+1) Cl rj γlp(j+1) + Dlp(j+1) Dl rj γlp(j+1)

where

0

Cl (.)

and

0

Dl (.)

denote derivatives with respect to

tions (3.83) and (3.84) as a function of

Clp(j)

and

Dlp(j) ,

r.

(3.84)

By solving equa-

it can be obtained

the matrix equation for a single homogeneous cylindrical layer:


72

"

#  gj,j+1 (βlp ) gj,j+1 (βlp )  " # 11 12 Clp(j) C Qj Qj lp(j+1)  =  gj,j+1 j,j+1 (βlp ) g22 (βlp ) 21 Dlp(j) Dlp(j+1) Qj Qj " # Clp(j+1) = Γ(j,j+1) Dlp(j+1)

The elements of matrix

Γj,j+1

and the term

Qj

(3.85)

are given as

0 j,j+1 g11 (βlp ) = γlp(j) Dl rj γlp(j) Cl rj γlp(j+1) 0 − γlp(j+1) Dl rj γlp(j) Cl rj γlp(j+1)

(3.86)

0 j,j+1 (βlp ) = γlp(j) Dl rj γlp(j) Dl rj γlp(j+1) g12 0 − γlp(j+1) Dl rj γlp(j) Dl rj γlp(j+1)

(3.87)

0 j,j+1 (βlp ) = −γlp(j) Cl rj γlp(j) Cl rj γlp(j+1) g21 0 + γlp(j+1) Cl rj γlp(j) Cl rj γlp(j+1)

(3.88)

0 j,j+1 (βlp ) = −γlp(j) Cl rj γlp(j) Dl rj γlp(j+1) g22 0 + γlp(j+1) Cl rj γlp(j) Dl rj γlp(j+1) h

0

0

Qj = γlp(j) Cl rj γlp(j) Dl rj γlp(j) − Cl rj γlp(j) Dl rj γlp(j)  2  when βlp < ko nj π γlp(j) rj =  −1 when βlp > ko nj γ rj

(3.89)

i (3.90)

lp(j)

Therefore, if we extend the application of equation (3.85) along the radial direction of an optical ber having as a product of single layer:

N +1

layers, we obtain the global matrix

3.3. Study of OFGs by means of the transfer matrix method (TMM) "

73

# " # Clp(N +1) Clp(1) = Γ(1,2) Γ(2,3) · · · Γ(N,N +1) Dlp(1) Dlp(N +1) " #" # 1,N +1 1,N +1 g11 (βlp ) g12 (βlp ) Clp(N +1) = 1,N +1 1,N +1 g21 (βlp ) g22 (βlp ) Dlp(N +1)

(3.91)

It is worthy of highlighting that equation (3.92) relates the elds in the inner (j

= 1)

layer of the ber (core) to the most external (j

= N + 1)

layer, that

is to say the environment. Moreover, it is obvious that, for nite elds in the core and in the environment around the ber, the coecients

CN +1

and

D1

must be zero. This condition allows us to write that

1,N +1 g22 (βlp ) = 0

(3.92)

which gives as roots the propagation constants the azimuthal order

l

under consideration.

βlp

of the optical ber for

In general, the system in equa-

tion (3.92) can be solved by means of several dierent techniques described widely in reference [105]. Having found all the propagation constants

βlp ,

the coecients

C

and

D

in each layer are normalized such that every mode with its transverse electric eld carries the same power

Plp

equal to 1 W, as just explained in section 3.2

by means of the equation (3.37):

Plp =

βlp 2 ω µo

Z

2π

Φ2l (φ) dφ

0

0

Any periodic RI perturbation

Z

∞ 2 Rlp(j) (r) r dr = 1W

∆ n (r, φ, z)

(3.93)

inside the ber can carry out

the power transfer from the fundamental core mode to one or more cladding modes. As highlighted in equation (3.39) before, the term

∆ n (r, φ, z)

is the

sum of two contributions, ie a DC and an AC refractive index variation, multiplied by an optional apodization function

σ (z) for reducing the spectral ripples

of the grating frequency response. In the case of gratings manufactured by an UV exposure, that means LPGs inside the ber core only with no azimuthal RI variations, the periodic RI perturbation becomes equal to

∆ ncore (r, z) and

can be expressed as in equation (3.39). Broadly speaking, the RI perturbation in a generalized grating can be described as the product of three functions:

∆ n (r, φ, z) = σ (z) S (z) P (r, φ)

(3.94)


74

where the function

P (r, φ)

is the transverse RI perturbation, while the func-

S (z) is the longitudinal RI perturbation, that is to say a periodic function the grating period Λ. It is worhy of noticing that S (z) depends strongly

tion of

on the way in which the grating was manufactured.

This function can be

approximated as

S (z) = s0 + s1 cos where

s0

and

s1

2πz Λ

(3.95)

are the coecients corresponded to the rst two coecients of

the Fourier series regarding the exposure function. This is a general expression that can be used for any types of grating manufacturing. For example, if the LPG is formed by periodic local heating as the case of CO2 laser with a width of the beam waist

W,

then the exposure function can be approximated by a

periodic rectangular wave of width

W

and period

Λ as depicted in gure 3.16.

In the case of an exposure due to a CO2 laser irradiation, the two Fourier

Figure 3.16: Longitudinal refractive index variation function of width

S (z)

due to an exposure

W

series coecients are equal to

W Λ and

− π2 sin

πW Λ , respectively. For gratings

having a longitudinal RI prole as that reported in gure 3.16, the transverse RI prole

P (r, φ)

is not uniform along the ber cross section. In fact, it was

proved that the RI perturbation is higher on the side where the laser beam shoots the ber.

Therefore, it is necessary to divide the ber cross section

into ring sectors having a constant index variation in order to approximate


75

the transverse RI perturbation. To understand that even better, we refer to gure 3.17 [103]. For the

j−th

cylindrical ring of radius

Figure 3.17: Azimuthal refractive index variation

P (r, φ)

sectors

transverse RI prole

Pj (r, φ)

rj−1 < r < rj ,

has the following form:

the

divided into ring


76

Pj (r, φ) =

where

pq,j

various

  p1,j     p2,j

for

θ1,j ≤ φ < θ2,j ;

for

θ2,j ≤ φ < θ3,j ;

. .   .     ps,j

for

θs,j ≤ φ < 2π + θ1,j

(3.96)

q = 1, . . . , s are the RI modulation values around the ring for angles θq,j . It is important to point out that equation (3.96) can be for

used to discretize any arbitrary RI perturbation on a plane transverse to the ber. At this point, we have to recurse again to the CMT for modeling the interactions among LP modes inside the ber under consideration. As mentioned in the previous section, according to the CMT the coupling between optical modes is proportional to their transverse coupling coecient

t . Klp

By assuming

a power normalization between modes equal to 1 W as already done in equation (3.93), remembering equation (3.82) and starting from equation (3.40), we are able to rewrite this last equation into a generalized expression of the transverse coupling coecient between the LPlp and the LPµν modes:

t Klp,µν

where

ω = 4

Ψ (r, φ)

Z

2π

Z

∞

∆ (r, φ, z) Ψlp (r, φ) Ψµν (r, φ) rdr dφ 0

represents the product between the radial and the azimuthal

component of the transverse electric eld about an LP mode, ie

Φl (φ) Rlp (r),

(3.97)

0

Ψlp (r, φ) =

∆ (r, φ, z) is the permittivity perturbation which is related to the RI perturbation ∆ n (r, φ, z) by means of the following expression: while

∆ (r, φ, z) ∼ = 2 o no (r) ∆n (r, φ, z)

(3.98)

no (r) represents the unperturbed RI of the ber. It is worthy of pointing that the term ∆ (r, φ, z) is the generalization of the term ∆χ (r, z) given

where out

in equation (3.40) for a ber having an arbitrary RI perturbation. Thus, by using equations (3.94), (3.95) and (3.98), equation (3.97) takes the following nal form:

3.3. Study of OFGs by means of the transfer matrix method (TMM) t Klp,µν

2πz Λ

= σ (z) s0 + s1 cos Z Z ωo 2π ∞ × no (r) P (r, φ) Ψlp (r, φ) Ψµν (r, φ) rdr dφ 2 0 0 2πz = σ (z) s0 + s1 cos κlp,µν Λ

where the term

κlp,µν

77

(3.99)

is the generalized expression of the coupling constant

between the LPlp and the LPµν modes. As already discussed in section 3.2, traditional UV-photoinduced gratings having uniform RI perturbations within the core of the ber generate LP01 −to−LP1p mode couplings.

Since these

modes do not have any angular dependence, the azimuthal integral is equal to

2π .

prole

For generalized LPGs with azimuthal variation of the perturbed RI

∆ n (r, φ, z),

there is a power transfer from the LP01 mode to the LPlp

modes with arbitrary

l, p non-negative numbers.

The crucial point is that each

LPlp is treated as two independent modes, one with second with

Φl (φ) = sin (lφ).

κCS,CS lp,µν

κlp,µν

can be achieved from

r0 = 0:

Z rj N ωo X = Rlp (r) Rµν (r) rdr no (rj ) 2 r=rj−1 j=1  " #" #  s Z θq+1 X  cos (lφ) cos (µφ) × pq,j dφ   sin (lφ) sin (µφ) q=1 φ=θq

Note that the

and the

Therefore, by using equations (3.82) and (3.96),

the generalized expression of the coupling constant equation (3.99) by enjoining

Φl (φ) = cos (lφ)

κ superscripts C

or

S

(3.100)

correspond to the azimuthal cosine or sine

dependence of the LPlp and LPµν modes. It is important to point out that the division of a generic RI perturbation into sector rings given by Anemogiannis et al [103] was proved to be computationally ecient because it allows the calculation of azimuthal coupling coecients between modes without using double integration. In fact, the integration along the radial direction is done once per ring, while the integrations along the azimuthal direction can be calculated analytically. Now, by substituting equation (3.99) into the general coupled mode equation (forward-going amplitudes) given in equation (3.47), we can obtain the


78

coupled dierential equation system which describes all the LP mode couplings into the ber. The system is not explicitly reported in this dissertation but it can be found in reference [103] disguised as matrix representation. Broadly speaking, the number of cladding modes supported by an optical ber is very large and hence the system dimensions are large as well. But the number of modes that interact with the LP01 mode within the wavelength range of inter-

l have Rl (r) conned within the ber core for coupling

est are usually limited. Moreover, only modes with low azimuthal order the most power of radial eld

eciently to LP01 mode. As already explained in section 3.2, starting from the LPG characteristic equation (3.58), the expression that generalizes the equation (3.60), because takes into account any arbitrary RI perturbations and then any azimuthal order cladding modes, is the following:

2π βlp + s0 κCS ⇐⇒ lp,lp = Λ λLPG res (lp) e e = ncore − nclad (lp) + s0 κ01,01 − s0 κCS lp,lp 2π

β01 + s0 κ01,01 λLPG res (lp) Λ

−

This condition is known in the literature as

(3.101)

modied rst-order Bragg condition

even if it is related to LPGs. This generalized condition takes into account that the propagation constants

CS self-coupling coecients κlp,lp .

βlp

of LPlp modes are also perturbed by the

Anemogiannis et al [103] demonstrated the

accuracy of the just given condition by means of some examples. It is worthy of stressing a crucial point.

In the case of LPGs with RI

perturbation only in the ber core, ie UV-gratings, it was proved that the optical characteristics (resonance wavelengths, intensity of dips, FWHM, etc.) of the ber transmission spectrum are very similar by comparing the results obtained by means of the LP and the hybrid mode formulation. This is because, since for low

∆ bers the propagating modes satisfy the weakly guiding

condition and the hybrid modes, having much of their power within or near the core, have the longitudinal component of the elds tending to zero, they can be accurately approximated by LP modes.

Thus, for LPGs having RI

perturbation only within the core region, the LP mode approach is simpler and as accurate as the hybrid mode formulation.

On the contrary, in the

case of generalized LPGs with RI perturbation in both the core and cladding regions, ie non-UV-gratings, the transmission spectrum is dominated by the

3.4. Study of OFGs by means of the nite element method (FEM)

79

resonance wavelengths due to LP1p and LP2p modes. The reason for this is that higher order modes have much smaller eld amplitudes within the ber core in comparison to the lower order modes. coupling coecients

κ01,lp .

This yields very small cross-

Thus the lack of high-order resonance wavelengths

justies the use of LP mode formulation instead of the more complicated hybrid mode formulation. In this case the modied rst-order Bragg condition approximates the true value of the resonance wavelengths better than the classic rst-order Bragg condition [103]. In general, a key parameter is the value of the induced RI perturbation along the ber (∆n (r, φ, z)). Moreover, for the sake of completeness, the dierences between the intensity about dips in the transmission spectrum with or without the cladding-cladding mode interactions are less than 0.05 dB. Larger errors occur at the narrower dips since the LP01 mode power is coupled to many other cladding modes which satisfy the PMC. Therefore, the cladding-cladding mode interactions can be neglected for LPGs.

Broadly speaking, both the classic and the modied rst-order

Bragg conditions are very close to the true resonance wavelength when only one cladding mode interacts with the fundamental core mode because of the reductions done in the CMT.

3.4 Study of OFGs by means of the nite element method (FEM)

A

mong the numerical methods that can be used for studying theoretically an optical ber gratings, one of the best known is unquestionably that

which combines the coupled mode theory with a nite element method (FEM). Once the coupling constants of the grating are known, the basic optical characteristics such as intensity of the dips, resonance wavelengths, FWHMs, etc., can be easily obtained as widely explained in next sections. For simple grating structures, the coupling constants can be achieved analytically. However, for more complicated grating structures such as gratings made in photonic crystal bers (PCF), gratings made in dierent types of bers (ie multimode and single mode bers), gratings with fringes tilted by a certain angle, etc., it is dicult to obtain an analytical expression for the coupling constants. From this point of view, the methodology that combines FEM and CMT is the best


80

and the most used for complex grating structures. In fact, the nite element method is used to obtain the expression of the coupling coecients regarding the grating structure under consideration, whereas the coupled mode theory is then used to evaluate the spectral and optical characteristics of the grating structure by means of the coupled mode equations. By entering into details, the FEM is applied only to the region corresponding to one period of the grating structure in order to achieve the coupling coecients to be putted into the coupled mode equations. In reference [106] Fujisawa and Koshiba proved that the FEM-CMT method was computationally ecient compared to other full numerical simulation methods such as the nite-dierence time-domain method and the nite-element time-domain beam propagation method, because in combined FEM-CMT only the region corresponding to one period of a grating structure at any one time is analyzed. In the bargain, once the coupling coecients of the grating structure are known, both the optical and spectral characteristics of the grating structure with an arbitrary number of periods can be easily achieved by using the CMT. The present methodology will be briey described referring to [106]. Here we consider a grating structure of total length periodicity

Λ

L

made up of

N

periods of

written inside the core of an optical ber. Its longitudinal sec-

tion is depicted as a sketch in gure 3.18. For this type of grating structure a pair of coupled mode equations, which express the amplitudes of the electromagnetic elds as a function of the coupling coecients, can be written in the same form of equations (3.47) and (3.48) reported in section 3.2.

The

coupling coecients, which make possible to obtain both the optical and spectral characteristics of the grating structure under consideration, are in turn as a function of some optical parameters. These parameters, which concern the standing wave distribution of one period of the grating structure as highlighted in gure 3.18 by means of the dashed rectangle of length equal to the grating period

Λ,

can be easily evaluated from FEM [107] applied only to one

period of the periodic structure. For the sake of completeness, the overall procedure to calculate the characteristics of a grating structure by using combined FEM-CMT method is reported and summarized in ve points: 1. determine the structure of the grating;

3.4. Study of OFGs by means of the nite element method (FEM)

Figure 3.18: Sketch of periodic grating structure of total length period

Λ

81

L = N Λ and

with input and output unperturbed regions

2. calculate the dispersion curves of the grating structure by means of FEM [107] and obtain the optical parameters concerning the standing wave distribution of one period of the grating structure at the wavelength range of interest; 3. calculate the propagation constants of the unperturbed structure by means of FEM and obtain the same optical parameters; 4. calculate the coupling coecients; 5. calculate the characteristics of interest about the grating structure throughout its length

L.

It is worthy of noting that this procedure can be also applied to waveguide

82

grating with the same steps.


Chapter 4

Manufacturing of optical ber gratings Not everything that can be counted counts, and not everything that counts can be counted. Albert Einstein

4.1 Basics about gratings manufacturing n this chapter a comprehensive overview about the manufacturing tech-

I

niques of OFGs is given.

As mentioned in the introduction of this PhD

thesis (section 1.1), the most distinguishing feature of OFGs is the exibility that they oer for achieving the desired spectral characteristics. This can be mostly obtained because of the exibility about the manufacturing methods pertaining to OFGs.

In fact, numerous physical parameters can be varied,

including the induced-index change, or rather the value of the periodic modulation (∆ ncore ), the grating length (L), the type of apodization (σ ), the chirp of the grating period (grating with aperiodic change in grating period), the tilt of the grating fringes (grating with fringes tilted at a well-dened angle with respect to the grating normal) and whether the grating supports counterpropagating or forward-propagating couplings at a desired wavelength according to the grating period (Λ).

But exibility is only one key features that

characterizes a particular manufacturing technique. Other important features are, for example, an economical mass production capability, a good physical and optical qualities of the manufactured gratings and a good repeatability, that is to say, the technique should be good enough under the condition of mass production and interchangeable without a calibration procedure.

Re-

garding the physical and optical qualities especially, we are dealing with the mechanical strength of the grating, which should not be degraded after the

4. Manufacturing of optical ber gratings

84

production, the narrow bandwidths, which should be themselves suciently separated in wavelength, one with the other, and nally the low losses, which are required to achieve high resolution measurements. As already explained in chapter 2, the periodic modulation (∆ncore ) of the core refractive index (ncore ) along the

z

axis of an optical ber causes perma-

nent changes in the core refractive index prole and determines a specic value

e

of the eective RI (ERI) of the ber core (ncore ) responsible for the coupling of modes. For a better understanding, we refer to gure 2.2 again. These changes

LPG res(p)

lead to a specic value of both the resonance wavelength (λ the peak intensity (transmission

T

for LPGs or reectivity

or

λFBG res ) and

R for FBGs) about

the coupled modes. This concept has been already expressed mathematically in section 3.2, but it is important to point out that the periodic modulation can be divided into two dierent terms with a dierent meaning regarding the manufacturing parameters, as reported below:

ne core (z) = ncore + ∆ ncore (z)

(4.1)

AC = ncore + nDC core (z) + ncore (z)

The term

nDC core

is the induced-index change of the ber core spatially averaged

over the grating length, which sets out the value of the resonance wavelength. On the contrary, the term

nAC core

is the induced-index modulation of the ber

core, which sets out the value of the peak intensity. From a practical manufacturing point of view, it is worthy of highlighting that these two parameters can not be varied independently but they are bound themselves. Therefore, a trade-o between them is necessary in order to achieve a coupling between two modes at the desired resonance wavelength and with the desired peak intensity. It is important to stress that the optical properties of a ber grat-

∆ ncore , namely, axis z . Figure 4.1

ing are substantially determined by the periodic modulation the variation of the induced-index change along the ber

illustrates some common variations in induced-index change which include the uniform variation (4.1(a)), the Gaussian-apodized variation (4.1(b)), the raised-cosine-apodized variation (4.1(c)), the chirped variation (4.1(d)), the discrete phase-shift variation (4.1(e)) and, nally, the superstructure variation (4.1(f )). As the uniform variation is the simplest one and then the most used, especially for LPGs, we focused on this last type of structure.

4.1. Basics about gratings manufacturing

85

Figure 4.1: Common types of ber gratings classied by the variation of the induced-index change along the ber axis:

(a) uniform, (b) Gaussian-

apodized, (c) raised-cosine-apodized, (d) chirped, (e) discrete phase-shift and (f ) superstructure

After some general concepts about the grating manufacturing, we are ready to start the description of the manufacturing techniques of OFGs. In fact, this chapter is organized as follows: the rst section describes the manufacturing


86

techniques about FBGs, while the second section deals with the manufacturing techniques about LPGs. All the methods are those of reported in the literature until now. We focus the attention on the physical principle of grating formation which leads to dierent optical and physical qualities of the grating itself. We deal also with both the advantages and disadvantages about each manufacturing technique.

4.2 Fiber Bragg gratings

B

efore starting the description about manufacturing techniques of FBGs, it is worthy of discussing the classication of the FBGs with respect to

both the grating period

Λ and the tilt angle γ

three dierent types of FBGs:

of the grating planes. There are

uniform FBG , blazed FBG

and

chirped FBG .

An uniform FBG is the classical FBG which has been already discussed in chapter 2. Looking at gure 2.3, in fact, we can see that this type of gratings is characterized by both a uniform spacing of the grating fringes, hence a constant

Λ,

and a tilt angle of 0° degrees (ie 90° degrees with respect to the

ber axis). As regards the blazed FBGs, they are characterized by a uniform spacing of the grating planes, hence a constant

Λ

again, but a tilt angle

γ

greater that 0° degrees as can be seen in gure 4.2. Typical tilted angles are in the range between 2°

−20°

degrees.

In this type of gratings, the grating

period along the ber axis, which determines the resonant wavelengths for coupling, is

Λ = Λg / cos γ .

The most interesting feature of this gratings is

possibility of the coupled mode to propagate also in the ber cladding and hence to have access to the medium surrounding the ber, due to the tilted grating period. This opportunity makes possible to use them as SRI sensors in both physical and biochemical eld, as explained in part I. A comprehensive explanation about the coupling in blazed (or tilted) gratings, which goes beyond the aim of this dissertation, can be found in this reference [76]. Finally, the chirped FBGs are characterized by a tilt angle of 0° degrees (that is to say 90° degrees with respect to the ber axis), but a nonuniform spacing of the grating planes, or else an aperiodic change of

Λ

with monotonic increase.

This conguration can be observe in gure 4.3. Looking at the same gure, when the incident light encounters a nonuniform spacing of the grating planes,

4.2. Fiber Bragg gratings

87

Figure 4.2: Blazed ber Bragg grating: physical depiction

Figure 4.3: Chirped ber Bragg grating: physical depiction

this can be seen as a periodic nonuniform change of the ber core RI. This means that shorter wavelengths are reected back before the longer ones. As a result of this phenomenon, the peak or the dip of the ber spectrum will be widened. This type of gratings is used in the eld of telecommunications


88

as dispersion compensator [108]. After this introduction regarding the FBGs' structures, we are able to talk about the dierent manufacturing techniques of FBGs. Before entering into details of the description of the various manufacturing techniques about FBGs, some general remarks have to be pointed out. First of all, the index modulation of the ber core is permanent, that is to say, its life time is about 25 years. Furthermore, the value of the induced

∆ ncore

depends on dierent factor: the irradiation conditions (ie wavelength, intensity and frequency of laser source pulses and total dosage of irradiating light), the material composition of the ber core (ie Ge-doped, Ge-Boron co-doped, etc) and any processing about the ber prior to irradiation (ie hydrogen loading treatments, etc).

As it will be explained afterwards, FBGs are written on

photosensitive optical bers.

The meaning and the reason of this will be

explained in next subsection, but it means that a laser source have to be used in order to write a FBG. Moreover, as explained in subsection 4.2.2, the best laser sources are those near the UV light spectrum. Thus the most commonly used sources are KrF (λ

=

248 nm) and ArF (λ

=

193 nm) excimer lasers,

−1 and total −2 to 1 J cm−2 . Under intensity of light irradiation ranging from 100 mJ cm which are characterized by pulse repetition rates of 50-75 pulses s

∆ ncore

these conditions, the value of the induced

−5 RIU to 10−3 RIU. bers ranges from 10

in photosensitive optical

4.2.1 Internal writing technique The rst technique for FBGs manufacturing was found away back in 1978 by Hill et al [72], [1] and it is known as

internal writing technique

experimental setup is shown in gure 4.4.

.

The

A continuous wave (CW) blue

(488 nm) light from an Argon ion laser was launched into a 1 m-long sample of single-mode germanium(Ge)-doped-core optical ber and the intensity of the light reected back from the ber was monitored by means of a power meter. Initially, the reected light intensity was low, but after a period of few minutes, it grew in strength until almost all the light launched into the ber was reected back. This last feature can be observed in gure 4.5 in which the reectivity changes from 4% to 44%. Note that the grating reects the light within the ber core, therefore the true value of reectivity corresponds to 88%


89

Figure 4.4: Schematic of the original experimental setup used for writing ber Bragg gratings within the optical bers [1]

by assuming a realistic launch eciency of 50%. Moreover, the insets (a) and (b) in the same gure show the reection and transmission, respectively, of a typical FBG manufactured by means of this technique. However, the growth in back-reected light was explained in terms of a new nonlinear eect called

photosensitivity

which enabled to create an index modulation within the ber


90

core. The reasoning is as follows: the coherent light propagating into the ber

Figure 4.5: Time evolution of reectivity of a 1 m-long Ge-doped-core optical ber (NA = 0.1 and core diameter = 2.5

µm).

Insets (a) and (b) show typical

FBG reection and transmission, respectively

interfered with a small amount of light reected back from the end of the ber and this set up a standing wave pattern, which created an index modulation within the ber core by means of the photosensitivity (

Hill grating ).

As the

strength of grating increased, the intensity of the back-reected light increased until it saturated near 100%. The grating resulted written over the total length of ber. It represents a rst disadvantage of this technique. At the time, it was recognized that gratings in optical bers would have many potential applications in ber optic communications [72], such as optical lters in laser mode control, as synthesized lters with tailored response characteristics for use in high-capacity wavelength-multiplexed light-wave communication systems and in wavelength-selective switches and couplers. In fact, it was shown that

Hill gratings could be used as a feedback mirror for a laser and

as a sensor for strain by stretching the ber. In addition, the photosensitivity of Ge-doped-core optical bers had relevant implications for the performance of this type of waveguide concerning the eld of telecommunications: it will be shown later that the photosensitivity does not aect both the dispersion and the losses of waveguide in the wavelength regions of interest to optical com-


91

munications (850 nm, 1300 nm and 1500 nm). Although the photosensitivity appeared to be an ideal means for gratings manufacturing in optical bers, the

Hill gratings

unfortunately work only at light wavelengths in the visible range

close to the wavelength of the laser source writing light. This represents the second drawback of the present technique. However, the discovery of photosensitivity gave rise to the era in technology of core-doped optical bers. This last issue will be resumed in next subsections.

4.2.2 Two-beam interferometer techniques Given the signicant limitations of the above-described technique, two other completely dierent techniques was implemented over the time: rst is known as

mask technique .

the

two-beam interferometer technique , while the second as phase

The former will be explained in subsection 4.2.2, while the

latter in subsection 4.2.3. At the end of subsection 4.2.3, we will highlight the main advantages of the phase mask technique compared with the twobeam interferometer one.

This issue has led us to choose the phase mask

technique for the FBGs manufacturing (see section 6.4).

Holographic technique The limitation on photosensitivity at light wavelengths in the visible spectrum was overcome about ten years later (around 1989) in an experiment given by Meltz et al [2], who recognized from the work of Lam and Garside [109] that photosensitivity was a two-photon process (low eciency) that could be made much more ecient if it were a one-photon process at a wavelength in the 5 eV (around 244 nm) germania oxygen-vacancy defect band [110] in germanosilicate optical bers. The FBG was formed by exposing a short length of bare photosensitive optical ber to a pair of overlapping coherent UV beams which came from a laser source. The schematic of the original experimental setup is

1

shown in gure 4.6. A tunable excimer

pumped dye laser, which worked at

a wavelength in the range of 486-500 nm, was used with a frequency-doubling crystal to provide a UV source that lay in the 244 nm band and had a good

1 For more details about excimer lasers see the website http://en.wikipedia.org/wiki/

Excimer_laser

92


Figure 4.6: Schematic of the original experimental setup used for writing ber Bragg gratings in optical bers by means of transverse holographic method [2]

coherence length. The two overlapping UV light beams interfered producing a periodic interference pattern that wrote a corresponding periodic index modulation in the ber core. This technique, which is known in the literature as

transverse holographic technique ,

was possible because the pure fused silica

(SiO2 ) cladding of the ber was transparent to the UV light whereas the core of the ber, doped with germanium oxide, was highly absorbing to the UV light. Moreover, the intensity of the produced pattern could be increased by focusing the two beams on the ber by means of a pair of cylindrical lenses with a rectangular focal spot (ie 4 mm in length and 125

µm

in width). A ltered


93

mercury arc source was used together with a high-resolution monochromator to measure both the reection and transmission spectra of the grating. The reected signal was monitored by inserting a beam splitter at the ber input and the value of the reectivity was evaluated by comparing the reected signal level to the power reected, at a wavelength near but out the lter band, from a mirror placed at the ber output. Figure 4.7 shows a sketch of the above-described experimental setup for writing ber Bragg gratings by means of transverse holographic method. The

Figure 4.7: Sketch of the experimental setup used for writing ber Bragg gratings by means of transverse holographic method [3] change of the angle

ϕ,

which is the angle between one beam of the UV laser

source and the normal to the ber axis at the focusing point of the interference pattern, allows us to change the FBG pitch

ΛF BG

according to the following

equation:

ΛF BG = where

λU V

λU V sin ϕ

(4.2)

is the wavelength of the UV laser source. Thus varying the grating

period and remembering equation (3.59), a group of FBGs with dierent

λFBG res

can be obtained, which attests the exibility of the present method. It is clear that the value of

ϕ

must belong to a narrow group of values around 40°.

This implies that the pitch of a FBG made by means of this technique can be changed in a small amount.

Furthermore, equation (4.2) shows that an

alternative way to vary the grating period is to tune the wavelength of the UV


94

source.

This last feature greatly depends on the characteristics of the used

laser source, thus representing a limitation of this method. It is worthy of noticing that this technique oers many advantages in comparison with the internal writing technique. It works at any wavelength regardless of the wavelength of laser source, thus it still operates at much longer wavelengths in the spectral region of interest for many optical devices and sensors. In addition, it had been proved that the photosensitivity mechanism for this technique is a one-photon process consequently with more eciency than the rst-described technique.

The main drawback was characterized

by the high costs of the entire fabrication setup, especially due to the highcoherence UV laser source. For the sake of completeness, standard single-mode optical bers (eg SMF28) can be also used for FBGs manufacturing by means of this technique after a hydrogen loading treatment to make the ber photosensitive.

The

trouble of using this type of ber is that it requires a long-lived post-fabrication treatment, eg heat treatment at high temperature (around 200

−300 )

or

rather annealing process, in order to provide the thermal stability of FBGs.

Source-tunable interferometer technique The second method based on a two-beam interferometer technique, known in the literature as

source-tunable interferometer technique , was demonstrated

by Dockney et al in 1996 [111]. It is able to overcome some disadvantages of the transverse holographic technique.

A schematic of this method is shown

in gure 4.8. Unlike the above-mentioned transverse holographic technique, the FBG resonance wavelength can be selected by tuning the wavelength of the UV laser source

n λU V

rather than precisely adjusting the angles

θm

of

mirrors, whilst the change in FBG resonance wavelengths can be extended by varying the angles of the two mirrors. The obtainable resonance wavelength of FBGs, which is determined by

θm

in the interferometer method based on a

phase mask and two mirrors, is given by the following equation:

λFBG res =

n λU V sin (θpm + 2 θm )

(4.3)


95

Figure 4.8: Sketch of the experimental setup used for writing ber Bragg gratings by means of source-tunable interferometer method [3]

where

θpm = sin−1

λU V Λpm

is the angle between the normal to the ber axis

and the beam of the phase mask related to the rst-order diraction and

Λpm

is the pitch of the phase mask. In fact, the phase mask is an optical diractive element made of a at slab of silica glass, which is transparent to UV light. On one of the at surfaces, a one dimensional periodic surface relief structure is etched using photolitographic techniques. The shape of the periodic pattern can be approximated as a square wave in prole with a pitch equal to

Λpm .

Therefore, when the UV light is incident normal to the phase mask, the light passes through and is diracted by the periodic corrugations of the phase mask. In general, most of diracted light energy is contained into the 0 and

±1

diraction orders. However, the phase mask are designed to cut the zero-

order diraction by controlling the depth of the corrugations. Thus only

±1

diraction orders pass through a phase mask. Therefore, precision FBGs writing can be achieve by means of this approach with a wide wavelength range, if the entire interferometer system is well stabilized during the fabrication steps. It is obvious that it is necessary to have a high-coherence UV laser source in order to manufacture FBGs with


96

good optical properties. Consequently, the use of a tunable UV laser source with a large coherence length increases the system costs unquestionably. This last issue represents the main drawback of the present technique. Finally, it is interesting to make a comparison between the internal writing technique and the two-beam interferometer techniques about the eciency of FBGs writing. The internal writing technique is based on a two-photon process at 514.5 nm, whereas the two-beam interferometer techniques are based on one-photon process with coherent UV radiation at 244 nm [2]. It was reported that, to obtain an index perturbation of 3 x 10

−5 RIU using a CW argon-

ion radiation at 514.5 nm, it required a writing power of 90.7 mW with an exposure of about 6 minutes [109]. This is equal to expose the ber core to an

−2 . A FBG with the same strength could be −2 at a wavelength of 244 nm by obtained with an energy ux of only 1 kJ cm energy ux of about 665 MJ cm

directly bleaching the absorption band of Ge-doped-core optical bers. Thus

5 in writing eciency had been achieved.

an improvement of 6.7 x 10

4.2.3 Phase mask techniques Because of the limitations of the two-beam interferometer techniques, mainly due to the high costs of the manufacturing apparatus, a completely dierent approach for FBGs fabrication was developed in 1993 by Hill et al [112]. This new technique was simply based on the use of a phase mask and a UV laser source, so gratings were written in single-mode photosensitive optical bers. The main advantages of this technique compared to two-beam interferometer techniques are as follows: simpler writing apparatus and greater repeatability. In the literature, two dierent methodologies about this approach had been reported: a simple

phase mask method ,

and a

modied phase mask method .

The former will be explained in the following subsection, while the latter in subsection 4.2.3.

Phase mask method The phase mask technique is obviously based on the use of a phase mask. In gure 4.9 we show its sketch. As above-mentioned, only the two rst

m = ±1

diraction orders pass through a phase mask. These two orders interfere each other and generate an interference pattern in the middle of the phase mask.


97

Figure 4.9: Sketch of the phase mask used for writing ber Bragg gratings by means of phase mask technique

The periodic interference pattern was used to photoimprint a refractive index modulation into the core of a photosensitive optical ber placed immediately behind, in proximity, and parallel to the phase mask. the grating manufactured is related to the period

Λpm

The period

ΛF BG

of

of the used phase mask

according to the following equation:

ΛF BG =

Λpm 2

(4.4)


98

This method is essentially based on a precision photolitographic apparatus together with a UV laser source, ie a KrF excimer laser source at a wavelength of 248 nm.

Hill et al used an unmodied Lumonics excimer laser, which

2

operated at 249 nm, with a cross-section of 0.7 x 2 cm , a pulse duration of 12 nm and a pulse repetition rate of 50 Hz.

Moreover, the unfocused

−2 . With these parameters energy density per pulse was about 100−200 mJ cm −4 RIU and a an induced RI modulation of the ber core in the order of 10 reectivity lower than 20% were been obtained. The phase mask technique was simple to use, resulted in reduced mechanical sensitivity of the grating writing apparatus and was correctly functional even with low coherence laser sources. In addition, because the phase masks were manufactured under computer control, photolitographic imprinting processes, this technique oered much exibility for changing both the grating period and strength of the coupling coecient

κ01−01 core-core

given in equation (3.43),

as a function of the distance between the optical ber and the phase mask. By means of this technique, the value of the induced

∆ ncore

is also inuenced

both by ber/mask alignment during the fabrication process and by some intrinsic characteristics, such as nonlinearities in the photosensitive response of the ber, the imperfect nulling of the zero-order diraction, the presence of higher order diracted beams downstream from the phase mask and the low coherence of the laser source. Finally, it was demonstrated that phase masks have a tolerance uence level per pulse of 1 J cm

−2 without any damage.

Modied phase mask method To remove some limitations of the simple phase mask method, a modied version had been developed in 1993 by Prohaska et al [113]. version made possible to tune the FBG resonance wavelength

The modied

λFBG res

with a

xed phase mask by using a diverging or converging wavefront incident on the phase mask. The very simple principle of this technique is shown in gure 4.10. Let us consider a plane wavefront that hits on a positive lens of focal length

f,

hence the grating period photoimprinted on the ber is given by the following equation:

ΛF BG = M Λpm

(4.5)


99

Figure 4.10: Schematic of modied phase mask technique used for writing ber Bragg gratings

where the term

M

represents the demagnication factor, which expression is

as follows [3]:

M= where

p

and

q

f − p − q f − p

(4.6)

are the distances between the cylindrical lens and the phase

mask and between the phase mask and the optical ber, respectively. Thus the grating period could be tuned by varying

p and/or q .

However, the tuning

range was estimated to be within a few tens of nanometers as

q

was limited

by the coherence length of the laser source. The techniques that make use of a phase mask are characterized by the fact that the grating is as long as the length of corrugations in the phase mask itself. Moreover, narrower the FBG bandwidth is, more accurately the shift of the FBG resonance wavelength induced by a measurand can be detected. Having said that and remembering that the FBG bandwidth is inversely proportional to its length, very long (in the order of mm) gratings with high reectivity are required. Thus to achieve this goal, a number of variations of the phase mask technique based on phase mask scanning had been reported in the literature [114116]. For the sake of completeness, the basic idea was to keep the phase mask and the optical ber held together in proximity and parallel, as shown in


100

gure 4.9, except that the UV light beam was scanned along the phase mask and optical ber assembly.

After the roundup of the manufacturing techniques of ber Bragg gratings, it is worthy of highlighting the advantages of the phase mask techniques compared with the two-beam interferometer ones, which are reported and summarized down here [1]:

the FBG resonance wavelength

λFBG res

depends on the period of the phase

mask and is independent of the wavelength

λU V

of the UV laser source;

they oer a high mass production with good repeatability at relatively lower costs;

single-beam writing methods improve considerably the mechanical stability of the FBG fabrication apparatus and so they are easy to use in practice;

the requirement for coherent UV laser sources is highly reduced and hence laser sources with low spatial and temporal coherence can be used to replace highly coherent, very expensive UV lasers which are required by the two-beam interferometer methods.

4.3 Long period gratings

T

he rst long period gratings were written photochemically by means of the use of UV laser light at wavelengths coinciding with the maximum

of the absorption band of defects in Ge-doped optical bers near 5 eV (see gure 4.11). This meant that the inscription took place in the ber core and it was realized by either KrF excimer laser radiation (λ second-harmonic radiation of a CW argon-ion laser

= 248 nm) [5] or the (λ = 244 nm) [44]. Both

the techniques were conventional low-excitation-energy (5 eV)

photochemical

approach, which led to LPGs fabrication via single-quantum photochemical reactions. Therefore, both techniques were based on an ultraviolet laser source at a wavelength around the maximum of the absorption band of ber defects,

4.3. Long period gratings

101

Figure 4.11: Absorption spectrum of 3.5 mol% Ge-doped fused silica [4] compared with that of pure fused silica

but the gratings writing could be obtained by means of two dierent methods: using an amplitude mask technique (see subsection 4.3.1) or a point-to-point technique (see subsection 4.3.1). Later, other

non-photochemical

approaches of LPGs inscription were de-

veloped, which were based on a change in refractive index. This RI change could be induced in several ways:

by heating the ber by means of both

a point-to-point laser radiation of dierent kind (see subsection 4.3.2), by applying an electric arc (see subsection 4.3.2), by varying the material properties of the ber (see subsection 4.3.2) or by applying a mechanical pressure (see subsection 4.3.2).

Finally, it is worthy of emphasizing that all listed

non-photochemical approaches pertain to a material excitation by heating or stressing the ber cladding, that is to say, the deposition of the absorbed energy in the ber cladding.


102

More recently, various high-excitation-energy point-to-point techniques of LPGs fabrication in standard optical bers had been developed. These methods included single-photon femtosecond UV (λ

=157

nm) fabrication with an

excitation energy of 7.9 eV and multi-photon femtosecond IR (λ

=800

nm)

fabrication with an excitation energy of 7.8 eV. This meant that the energy band-gap for the core of a low-level Ge-doped standard ber was lower than 7.8 eV and hence also lower than that of the pure fused silica cladding, which was about 9.3 eV [4].

Looking at gure 4.11, it is worthy of noticing that

Figure 4.12: Schematic of photoexcitation pathways for dierent LPG writing techniques in standard optical ber: the conventional single-photon (5 eV) and three multi-photon approaches [4]

the wavelengths at 211 nm, 264 nm and 352 nm (not explicitly shown in that gure) (ie the fth, the fourth and the third harmonics of the 1055 nm fundamental radiation of femtosecond Nd:glass laser, respectively) corresponded to the minimum values of linear absorption in germanosilicate bers as well as in pure fused silica ones. This last condition was necessary for carrying out a


103

two-photon or three-photon excitation with values of total excitation energy in the range from 9.4 eV to 11.8 eV (see gure 4.12). Such a high values of total excitation energy exceeded the values of energy band-gap mentioned above (ie 7.8 eV). Therefore, the two-photon or three-photon approach for grating writing could be used to imprint photochemically a LPG in both the cladding and the core. This last issues will be resumed in subsection 4.3.1.

4.3.1 Photochemical or UV methods As above-mentioned, photosensitive optical bers have a well known photoinduced refractive index change imprinted by UV light at a wavelength near 240 nm. The mechanism responsible for a permanent increase in the core RI is unquestionably the absorption of energy into the band of Ge-doped-core ber defects. This phenomenon was explained as a change in the UV absorption spectrum of the ber through the

Kramers-Kronig

principle [117]. It is also

true that there was an additional contribution to the RI change caused by the densication of the glass structure, which began with the annihilation of the defects responsible for the absorption. Mizunami et al [118] proved that the use of germanium oxide GeO2 served to increase the ber photosensitivity by increasing of value of core refractive index.

Therefore, several types

of high-doping GeO2 levels were fabricated during the time.

The increase

of GeO2 doping level from 4 mol% germania of standard low-loss bers to high-Ge-doped bers with greater than 10 mol% germania allowed to increase both the grating reectivity and the value of index perturbation (∆ and also to reduce the writing time of the grating.

ncore ),

Nevertheless, the value

of Ge-doping level could not be increased to innity because in this way the bers showed a high dierence in refractive indices, thus the bers could not fulll both the condition of low

∆

bers (remember the expression of

in equation (3.1)) and the condition of

total internal reection

∆

given

(TIR), which

left single mode the bers themselves. To compensate this problem, later, a new kind of photosensitive optical bers were manufactured. The core of these bers was doped with a boron (B) oxide B2 O3 too. In fact, they dealt with B-Ge co-doped optical bers. The addition of B2 O3 allowed the bers to keep the same photosensitivity though the dierence in refractive indices decreased at the same value of standard optical


104

bers. This meant that B-Ge co-doped optical bers still were low

∆

bers

and fullled the TIR condition. Moreover, Williams et al [117] demonstrated that, using B-Ge co-doped optical bers, the same order of magnitude of both index perturbation and grating reectivity could be achieved with a strongly reduced writing time of the grating (from one hour to about ten minutes). All that allowed the great diusion of these co-doped bers.

Amplitude mask The rst methodology for writing a LPG was developed in 1996 by Vengsarkar et al [5]. A photosensitive optical ber was exposed to a KrF excimer laser (λ

=248

nm) through an amplitude mask as shown in gure 4.13.

Figure 4.13: Experimental setup for writing LPGs by means of an amplitude mask


105

The amplitude mask is an array of windows that enlightens periodically the ber portion in which we want the grating to be inscribed. The UV radiation coming from the KrF excimer laser hits the amplitude mask and part is transmitted in the same direction of the incident wave, part encounters a diusion array, which diract the light beams in a way that they form an interference pattern with the beams not diracted. It is in these areas, where the interference takes place, which the core RI changes, thus to inscribe the grating. Therefore, a rectangular modulation structure is obtained.

It is worthy of

remembering that only the ber core absorbs the UV radiation, as explained above. Looking at gure 4.13, it is obvious that the grating length is as well as the length of the amplitude mask. The key parameter for the correct writing of the grating by means of this technique is the distance

d

between the ber

and the amplitude mask. In fact, the diusion relationship takes into account this distance too, which have to be kept within a certain value. Otherwise the intensity decay of the diracted beams will occur, which in turn would lead to the incorrect writing of the grating. By using the experimental setup discussed above, typical exposure condi-

−1 , pulse repetition frequency

tions were the following: energy of 250 mJ pulse

of 20 Hz and beam area of 2.6 x 1.1 cm. In these conditions, typical fabrication times were around 10 minutes for photosensitive bers. The time evolution of the grating with a period of

Λ=

474

µm

during the fabrication process is

reported in gure 4.14 by monitoring actively the transmission spectrum of the ber. The gure 4.14 shows the growth of the grating over the time by stopping the UV light exposure from 1 minute (curve A) to about 5 minutes (curve E). It is clear that the loss peak and the associated resonance wavelength of the coupled cladding mode increased during the time as a function of the total excitation energy absorbed by the ber core. Moreover, the spectral characteristics of the grating can be further modied by changing the length of the grating (or the number of grating fringes, equally) or the RI prole of the ber. The same results were achieved a year later by Bhatia et al [44]. LPGs with dierent periods were written in hydrogen-loaded bers with UV radiation (power of about 120−140 mW) from a frequency-doubled argon-ion continuous-wave laser by using the same physical and experimental mecha-


106

Figure 4.14: Time evolution of a LPG with period of

Λ=

474

µm

at 1-min

intervals [5]

nism. In fact, chrome-plated amplitude masks with rectangular transmittance functions were used to vary the grating periodicity from 340

µm

to 280

µm.

The gratings were annealed at 200 for approximately 15 hours to remove the residual hydrogen and the unstable UV-induced index changes.

In this

way, gratings experienced a good thermal stability.

Point-to-point As introduced in section 4.3, photosensitive optical bers had attracted much interest because they allowed one to imprint an index modulation in the


107

ber core. The rst gratings were written by UV radiation with the excitation of a singlet-singlet transition band (near 242 nm) of a germanium-oxygendecient center (GODC). It was also well known that a GODC had a weak forbidden absorption band with its maximum at 330 nm due to the singlettriplet transition [119], namely, a high-excitation-energy method. Dianov et al [6] showed for the rst time that the direct photoexcitation of the GODC triplet state could induce a change in germanosilicate glass structure similar to those induced by the band excitation of the GODC singlet state at 242 nm and hence could lead to an index change. This meant that it was also possible to use other wavelength values of laser sources around 330 nm for writing a LPG. In addition, Dianov et al [6] proved experimentally that the absorbance of the GODC triplet state band was three orders of magnitude smaller than that of the common GODC singlet state band.

Having said that, however, it was interesting to understand better the physical mechanism behind the direct triplet excitation. Therefore, Dianov et

+ laser, which

al [6] made some experiments using a coherent Innova 200 Ar operated in the 333364-nm multiline regime.

The gratings were written by

means of a point-to-point technique in step-index ber characterized by a 10 mol% GeO2 in the core and a cut-o wavelength of 0.92

µm.

The UV light

was focused at the ber core by means of a spherical silica lens.

Typical

diameter of focal spot measured by an optical microscope was about 20

µm.

The ber was placed upon a computer-controlled translation stage with a resolution of 3

µm.

The grating period of 200

µm was chosen in order to place

the resonance wavelengths of the coupled cladding modes (from p = 1 to p = 15) in the working spectral range of 12001600 nm. time of each point was 1 s.

A typical irradiation

After the irradiation of a half-period region,

the UV light was blocked by a shutter and the ber was moved to write the next grating period: from this manufacturing technique that came out the name of point-to-point technique. Following this procedure, they formed an approximately rectangular grating prole along the ber axis. The total grating length

L

was 4 cm.

Moreover, they varied the total UV intensity

−2 range by inserting broadband optical lters in the

in the 20170 kW cm

laser beam, by keeping a constant relation between the intensities of the laser lines and therefore between their contributions to the induced refractive index.


108

The grating spectrum measurements were performed by an optical spectral analyzer simultaneously with the grating preparation.

A halogen lamp was

used as a white-light source. An example of LPG recorded with this technique is given in gure 4.15. Figure 4.15 shows the transmission spectrum of a 4cm-

Figure 4.15: Transmission spectrum of a 4cm-long LPG with a period of 200

µm

written in 10 mol% Ge-doped ber [6]

long LPG with a period of 200

µm

written in 10 mol% Ge-doped ber by

means of a UV light source at a wavelength near 330 nm and with a power

5 W cm−2 .

density of about 1.7 x 10

From this gure, it is possible to see

that the strongest loss peak on the right, which corresponds to the coupling between the fundamental core mode and a high order cladding mode (p = 15), has a depth of 3 dB in accordance with what have just been said. This fact


109

limits unquestionably the pratical use of this band and so this methodology for the manufacturing of photoinduced grating structures. By the way, the obtained value of the induced RI change in the ber

−4 RIU. The

core for the grating shown in gure 4.15 was about 1.9 x 10

Figure 4.16: Dependence of induced refractive index on near-UV power density [6]

authors also studied the dependence of the induced RI in the core of the ber (∆

ncore )

on the power density of the UV radiation. The curve, reported in

gure 4.16, showed a saturable behavior as in the case of common singletsinglet excitation. Later, starting from the studies of Dianov et al, other authors aimed at contributing to the development of new high-excitation-energy techniques in order to understand better the physical mechanism behind the grating inscription. A good article about this topic was written in 2006 by Nikogosyan [4].


110

The author made a comparison with the dierent point-to-point LPG manufacturing techniques based on high-intensity femtosecond UV and near-UV laser pulses.

As mentioned previously and based on the analysis of the ab-

sorbed energy distribution (see gure 4.12), LPGs were induced by means of a two-photon (λ

=

211 nm and

λ=

264 nm) or three-photon (λ

=

352 nm)

absorption mechanism and were characterized by preferential energy deposition in the ber cladding, which led to a high asymmetry of RI prole and resulted in high birefringence properties of gratings. The experimental setup of high-intensity point-to-point LPG manufacturing is shown in gure 4.17.

For LPGs recording, the author used the fourth

Figure 4.17: Schematic of experimental setup for point-to-point LPGs manufacturing with high-intensity femtosecond UV and near-UV laser pulses [4]

(264 nm), the fth (211 nm) and the third (352 nm) harmonics of the fundamental radiation of a commercially available femtosecond Nd:glass Twinkle laser. The pulse duration was 220 fs (FWHM) for 264 nm pulses and about 250 fs (FWHM) for 211 nm and 352 nm pulses. The beam diameter at FWHM was 0.3 cm, 0.22 cm and 0.27 cm at 264 nm, 211 nm and 352 nm, respectively. The repetition rate was 27 Hz and the pulse energy was maximal in the case of the fourth harmonic (up to 200

µJ)

and minimal in the case of the third

4.3. Long period gratings and fth harmonics (up to 100

111

µJ).

The femtosecond UV pulses were focused

by means of a 45.4 cm fused silica lens (in the case of 264 nm) or by a 48.6 cm CaF2 lens (in the other cases) through a slit of width 150

µm (or 200 µm),

onto the ber (with the acrylate coating removed), which was placed behind the slit at a distance of about 100

µm.

This allowed author to approximate

the spatial distribution of light intensity on the ber by that on the slit. The displacement of the lens with respect to the ber allowed author to change

−2

both the incident UV irradiation intensity in the range of 100-1000 GW cm

−2 . The ber

and the uence (energy) per pulse in the range of 30-200 J cm was xed on a 50 mm (1

µm resolution) computer-controlled translation stage

PI 405.DG (Physik Instrumente) and was exposed point by point with a pe-

Λ = 300 µm and with a total length of the grating of 2 cm (or with a period Λ = 400 µm and total grating length of 2.5 cm). The total number of

riod

recorded fringes was 67 and 63, respectively. The evolution of loss peaks in the LPG transmission spectrum was monitored in situ with a halogen lamp and an optical spectrum analyzer AQ6317C (Yokogawa Europe BV). The UV exposure and ber translation processes were both computer-controlled using LabVIEW and a PCI-GPIB card (both from National Instruments). In the experiments, the author used the standard telecom ber SMF-28 with a core diameter of 8.2

µm

and cladding diameter of 125

µm.

The sensitization of

the ber was performed in a hydrogen atmosphere at 160 bar at 80 for 90 hours.

For the sake of clarify, the author gathered in several tables the experimental data regarding similar LPGs (with a period of 300

µm

and a length

of 2 cm) written by dierent laser sources in the spectral range between 157 nm and 352 nm, that is to say, from UV to near-UV spectrum. Looking at table 4.1, it follows that the LPGs, recorded in the hydrogenated SMF-28 ber by high-intensity 352 nm pulses, possess the highest value about the grating strength, not only in comparison with the other point-to-point femtosecond 211 nm and 264 nm techniques, but also in comparison with all the other known photochemical techniques (λ

=

248 nm and

λ =

157 nm).

Further-

more, such a high value about the grating strength was characteristic of LPGs inscribed in the same ber by non-photochemical techniques (eg CO2 laser irradiation, where practically all the absorbed energy was localized in the ber


112

Table 4.1: Comparison between the experimental data on LPG inscription eciency in a hydrogen-loaded Corning SMF-28 ber for point-to-point technique at dierent source wavelengths (LPGs of the same period, 300

µm,

and

of the same length, 2 cm).

Source

Incident

Incident

Grating

Resonance

wavelength

intensity

uence

strength

wavelength

(nm)

−2 ) (GW cm

−2 ) (J cm

(dB)

(nm)

1300

17

1464

5

21

1594

248

0.02

157

0.0002

264

470

38

24

1487

211

125

32

25

1434

352

1090

197

30

1450

cladding). An explanation of this fact was given by means of a photograph of the LPG section shown in gure 4.18.

The LPG was written in a stan-

dard SMF-28 ber with the laser radiation at 325 nm characterized by an incident intensity of 1350 GW cm

−2 and an incident uence of 208 J cm−2 .

From gure 4.18 it was easy to see regular damage in the cladding area near the incident laser radiation. It is worthy of noticing that the length of each periodic damage was 150

µm

as well as the length of the slit in gure 4.17.

Looking at that gure, two main observations followed: rst, the absorbed energy was distributed very non-uniformly inside the ber similar to that in the experiments on LPGs inscription involving a CO2 laser source and, second, as the value of band-gap energy for Ge-doped fused silica was more than 7.1 eV (see gure 4.12) and one photon of 352 nm radiation was equal to 3.53 eV, the excitation energy of two photons (7.05 eV) was not sucient for the excitation of either the cladding or the core. Thus these experimental data suggested a three-photon absorption mechanism for high-intensity LPG inscription. Finally an important observation can be made.

In fact, this last UV

method for LPG manufacturing can be seen as a special class of photochemical methods because, although the physical mechanism of grating formation is based on high-excitation-energy photochemical absorption, the grating inscrip-


113

Figure 4.18: Photograph of the LPG section written by means of point-topoint technique based on high-intensity femtosecond laser pulses at a wavelength of 352 nm [4]

tion depends strongly on the irradiation intensity (not a saturable behavior) and the gratings show the typical optical characteristics of gratings written non-photochemically as it will be explained in next subsection.

4.3.2 Non-photochemical or non-UV methods As described in subsection 4.3.1, the rst LPGs were written exposing a Ge-doped ber to UV radiation from a KrF laser through an amplitude mask. This method needed to make photosensitive the bers with high levels of germanium doping or to use already doped bers. During the time, several ways to improve the photosensitivity had been suggested, such as co-doping the ber with photosensitive elements, hydrogenation and exposure of the ber to other types of radiations. Unquestionably, ber hydrogenation was a


114

good way to increase the photosensitivity, although is was a time-consuming procedure that also required a post-UV irradiation heat treatment in order to restore the spectral position of the resonance wavelengths due to hydrogen out diusion. Moreover, the stability of UV-induced LPGs at high temperatures (greater than 400) was not so straightforward. In fact, it was proved that the decrease of RI modulation during the annealing process represented the main practical constrain in such applications. The necessity for a large number of amplitude mask with dierent pitches was another disadvantage, although it could be overtaken by means of the implementation of a more exible pointto-point writing technique (as described in subsection 4.3.1), but with the increase of both the fabrication time and the costs of the equipment. Consequently, several non-photochemical or non-UV techniques of LPGs manufacturing had been developed. These methods relied on physical deformation of the ber or on RI variation produced by CO2 lasers, femtosecond laser pulses in both the UV and IR spectra, ion implantation or electrical discharges. All these non-photochemical methods had proved to manufacture LPGs with high thermal stability due to the process of grating inscription characterized by a local heating of the ber.

Furthermore, they were much

simpler techniques and did not need expensive laser equipment. Finally, LPGs could be written in any type of ber, because the grating characteristics were mostly dened by the intrinsic properties of silica glass itself [10].

Point-to-point Among the non-UV techniques, the point-to-point techniques, which make use of infrared (IR) lasers, are widely used. The literature reports two dierent techniques, which use pulsed laser sources emitting in two dierent IR wavelength range: the former emitting in the 800 nm range, the latter in the 1060 nm (CO2 laser).

The rst technique was developed in 1999 by Kondo et al [7]. It was previously demonstrated with some experiments by Miura et al [120] that focused irradiation of femtosecond Ti:Sa laser pulses causing a permanent RI increase in various glasses and thus in optical bers. Therefore, Kondo et al showed


115

for the rst time how to induce a periodic RI modulation in the core of a single-mode optical ber by means of a light which wavelength was absorbed neither by the ber core nor by the ber cladding. The experimental setup for this fabrication technique is reported in gure 4.19.

The optical ber that

Figure 4.19: Experimental setup for LPGs manufacturing by means of a point-to-point non-UV technique based on a IR laser source [7]. ND, neutral density. CCD, charge-coupled device was used by the authors was a standard single-mode ber for telecommunication (NA = 0.11, mode eld diameter = 9.3 = 125

µm ±

2

µm,

cut-o wavelength = 1260

µm ± 0.5 µm, clad diameter nm ± 40 nm). The ber core

and cladding were Ge-doped and pure fused silica glass, respectively.

The

laser pulses that were used to induce a RI change were obtained from a regeneratively amplied Ti

3+ :Al O laser pumped by an Ar+ laser. The pulse 2 3

width was 120 fs, the wavelength was 800 nm and the repetition rate was


116

200 kHz. The laser beam was guided by means of a microscope and nally focused into the ber core by means of a 20X objective (NA = 0.46). The features produced during focused irradiation of femtosecond pulses were observed through a CCD camera mounted upon the microscope. The ber, which was xed on a computer-controlled XYZ-translation stage, was irradiated by the point-to-point method. An optical spectrum analyzer real-time monitored the transmission spectrum of the fabricated LPGs.

The laser power was set at

150 mW by use of a neutral density (ND) lter. The beam size before the objective was 6 mm and the irradiation time was 10 s for each spot. Assuming that the femtosecond laser beam had a Gaussian prole, the spot size at the

2

focal point and the Rayleigh length

were estimated to be 2

µm

and 3

µm,

−2 and each spot was subjected

respectively. The uence per pulse was 24 J cm

−2 . With this value of total exposure dose, the −3 RIU. expected value of the RI increase could be estimated to be about 10

to an energy dose of 50 MJ cm

The same authors proved also that, for a correct grating inscription, the acrylic polymer coating of the ber must be removed before writing the grating.

Otherwise, the index change in the core did not occur obtaining only

the ber coating ablation. So, after removing the ber coating, the ber was irradiated by means of the experimental setup described above. Figure 4.20 showed the transmission spectrum of a 29.9 mm-long LPG with a grating period of 460

µm.

Large loss peaks whose FWHM were approximately from

10 nm to 20 nm could be clearly observed. Moreover, many small loss peaks could also be observed and the transmission spectrum of the ber went to a more complicated shape.

This feature conrmed that the focused radiation

induced a RI increase in the ber core as well as in the ber cladding. Thus, unless laser pulses were focused only in the core, the RI of the cladding also changed.

The complexity of the spectral shape had been attributed to the

irregularity of the index modulation. The authors demonstrated that the RI increase induced by focused irradiation of femtosecond pulses at 800 nm could not be attributed to Ge-related defects. In fact, from observations given by Miura et al [120] with an atomicforce microscope (AFM), it was proved that a local densication in glass irradiated by focused radiation of femtosecond pulses at 800 nm was the main

2 For more details see the website http://en.wikipedia.org/wiki/Rayleigh_length


117

Figure 4.20: Transmission spectrum of a 29.9 mm-long LPG with a period

Λ=

460

µm

[7]

physical mechanism involved in the grating inscription. In addition, a nonlinear reaction through a multi-photon process and/or conventional heating by a multi-photon transition occurred during laser irradiation. Furthermore, by varying the laser uence, it was revealed that the photoreaction, which induced the RI change, had a threshold in uence (a saturable behavior). Finally, it was also proved that LPGs fabricated by a focused radiation of femtosecond pulses showed high resistance to thermal decay despite of having no special stabilization. This thermal stability was achieved because the cause of the RI increase induced by a focused radiation of femtosecond pulses was dierent (non-photochemical) from that of the UV-induced RI increase. Although this methodology had the advantage to allow the writing of gratings in both photosensitive and standard SMF bers, it showed the drawback of changing the RI not only in the core of the ber, but also in the cladding, even though the laser beam was focused into the ber core only. This means that the loss peaks in the ber transmission spectrum were very close to each other making more complicated to explain the transmission spectral shape (see


118

gure 4.20), which is aected by the coupling occurring between the asymmetric cladding modes.

Moreover, looking at gure 4.19, the experimental

setup was clearly dicult to use in practice and made up of a very expensive equipment.

The second point-to-point technique was published for the rst time in 1998 by Davis et al [8]. The proposed LPGs manufacturing method was based on direct exposure of the optical ber to focused CO2 laser pulses (10.6

µm).

By this new, simple and high controllable technique, the ber was not physically deformed, as occurred in the case of an ultraviolet exposure, thus the physical mechanism giving rise to the RI increase was both the residual stress relief and the densication of the ber glass rather than the photoexcitation. LPGs were written into both non-H2 -loaded and H2 -loaded dispersionshifted bers.

The experimental conguration consisted of a computer-con-

trolled translation stage, which positioned the ber in an alignment xture. Under the control of a computer, each laser pulses (intensity of 0.5 W, duration of 300 ms) were focused onto a 140

µm diameter spot (uence per pulse of 7.7

−2 ) at the desired position along the axis of the ber. An optical imaging J mm system mounted above the ber aided in the alignment and enabled verication that no physical deformation was occurred. A broadband source with a freespace wavelength in the range from 1.4

µm

to 1.6

µm

and an optical spec-

trum analyzer were used to monitor the ber transmission spectrum during the grating inscription. Figure 4.21 shows transmission spectrum of LPG written in non-H2 -loaded and H2 -loaded dispersion-shifted bers. The diraction of the core guided light into the cladding modes produced the characteristic loss peaks shown for both bers. The H2 -loaded ber exhibited higher writing sensitivity, and therefore a shorter pulse duration (200ms) was used. Only 20 periods were written instead of the 40 periods used for non-H2 -loaded ber. The periodic spacing (Λ

=

480

µm)

of the pulses, and thus the grating period

was the same for both the ber gratings. However, the values of the resonance wavelengths of the grating written in H2 -loaded ber were dierent compared to the non-H2 -loaded ber, indicating that the couplings to cladding modes occurred with dierent propagation constants. Later, the same point-to-point CO2 laser technique was resumed in 2004


119

Figure 4.21: Transmission spectrum of LPG written in non-H2 -loaded and H2 -loaded dispersion-shifted bers [8]

and was improved by Braiwish et al [9]. One of the main advantages of using a CO2 laser for the LPGs fabrication was unquestionably the possibility of using also standard SMF optical bers. No hydrogen loading or dopant was needed. In addition, the point-to-point method gave a higher degree of control over the grating parameters and allowed one to monitor real-time the spectral response during the grating fabrication. These features made the point-to-point CO2 laser technique one of the most attractive and desiderable technique for LPGs manufacturing. Gratings were written into hydrogen-free Corning SMF-28 single-mode ber using the conguration shown in gure 4.22.

A cylindrical lens was

120


Figure 4.22: Fabrication apparatus for writing LPGs by point-to-point CO2 laser exposure [9]

used to focus the CO2 laser beam into a narrow line. The ber was aligned at a right angle to the focal line of the lens and was attached to a computercontrolled motorized translation stage that could be translated to create any desired grating period. A shutter was placed before the lens to accurately control the exposure time of the CO2 laser beam. An optical spectrum analyzer,


121

in combination with a broadband source, was used to monitor the transmission spectrum of the grating. A polarizer was also used to control the CO2 laser beam polarization.

Additional instruments such as an optical power meter

and a CO2 laser spectrum analyzer were used for monitoring purposes.

To

control the ber during fabrication, a camera with a high-magnication longworking-distance microscope was mounted above the ber and connected to a video monitor. This allowed any physical deformation to be observed. The laser beam wavelength was set to 10.59

µm

since material reectance was low

and absorption was high at this wavelength.

The entire fabrication process

was computer-controlled with a custom LabVIEW program. The fabrication program was designed to allow monitoring of the transmission spectrum as well as the laser power for each grating period.

It also allowed authors for

continuous control of the shutter during the fabrication. These features made it possible to change the number of shutter exposures per period, and thus to tailor the transmission spectrum of the grating. Because of the high absorption at the wavelength of about 10.6 laser-induced LPGs had azimuthally varying RI proles.

µm,

CO2

Although the RI

change in an UV-induced grating occurred mainly in the ber core, the index modulation induced by the CO2 laser radiation occurred over the entire crosssection of the optical ber and was higher on the side of the ber toward the laser beam. Thus the RI change was induced not only in the ber core but also in the ber cladding, which meant that the couplings occurred also to antisymmetric cladding modes. That is to say, when the ber was exposed to the CO2 laser beam, the absorption was higher on the ber side that faced the laser beam. As a result of the azimuthal asymmetry, CO2 induced LPGs were very sensitive to ber bending. Therefore, the transmission spectrum of the ber was signicantly aected by any axial rotation of the grating.

Electric arc Among the non-UV methods of LPGs manufacturing, the most promising was that based on electrical discharges.

This technique was developed

for the rst time in 1998 by both Godbout et al [121] and Kosinski and Vengsarkar [122].

As above-mentioned in subsection 4.3.2, the electric arc

technique is much simpler and did not required expensive laser equipment.


122

This features together with the good thermal stability of the fabricated LPGs allowed electric arc technique to spread greatly. The rst comprehensive study about the performance and the physical mechanism behind the grating inscription was reported for the rst time in 2001 by Rego el at [10]. The authors studied also the spectral characteristics of LPGs written in both standard SMF and photosensitive bers using the exible and low-cost electric arc technique. For LPG inscription, Rego et al [10] used a technique similar to that described in previous works [121, 122] but with some dierences. A schematic of the fabrication setup is shown in gure 4.23.

The fabrication process

Figure 4.23: Fabrication apparatus for writing LPGs by electrical discharges produced by a commercial splicer

consisted of positioning a portion of uncoated ber between the electrodes of a commercial splicing machine. One end of the ber was clamped in a ber holder on top of a computer-controlled translation stage with a precision of 0.1

µm.

At the other end of the ber, a mass was attached to keep the ber

under a constant axial tension. An electric discharge was then produced with a current less than 10 mA and duration of about 1 s, exposing a portion of the ber of about 150

µm length.

Afterwards, the ber was moved by the selected

grating period, typically in the range from 400

µm

to 700

µm.

The last two


123

steps were repeated 15−55 times, depending on the grating length that we want to achieve, in order to give rise to periodic perturbations along the ber axis due to its local heating. The local temperature of the ber during the arc exposure was more than silica glass softening temperature (about 1660 ) because, for moderate applied tension (a mass of about 10 g as in gure 4.23), a tapering of the ber was observed, which increased as the axial tension was increased. The same authors suggested three main physical reasons, which could explain the mode couplings in these gratings: the ber diameter decrease, or rather the periodical tapering of the ber cladding, the dopant diusion in photosensitive optical ber and, nally, a change of the glass properties by the fast local heatingcooling process. Although the local dopant diusion out of the ber core could not be totally excluded, it was demonstrated that the dopant diusion played a minor role in the grating formation. Furthermore, when low axial tension was applied to the ber (mass of about 5g) a very small decrease in the ber cross−section was observed (change in the diameter lower than 1%). On the contrary, the changes in glass properties due to the fast local heating−cooling process, annealed periodically the residual stresses of the ber, creating new stresses in the ber itself, which gave rise to mode coupling.

In details, it was discussed [10] that such a process having more

than 1000 s

−1 cooling rate had to result in a change of the ctive temper-

ature of the glass in the local portion of the ber exposed to the electric arc. The change of the ctive temperature resulted, in turn, in a change of glass density, viscosity, refractive index and Rayleigh scattering. To prove all that, Rego et al [10] exhibited the transmission spectra of LPGs written in three dierent optical bers by means of the electric arc technique.

The gratings were written in a 1.5 mol% GeO2 -doped (dotted

curve in gure 4.24) and sulfur-doped (solid curve in gure 4.24) bers under an axial tension caused by a mass of 22.8 g (GS ) and exposed to the electric arc for 17 and 35 times, respectively. The electric discharge (one per period) was characterized by a current of 9 mA and a duration of about 1.1 s. A mass of 5.1 g (lowest axial tension) was used in the case of the nitrogen-doped (dashed curve in gure 4.24) ber that was exposed for 1 s to a 10 mA electric arc current for 55 times. It is clear that fabrication conditions as well as the types


124

Figure 4.24: Transmission spectra of three dierent LPGs with the same period of 540

µm

[10]

of the bers used are dierent, thus the resonant loss peaks show dierent spectral position. The authors studied also the inuence of the axial tension on grating inscription. The LPGs reported in gure 4.25 had the same period of 540

µm

and were written in 1.5 mol% GeO2 -doped ber (as the dotted curve in gure 4.24) after a number

n

of electric arc discharges (one per period).

eect of pre-annealing at 1100 for 30 minutes was also shown.

The

As can

be seen in gure 4.25, by keeping the arc parameters constant, as the axial tension increased from the lowest value GB to the highest one GSS it was possible to obtain higher isolation loss with less discharges, although the insertion loss increased. So it was possible to notice that the increasing axial tension, which also aected the ber cross-section, was favorable to the writing process. Another important aspect, that it was possible to note as well, was that the reproducibility of this technique increased using the lower axial tension (GB ). Looking at gure 4.25, another observation could be made: the


125

Figure 4.25: The inuence of dierent axial tension (GB , GS and GSS ) on grating inscription [10]

ber tapering was the secondary physical eect to the grating inscription since it was possible to write gratings with a large value of transmission after few discharges (about 10) without a change of the ber cross-section. Due to the physical mechanism behind the grating formation using the electric arc technique, the RI perturbations along the ber axis were induced not only into the ber core but also into the ber cladding.

As discussed

previously, this meant mode couplings to antisymmetric cladding modes. In 2007, Ivanov and Rego [11] studied for the rst time the origin of antisymmetric perturbations in arc-induced LPGs.

They demonstrated that these

perturbations were caused by the temperature gradient in the ber, which was induced, in turn, by the temperature gradient in the arc discharge. As above-discussed, dierent mechanisms were involved in the inscription of arcinduced gratings. Among those mechanisms, an important role was certainly played by the modulation of the core diameter, which was due to ber tapering, strain induction or relaxation, microbending and microdeformation.

126


In fact, one of the consequences of the temperature gradient was the periodical microdeformation that consisted in a shift of the ber core under arc discharges. The authors proved that such microdeformation was responsible for the coupling to antisymmetric cladding modes. To give evidence in favor of this, a photograph of the arc discharge produced by a commercial splicer is shown in gure 4.26. The current produced during an arc discharge is a direct

Figure 4.26: Photograph of the arc discharge showing its asymmetry [11] current, hence the arc is directional and the center between the electrodes is not the center of symmetry.

Moreover, the electrode at the bottom (cath-

ode) glows only at its tip, while the electrode at the top (anode) glows over a much larger area. The arc itself is brighter near the lower electrode. Thus, it could be expected that there is a gradient of temperature explaining the origin of the antisymmetric perturbations.

The authors found two dierent


127

types of geometric deformation of the ber during an arc discharge: tapering and microdeformation. Tapering was a symmetric diameter reduction and an elongation of the ber. The degree of the ber tapering depended on both the pulling axial tension and the value and duration of the electric current in the arc.

With typical arc discharge parameters, ber deformation induced cou-

pling to symmetric modes only. However, the coupling constant corresponding to a typical ber diameter reduction of a few percent was too small to explain the grating formation. Therefore, microbending occurred when the ber was locally displaced in the plane lateral to the ber axis due to some asymmetry in the fabrication setup. Such a dierence between the two sides of the ber, which was caused by the dierence in silica viscosity, induced a core shift or geometrical microbending that led to the grating formation. This dierence in viscosity itself was due to the temperature dierence between the two electrodes. To estimate the viscosity dierence between the two sides of the ber heated by the arc, the authors proposed to place a silica capillary into the arc instead of the ber (too dicult) as shown in gure 4.27. From the gure 4.27

Figure 4.27: Photograph of the asymmetric deformation of a silica capillary (56

µm

/ 125

µm)

submitted to an arc discharge [11]


128

it could be clearly seen that the capillary was asymmetrically swollen as could occur in optical bers. Finally, it is worthy of highlighting that, although the symmetric tapering of the ber did not induce coupling to the antisymmetric cladding modes, it had a strong inuence on the LPGs spectra because the average decrease of the ber diameter caused a wavelength shift of the LPGs resonance wavelengths. During the rst time of my research activity about optical ber gratings, we focused our attention on arc-induced LPGs.

Due to a exible, simple

and cheap manufacturing system, a lot of measurements were carried out in order to nd the correct values of both the current intensity and the arc duration for manufacturing gratings with high eciency mode coupling.

In

the rst measurements we decided to use arcs characterized by high current intensity (about 40 mA) and very short duration (about 1 ms).

By using

these parameters, we saw clearly that gratings were very sensitive to both ber bending and the position of the ber (birefringence). This phenomenon was easily explained if we assumed that the grating was written mainly in the cladding of the ber. In fact, despite having high current intensity, the arc duration of the arc was too short to ensure an ecient heat diusion into the core of the ber as well. Thus, we decided to decrease the current intensity up to 12 mA and to increase the arc duration until to 200 ms. With these choices, the change in refractive index regarded not only the ber cladding but also the core of the ber. To better understand the mechanism of grating inscription using the electric arc technique, we made a photograph of an electric arcinduced LPG written in a standard step-index SMF-28 optical ber by means of the transmission optical microscope Nikon Optiphot (see gure 4.28).

As

can be seen, the eect of both core and cladding perturbation was clearly visible (brighter regions) together with the physical deformation of the ber (ber tapering), which was caused by the electric discharges generated by the arc of the splicer. By the way, the main constrain of this methodology was the poor reproducibility for the arc-induced LPGs together with the great number of loss peaks in the ber transmission spectrum due to antisymmetric couplings too. For the sake of completeness, it is worthy of noticing that some of the above-discussed features about arc-based LPGs, and more generally of the


129

Figure 4.28: Photograph made by the transmission optical microscope Nikon Optiphot of an electric arc-induced LPG written in a standard step-index SMF-28 optical ber

dierence between UV and non-UV methods, have been recently called into question by Smietana et al [123]. The authors presented for the rst time a comparative study of LPGs written by point-by-point UV radiation at

λ =

248 nm and by electrical arc discharges. The gratings used for comparative purposes were inscribed in a highly photosensitive B-Ge co-doped step-index optical ber with two dierent grating periods, 350

µm

and 400

µm.

They

observed that the spectra of the gratings manufactured by electric arc were shifted to the shorter wavelengths, while the gratings manufactured by UV radiation showed some distortions and an extra attenuation band at 1200 nm. As previously mentioned more than once, it is certainly true that the characteristics of a gratings, while inuenced by the ber properties, depend mainly

Λ, on the induced change in the refractive index ∆ n, on technology and on the grating length L. The dierence between

on the grating period the writing

the spectra has been explained by the fact that the arc discharge induced a ber tapering, thus resulting in decreased core and cladding diameters.

In

detail, the ber tapering was caused by the axial tension applied to the optical ber during the grating fabrication. It has always been said that LPGs manufactured by means of the UV exposure can be considered as symmetric in terms of the induced RI modulation along the azimuthal direction of the ber [11]. But the resonance observed by Smietana et al [123] at a wavelength of 1200 nm in the spectrum of the UV-irradiated grating was the result of the coupling to an asymmetrical cladding mode. The same authors proved by the polarization-dependent loss measurements that there was a strong azimuthally


130

asymmetric RI change due to single-side exposure and deposition of the energy in the cladding [124]. This could be expected because the B-Ge co-doped bers required much higher UV radiation to obtain a grating eect than did the hydrogenated bers [125].

Anyway, the good quality of the spectra ob-

tained by Smietana et al in our proved the possibility of achieving coupling to only symmetrical cladding modes, by reducing the power of the laser and thus avoiding damage to the surface of the ber.

Moreover, the statement

that gratings manufactured by means of the arc electric method gave rise to couplings to antisymmetric cladding modes only seems to be not necessary true considering the work of Smietana et al [123].

Ion implantation Another non-photochemical method for the fabrication of long period gratings was based on the use of a RI increase induced by ion implantation. This technique was reported for the rst time in 2000 by Fujimaki et al [12]. In fact, it was well known that a relatively high RI increase in the order of magnitude of 10

−3 RIU could be obtained by ion implantation in almost all silica-based

optical bers.

The physical mechanism behind the RI increase was proved

to be the compaction of the glasses [126].

Figure 4.29 shows the schematic

of ion implantation technique. The optical ber used in the experiment was a Corning SMF-28 ber. The core of the ber was Ge-doped silica glass of 97SiO2 :3GeO2 and had a diameter of 9

µm.

The core was embedded in a

cladding of pure silica glass with a diameter of 125

µm.

The ber was im-

2+ ions at room temperature in a vacuum of 10−6 Torr through

planted with He

a metal amplitude mask by means of the use of 1.7 MV tandem accelerator. The acceleration energy of the He ions was 5.1 MeV, the maximum attainable at that time.

The mask was made of Ni:Co and had 29 periods of 170

pitch grating with 60

µm

µm

spacing. The transmission spectra of the fabricated

gratings were observed with an optical spectrum analyzer (Hewlett-Packard 70951A). Figure 4.30(a) shows a photograph of the cross-section of the He-ion implanted optical ber, when a white light was launched through the ber itself. Obviously, the bright circle at the center was the light guided by the core of the ber. The light arc across the ber indicated the region in which the im-


131

Figure 4.29: Schematic of ion implantation technique with a metal amplitude mask [12]

planted He ions induced a signicant RI increase. As shown in gure 4.30(b), the depth of the arc from the optical ber surface was about 24

µm,

which

corresponds to the projected range of the 5.1 MeV He ions in silica glass. Since ions must reach the core of the optical ber to manufacture LPGs, the authors etched the cladding of the optical ber with hydrouoric acid (10% HF in H2 O) for 7 hours and prepared an optical ber with a cladding diameter of about 53

µm,

as shown in gure 4.30(c). Figure 4.31 shows the transmis-

sion spectrum of the grating fabricated by the ion implantation with a dose

15 He2+ cm−2 after the etching of the ber cladding in the way just

of 20 x 10

described. Looking at the transmission spectrum, a very sharp and eective loss peak owing to the coupling between the fundamental guided mode and a cladding mode was observed around 1410 nm. Moreover, as shown in gure 4.30, the induced RI increase indicated by the light arc was not only in the core but also in the cladding of the ber. This was so because the ion implantation induced a quite-high RI increase even in pure silica glass and hence in the ber cladding.

The RI increase in the cladding caused an issue for

the practical use of this gratings, because the fundamental guided core mode


132

Figure 4.30: Photograph (a) and sketch (b) of the cross-section of the He-ion implanted optical ber.

Sketch (c) of the cross-section of the optical ber

etched with hydrouoric acid [12]


133

Figure 4.31: Transmission spectrum of the He-ion implanted etched optical ber [12]

coupled not only to the symmetric cladding modes but also to asymmetrical ones (as mentioned above), which resulted in high background losses, as could be seen in gure 4.31. However, this losses could be removed by means of the use of a mask with narrow spacing, through which ions were implanted only in the core of the optical ber. Furthermore, it was demonstrated that, with an amplitude mask of about 1

µm

pitch gratings, FBGs could be manufactured

with this technique [72].

Mechanical gratings The last non-photochemical technique regarding the LPG fabrication was developed in 2000 by Savin et al [13].

It concerned the characterization of

mechanically induced LPGs by pressing a plate with periodic grooves against a short length of ber. Via the photoelastic eect, the pressure points between the ber and the grooved plate induced a periodic modulation of the refractive index: this was the physical mechanism behind the RI increase. In fact, as shown in gure 4.32, it was possible to induce a RI modulation mechanically by pressing the ber between a periodically grooved plate and a at plate. One of


134

Figure 4.32: Side view of a mechanically induced long period grating with period

Λ

[13]

the plates that the authors tested had V grooves with a depth of about 125

µm

and the at-topped prole shown in gure 4.32. An example of periodically grooved plate used to induce LPGs mechanically is shown in gure 4.33. The test ber was a Corning SMF-28 CPC ber (8.3-µm core diameter, 125-µm cladding diameter and 0.11 numerical aperture). 580

µm)

The grating period (Λ

was selected in order to achieve a coupling near 1.55

µm,

=

which

occurred to a low-order cladding mode. The pressure was applied through a springloaded clamp. An advantageous feature of this design was that one could adjust the grating period, and thus the positions of the loss peaks, by changing the angle between the ber and the grooves. Similarly, the length of ber under pressure, which controlled the bandwidth of the loss peaks, could easily be changed. Moreover, one could tune the depth of the loss peaks by adjusting the pressure. When the perturbation was removed, the transmission spectrum of the ber returned to its initial spectrum. Thus a wide range of lter functions could be generated with the same grooved plate and ber. The authors had found through experimentations that, if the ber under pressure was unjacketed, the loss peaks are broad and overlap, and the out-of-band losses increased. Far lower losses and cleaner spectrum were obtained when the ber remained jacketed. The reason for the lower losses given by the same authors was that the jacket reduced the ber microbending. This approach was also preferable


135

Figure 4.33: An example of periodically grooved plate used to induce LPGs mechanically

because it did not compromised the ber integrity. By the way, to reduce the out-of-band losses, the authors demonstrated that it was enough to place the ber under a slight tension before it was clamped. In addition, it is clear that using this method, the index modulation was created in both the ber core and cladding. As explained previously, this meant that the coupling occurred to asymmetric cladding modes too. Figure 4.34 illustrates the eect of increasing pressure on the transmission spectrum of the ber regarding a LPG recorded with a period of 712

µm.

Higher pressures resulted in stronger mode coupling and thus generally

in deeper loss peaks.

If the pressure was increased beyond a certain point,

however, one expected the depth of the loss peaks to begin to decrease. This behavior was supported, over certain ranges of grating length and coupling constant, by the expression of LPG transmission

T

given in equations (3.76)

and (3.78), as also conrmed from gure 4.34. In fact, when the pressure was increased from p4 to p5 , the attenuation of the loss peak on the left decreased, whereas that of on the right, which had not reached its maximum coupling

136


Figure 4.34: Transmission spectra of a grating with period

Λ =

712

µm

measured for an applied pressure increasing from p1 to p5 [13]

strength condition (see equation (3.79)), continued to increase. Finally, this technique oers the unique advantages of being tunable, erasable and recongurable together with the simplicity and low costs. But it has a great drawback: the grating does not remain permanently imprinted on the ber, namely, the grating vanishes when the grooved plate is removed. This is the main reason why the mechanical gratings can not be used for developing a real sensor (we should also take into account the thermal expansion of the plates) and hence may be useful for educational purposes only.

After the roundup of the manufacturing techniques about long period gratings, as already done in the case of FBGs, it is worthy of highlighting the main dierences between the photochemical methods and the non-photochemical


137

methods. The photochemical methods are characterized by:

the physical principle of the grating writing is based on the photochemical approach, namely, the maximum of the absorption band of ber defects;

the grating is written only into the ber core, which means that the coupling occurs between the fundamental guided core mode and symmetric cladding modes, or rather cladding modes with azimuthal symmetry;

the grating can be written on photosensitive optical bers (ie Ge-doped, B-Ge co-doped, etc) or on standard optical bers after a special treatment that makes the bers photosensitive to UV radiation (ie SMF-28 after hydrogen loading treatment);

the manufacturing apparatus plans to use an expensive laser equipment and a dicult fabrication setup, as general rule;

while the non-photochemical methods by:

the physical principle of the grating writing is based on the physical and/or structural deformation of the ber;

the grating is also written into the ber cladding, which means that the coupling occurs between the fundamental guided core mode and antisymmetric cladding modes, or rather cladding modes that do not have azimuthal symmetry;

the grating can be written on both photosensitive optical bers and non-photosensitive optical bers without any prior- and post-fabrication process, such as hydrogen loading (prior) and thermal annealing (post);

the manufacturing apparatus plans to use a little expensive and much simpler equipment, without the use of a laser source at times;

the manufactured gratings are very sensitive to ber bending and have a high thermal stability.

Chapter 5

Optical ber gratings for physical and biochemical sensing Things should be made as simple as possible, but not any simpler. Albert Einstein

5.1 Theory of optical ber gratings for physical sensing ptical ber sensor technology based on optical ber gratings has been

O

used in a number of important and attractive application elds, which

range from the structural monitoring to chemical/biochemical sensing [3, 127]. Practical and cost eective systems are now available in the market due to the recent advances in grating manufacture and sensor readout instrumentation. Any change in ber properties, such as axial strain, temperature or surrounding refractive index, which induces a change in the eective refractive

e

index of the ber core (ncore ) and/or the ber cladding (n

e clad (p) )

and/or in

the grating period (Λ), will change, in turn, the resonance wavelength.

An

OFG is an intrinsic sensor which changes the transmission spectrum (or alike the reection spectrum) of an incident light signal by coupling energy to other ber modes. As widely discussed in previous sections, in the case of FBGs, the incident wave is coupled to the same counter-propagating core mode and thus it is reected back (the simplest case); on the other hand, in the case of LPGs, the incident wave is coupled to distinct forward-propagating cladding modes and thus it is transmitted ahead. The main drawback of using OFGs as sensor element is that both types of grating are sensitive at the same time to all the external perturbations.

5. Optical ber gratings for physical and biochemical sensing

140

Thus, if one has in mind to develop a real selective sensor using OFGs, it has to remember that the measurement has to be puried from the interferent measurands in order to obtain the eect of the measurand of interest. Therefore, a number of dierent techniques have been proposed in the past in order to get rid of the uctuations coming from these interferent measurands [14, 44]. In the case of LPGs, for example, the multiple bands of a LPG can be used to eectively separate two distinct eects acting simultaneously on the grating [44]. One of the most used technique recurs to the use of two in-line gratings, a LPG followed by a FBG. This type of hybrid grating conguration is that we were used.

A detailed description will be given in the

part II. It is worthy of highlighting that the combination of the use of optical bers with the fact that the signal modulation is spectrally encoded oers multiplexing and remote measurement capabilities, which the other technology platforms are not able to or can hardly oer [17].

It is very important to

stress that, because the optical modulation of the light signal is a wavelength modulation, this implies that the readout is not aected by changes of the optical power caused by either ber bending or source uctuations. Therefore, all the shifts of the resonance wavelength in the ber spectrum, seen as a narrowband reection in the case of FBGs or loss peak in transmission in the case of LPGs, are independent of the optical intensity and uniquely associated with each grating. With care in selection of the resonance wavelengths, each sensor based on OFGs only registers a measurand change along its length. The sensitivity of the OFGs properties to perturbations of the optical ber caused by the surrounding environmental conditions has led to an extensive study of their use as ber sensor elements. In subsections 5.1.1 and 5.1.2, a detailed discussion about the sensing principles of FBGs and LPGs, respectively, in physical eld applications is reported.

5.1.1 Fiber Bragg gratings FBG sensors have been reported for the measurements of strain, temperature, pressure, dynamic magnetic eld [3].

The physical mechanism relies

upon the shift of the FBG resonance wavelength induced by a change of these parameters. The FBG sensitivity is governed by the ber elastic, photoelastic

5.1. Theory of optical ber gratings for physical sensing

141

and thermo-optic properties of the used optical ber and by the nature of the load or axial strain, which is applied to the structure that the ber is attached to or embedded within. The sensitivity to a particular measurand is similar to that of the ber interferometric congurations [1]. In fact, the fractional change in phase of an interferometer is the same as the fractional wavelength shift in FBG resonance wavelength. However, in the case of a ber interferometric conguration, an optical leverage is realized because of the large phase path associated with a long length of ber. This multiplier in the measurement resolution can be regained in the case of a FBG sensor, but not without some additional complication in the wavelength demodulation technique. The most studied and full-grown optical ber sensor technologies based on FBGs are undoubtedly those that concern the strain and temperature sensors. The sensing principle about the strain sensor based on FBGs will be discussed in subsection 5.1.1, while the sensing principle about the temperature sensor based on FBGs will be discussed in the subsection 5.1.1.

Strain sensor By dierentiating the Bragg resonance wavelength with respect to the applied axial strain expression:

,

λFBG res

in equation (2.7)

it can be obtained the following

e d λFBG res = 2 Λ d ncore + ne d Λ core d d d

(5.1)

d ne core takes into account the eect of material dispersion of d dΛ the ber core, whereas the term d takes into account the eect of change in where the term

grating periodicity due to an applied axial strain over the ber. By considering a limited range of applied axial strain (up to about 3 m), equation (5.1) can be linearly rewritten as follows:

FBG ∆ λFBG res = λres (1 − ρα ) ∆ = SFBG ∆ where the term

∆ λFBG res

is the shift of the Bragg resonance wavelength,

the photoelastic coecient of the ber, strain over the ber, while the term

(5.2)

ρα

is

∆ is the variation of the applied axial

S FBG

represents the linear coecient of


142

the strain sensitivity about the FBG. Writing equation (5.2), we have assumed an isotropic and homogeneous strain [1].

Moreover, equation (5.2) can be

simplied to its more common form given by:

∆ λFBG res = (1 − ρ ) ∆ ∼ 0.78 ∆ = α λFBG res For the sake of completeness, the photoelastic coecient of the ber

(5.3)

ρα

can

be expressed by means of the following equation:

ne ρα = core 2 where the term

$

2 h i ρ12 − $ (ρ11 + ρ12 )

is the Poisson ratio and

ρij

(5.4)

are the Pockel's coecients of

the ber. Typical values for the FBGs sensitivity to an applied axial strain are gathered in table 5.1 [3].

It was proved that the strain response is linear with

Table 5.1: Comparison between the experimental data on FBG strain sensitivity at dierent wavelengths.

Resonance wavelength

λFBG res (nm) 820

Strain sensitivity

SFBG −1 ) (pm µ 0.64

1300

1

1550

1.2

no evidence of hysteresis at temperatures as high as 370 [1]. It is worthy of noticing that the value of the strain sensitivity coecient of FBGs

SFBG

depends on the value of both the FBG resonance wavelength and the photoelastic coecient of the used optical ber. The latter depends, in turn, on the material structure of the ber itself. Anyway, the slope of the strain response of a FBG will be always positive because the same counter-propagating core mode is coupled.


143

Figure 5.1: Typical FBG characterization in axial strain of a standard Corning SMF-28 optical ber

An example of the typical FBG characterization in strain sensitivity is shown in gure 5.1.

The used ber is a standard Corning SMF-28 optical

ber. The circles in the gure represent the experimental points at dierent values of applied axial strain, which induce a shift of the FBG resonance wavelength at longer wavelengths. As it can be observed from the gure, the best tting curve of the experimental points is a linear trend characterized by a slope value of about 1 pm

µ−1 ,

which represents the value of the FBG

strain sensitivity coecient.

Temperature sensor Starting from the dierentiation of the Bragg resonance wavelength in equation (2.7) with respect to the temperature following expression:

T,

λFBG res

it can be obtained the


144

e d λFBG res = 2 Λ d ncore + ne d Λ core d T dT dT

(5.5)

d ne core takes into account the eect of material dispersion of dT dΛ the ber core, whereas the term d T takes into account the eect of change where the term

in grating periodicity due to a temperature variation along the ber.

The

rst term in equation (5.5) is better known in the literature as thermo-optic coecient of the ber core, whereas the second term as thermal expansion coecient of the ber. By considering a limited range of temperature (from 10 to about 150 ), equation (5.5) can be linearly rewritten as follows:

FBG ∆ λFBG res = λres (α + ξ) ∆ T = STFBG ∆ T where the term

α

∆ λFBG res

is still the shift of the Bragg resonance wavelength,

is the thermal expansion coecient of the ber,

ecient of the ber core, ber, while the term

(5.6)

STFBG

∆T

ξ

is the thermo-optic co-

is the variation of the temperature along the

represents the linear coecient of the temperature

sensitivity about the FBG. It was proved [1] that the temperature sensitivity of a bare optical ber is primarily due to the thermo-optic eect. Therefore, equation (5.6) can be simplied to the following form given by:

∆ λFBG res = (α + ξ) ∆ T ∼ 6.7 × 10−6 ∆ T = λFBG res

(5.7)

Typical values for the FBGs sensitivity to a temperature variation up to 85

are gathered in table 5.2 [3].

It was proved that the temperature

response is linear with no evidence of hysteresis, as occurs in the case of the above-described strain response. It is worthy of noticing that the value of the temperature sensitivity coecient of FBGs

STFBG

depends on the value of the

FBG resonance wavelength and as well as on the value of both the thermal expansion and thermo-optic coecients of the used optical ber. The latter two depend, in turn, on the material composition of the ber itself. Anyway, the slope of the temperature response of a FBG will be always positive because the same counter-propagating core mode is coupled, as occurs in the case of strain response.


145

Table 5.2: Comparison between the experimental data on FBG temperature sensitivity at dierent wavelengths.

Resonance wavelength

λFBG res (nm) 820

Temperature sensitivity

STFBG −1 ) (pm 6.8

1300

10

1550

13

A typical value for the temperature sensitivity coecient of FBGs at 1550 nm is 0.01 nm

−1 .

At temperatures higher than 150 , the sensitivity in-

creases and the response becomes slightly nonlinear [1]. If the ber is jacketed or embedded in another substance then the sensitivity changes due to the thermo-optic eect of the substance itself. In fact, this allows one to eliminate or, in any case, to greatly reduce the temperature sensitivity of the grating by means of the proper choice of the surrounding material.

This is clearly

desirable in special applications, such as if the grating has to be used as a lter or for wavelength control and stabilization of a semiconductor laser. An example of the typical FBG characterization in temperature sensitivity is shown in gure 5.2. The used ber is still a standard Corning SMF-28 optical ber. The circles in the gure represent the experimental points at dierent values of applied temperature, which induce a shift of the FBG resonance wavelength at longer wavelengths. As it can be observed from the gure, the best tting curve of the experimental points is still a linear trend characterized by a slope value of about 10 pm

−1 ,

which represents the value of the FBG

temperature sensitivity coecient. Fiber Bragg gratings are also sensitive to changes in both the pressure and dynamic magnetic eld.

Both of sensor elds will not be discussed in

this thesis because it goes out the aim of the work, even if the use of FBG as pressure sensor has been reported in the past literature. In fact, a FBG sensor is also used to measure pressure changes and to detect acoustic signals. However, the sensitivity is far less because the glass ber is very sti. Some


146

Figure 5.2: Typical FBG characterization in temperature of a standard Corning SMF-28 optical ber

enhancements are possible by using a thick, low bulk modulus jacket, but the intrinsic response is still quite small. It was demonstrated that large changes in pressure are detectable with simple readout systems, but however complicated interferometric systems are required to use the FBG device to detect sound elds and other low-level transverse strains. However, a clear description of FBGs used as both pressure and dynamic magnetic eld sensor is reported in references [1, 3].

5.1.2 Long period gratings pGs are characterized by mode coupling between the propagating core

L

mode and co-propagating cladding modes, which gives rise to a series of

loss peaks, or rather attenuation bands in the ber transmission spectrum centered at the wavelengths (resonances) that verify the phase-matching con-


147

dition of each coupled cladding mode. The exact shape of the spectrum and the resonance wavelengths of the attenuation bands are sensitive to the grating period

Λ,

L

to the grating length

the temperature

T,

axial strain

,

ber bending

of the medium surrounding the ber eters modify the period of the LPG and cladding modes

e ne core − nclad (p)

and to the local environment, such as

nsur [16]. Λ and/or

R

and the refractive index

Any changes in these paramthe dierential RI of the core

according to the LPG characteristic equa-

tion (2.9). This modies the PMCs for coupling to the cladding modes and causes a change in the resonance wavelengths of the attenuation bands, which can be measured by means of an optical spectrum analyzer. In next subsections, it will be shown as the sensitivity to a particular measurand is dependent upon the material composition of the used optical ber and upon the order

p

of the cladding mode to which the guided optical power is coupled. Moreover, it will also be discussed as the sensitivity to a particular measurand is thus dierent for each cladding mode and hence for each attenuation band.

All

these reasons make LPGs particularly attractive for sensor applications, with the prospect of using for both single-parameter sensing and multi-parameter sensing by means of a single sensor element [14]. As above-mentioned, LPGs are also sensitive to the bending of the optical ber. This sensitivity characteristic of LPGs will not be taken into account in this work because the ber bending can be avoided by xing the portion of the ber where the grating (or more than one) has been previously written. By the way, this sensitivity characteristic of LPGs has been widely studied in the past not only for sensing purposes, but also in the case of non-UV manufacturing techniques of LPGs, especially in the case of LPGs fabricated by means of electric arc (see subsection 4.3.2). In fact, it has been mentioned that a great sensitivity to ber bending can be achieved for LPGs manufactured by means of non-UV methods due to the coupling to antisymmetric cladding modes [11]. In the rst subsection 5.1.2 of this section, it will be presented a general formulation for studying the sensitivity characteristics of LPGs, which is based on a general sensitivity factor (γ e) and specic sensitivity factors (Γ ,

Γsri )

ΓT

and

for each of the three sensitivity parameters of interest. This attractive

and fascinating theory was developed in 2002 by Shu et al [92] and represents still now one of the most used way for describing the dierent sensitivities of


148

LPGs by means of general analytic expressions. As for FBGs, the rst studied optical ber sensor technologies based on LPGs are undoubtedly those that concern strain and temperature sensors. However, during the last decade especially, LPGs have been reported many times as surrounding refractive index (SRI) sensor.

In fact, it was demon-

strated that they showed great SRI sensitivity [27]. In subsection 5.1.2 the sensing principle about the strain sensor based on LPGs will be discussed, whereas in subsection 5.1.2 the sensing principle about the temperature sensor based on LPGs will be faced.

The last subsection 5.1.2 will provide a

comprehensive description about the LPGs response to changes in the refractive index of the medium surrounding the ber.

The analysis will include

not only the case where the surrounding refractive index is lower than that of the ber cladding, but also the one that is greater than the RI of the ber cladding. This is because the developed optical ber sensor is based on these three sensitivity characteristics of both FBG and LPG and, in particular, on the SRI sensitivity characteristic of LPG.

General sensitivity factor of LPGs One of the most interesting way to study the sensitivity characteristics of LPGs is unquestionably that was developed by Shu el al [92].

The authors

presented a detailed investigation into the LPGs sensitivity as a function of temperature, axial strain and surrounding refractive index (SRI), with particular attention to the higher order cladding modes. In fact, following a general theoretical analysis, they identied a general sensitivity factor together with a set of measurand-specic sensitivity factors, which oered a new physical insight into LPGs behavior and turned out to be a useful design tool. Moreover, they demonstrated that some higher order cladding mode showed greater sensitivity than all the others, because of the existence of turn around points (TAPs) in the mode dispersion characteristics (see gures 3.9, 3.10, 3.11) at which ultrasensitive operation can be achieved.

This subsection provides a

brief description of the present method. As done above in the case of FBGs, starting from the LPG characteristic equation (2.9), it is possible to derive the analytic expressions for the strain sensitivity

d λLPG res (p) /d ,

the temperature sensitivity

d λLPG res (p) /d T

and SRI

5.1. Theory of optical ber gratings for physical sensing sensitivity

d λLPG res (p) /d nsur

of the resonance wavelength as

d λLPG res (p) d d λLPG res (p) dT

γ e α + Γ = λLPG res (p)

(5.8)

e 1 + ΓT = λLPG res (p) γ

(5.9)

d λLPG res (p) d nsur where

α

149

e Γsri = λLPG res (p) γ

(5.10)

is still the thermal expansion coecient of the optical ber,

γ e

is the

general sensitivity factor, which describes the waveguide dispersion, and is dened by the following expression [91]:

d λLPG res (p) γ e = e d Λe ncore − nclad (p) The terms

Γ , ΓT

and

Γsri

(5.11)

are the measurand-specic sensitivity factors, which

describe the axial strain, temperature and surrounding RI dependences, respectively, of the waveguide dispersion and are dened by the following expressions [92]:

Γ =

e ρα,core ne core − ρα,clad nclad (p)

(5.12)


ΓT =

e ξcore ne core − ξclad nclad (p)

(5.13)


3 u2p nsur λLPG res (p) Γsri = − 3/2 e 2 2 8 π a3clad nclad ne − n n − n core sur clad clad (p) where

ρα,core , ρα,clad

and

ξcore , ξclad

are the photoelastic and thermo-optic

aclad zero−th

coecients of the core and cladding materials, respectively, of the ber cladding and

up

is the

(5.14)

p−th

root of the

is the radius order Bessel


150

function of the rst kind

J0 (up ) = 0

J0 ,

that is to say, the values at which the condition

is satised.

It is worthy of observing that the factor

γ e

is related to the LPGs sensi-

tivity to all the types of external perturbation including temperature, strain and surrounding refractive index. Thus the term

γ e

was rightly known as the

general sensitivity factor. Furthermore, broadly speaking, each sensitivity to a particular measurand for both the gratings can be divided into two dierent contributions:

the former is known as material dispersion, while the latter

is known as waveguide dispersion which takes also into account the phasematching curve of the ber

d λLPG res (p) /d Λ.

The next step consists of calculating the relationship between

Λ

λLPG res (p)

and

for all the cladding modes, namely, the phase-matching curve of the used

optical ber. An example is shown in gures 3.9, 3.10, 3.11. Having said that, the general sensitivity factor

γ e=

γ e

can also be expressed as

e ne ∆ ne core − nclad (p) = ∆ ng ngcore − ngclad (p)

(5.15)

∆ne is the dierence in eective refractive index between the core mode g the p−th cladding mode, whereas ∆ n is the corresponding dierence in

where and

group refractive index. By dening the group RI of the core mode as

LPG ngcore = ne core − λres (p) whereas the group RI of the

p−th

d ne core d λLPG res (p)

λLPG res (p) . (from

∆ ng

d ne clad (p)

1 to

p=

d λLPG res (p)

! (5.17)

as a function of the resonance wavelength

Figure 5.3 shows the plots of

p=

(5.16)

cladding mode as

LPG ngclad (p) = ne clad (p) − λres (p) it is possible to plot the curve

!

∆ ng

for the rst 30 cladding modes

59). From the gure 5.3, it can be observed that, in the

∆ng is always positive always negative for the p =

considered wavelength range (from 800 nm to 2000 nm),

p=1 p = 59

p=

for the

to

13 cladding modes, and is

45 to

cladding modes. This is in agreement with the corresponding


151

Figure 5.3: Dierence in group RI between the fundamental core mode and

p =

each of the rst 30 cladding modes (from

1 to

p =

59, only a few are

numbered) as a function of LPG resonance wavelength, calculated for BGe

∆ng = 0 |e γ| > 5

co-doped optical ber. The intersection points of the curves with the axis correspond to the turn around points. In the shaded region,

signs of the slopes of the phase-matching curves shown in gures 3.9, 3.10, 3.11. Because

∆ ne

is always positive, the sign of the sensitivity factor

determined by that of the

∆ ng = 0

∆ ng

∆ ng .

The regions of

is

γ e > 0 and γ e < 0, above and below

line, are depicted in gure 5.3 as well. The intersections of the

curves for each cladding mode with the

where

γ e

|e γ| → ∞

∆ ng = 0

line dene the points

and hence correspond to the turn around points depicted as

circles in gures 3.9, 3.10, 3.11. The shaded area shown in gure 5.3 represents the high sensitivity region in which

|e γ | > 5.

Looking at equations (5.12), (5.13) and (5.14), it is clear that greater is the value of the sensitivity factor

γ e

and greater is the value of the sensitivity

to the measurand of interest. Shu et al [92] showed that the greatest values of the sensitivity factor was achieved for the

p=

19 to

p=

25 cladding modes

(shaded area in gure 5.3) at dierent wavelengths ranging from 1450 nm


152

to 1650 nm.

Moreover, equations (5.12) to (5.14) allow us to separate the

sensitivity of a LPG to any measurand of interest into a general factor (γ e) and a measurand-specic factor (Γ) that reects the inuence of the measurand on the dispersion of the LPG. The strain sensitivity factor

Γ

is determined by the photoelastic coe-

cients of the core and cladding materials and by the mode order proved [92] that the magnitude of with

ρα,clad

Γ

p.

It was

decreases with increasing mode order,

held constant at a value of -0.22 for pure fused silica cladding.

dλLPG res (p) /d is determined by Γ > −1 sign of γ e. Finally, following this anal-

However, the sign of the strain sensitivity or

Γ < −1

(see [92]), as well as by the

ysis, Shu et al demonstrated that, to produce strain-insensitive LPGs, the condition to be satised was

Γ = −1.

This is usually possible for only one

mode, which changes depending on the material composition of the optical ber. The temperature sensitivity factor

ΓT

is determined by the thermo-optic

coecients of the core and cladding materials and by the mode order a given value of

ξcore

and by holding constant

for pure fused silica, the absolute value of order because

∆ ne

observed that

ΓT

ΓT

ξclad

For

at a value of 7.8 x 10

−6

decreases with increasing mode

is larger for higher order cladding modes.

It was also

increases with increasing dierence between the thermo-

optic coecients of the core and cladding materials. The sign of either positive or negative, as determined by

e ξcore ne core < ξclad nclad (p) . co-doped bers,

p.

ΓT < 0,

ΓT

can be

e ξcore ne core > ξclad nclad (p)

For standard bers,

ΓT > 0,

or

whereas for BGe

because boron doping decreases signicantly the

thermo-optic coecient of the core [92]. Thus, it was proved that the thermal responses of LPGs produced in these two dierent optical bers exhibit opposite trends. Broadly speaking, for pure fused silica optical bers, with

α=

4.1 x 10

−7

−1 .

α 100 µm,

the


156

material dispersion contribution is negative, whereas the waveguide dispersion contribution is positive.

For LPGs with grating periodicity

Λ < 100 µm,

both the contributions to the strain sensitivity are negative. In fact, a LPG with grating period of 40

µ−1 [16].

µm

exhibited a larger strain sensitivity of -2.2 pm

Broadly speaking, appropriate choice of grating period and material

composition of the optical ber will thus allow the generation of attenuation bands with positive, negative or zero sensitivity to axial strain. Besides the magnitude and the slope of LPG attenuation bands may be dierent if a BGe co-doped optical bers were used due to a dierent material dispersion contribution of the ber core.

Temperature sensor The origin of the temperature sensitivity may be understood by dierentiating the LPG resonance wavelength to the temperature

d λLPG res (p) dT where

L

λLPG res (p)

in equation (2.9) with respect

T:

d λLPG res (p) = d δ ne (p)

d ne d ne clad (p) core − dT dT

!

d λLPG res (p) 1 d L + Λ dΛ L dT

(5.22)

is the grating length. The rst term on the right-hand side of equa-

tion (5.22) is the material dispersion contribution and is related to the change in the dierential ERI of the core and cladding. This is related, in turn, to the thermo-optic eect.

The material dispersion contribution is dependent

upon the composition of the optical ber and is strongly dependent upon the order

p

of the coupled cladding mode.

Bhatia et al [128] showed that, for

coupling to low−order cladding modes (p

= 1, 3, ...19),

accessed using longer

grating periods (Λ

> 100 µm), the eect of the material dispersion dominates. For coupling to very−high−order cladding modes (p = 41, 43, ...59), accessed using shorter grating periods (Λ < 100 µm), the eect of the material dispersion for standard germanosilicate optical bers can be negligible. The second term is the waveguide dispersion contribution as it results from changes in the grating period. This is related, in turn, to both the thermal expansion eect of the ber and the local slope of the phase-matching curve

d λLPG res (p) /d Λ

for

a particular cladding mode. The magnitude and sign of the second term still

5.1. Theory of optical ber gratings for physical sensing depend upon the order

p

157

of the coupled cladding mode.

Bhatia et al [128]

showed again that, for coupling to low−order cladding modes (p the local slope of the phase-matching curve the very−high−order cladding modes (p


= 41, 43, ...59),

= 1, 3, ...19),

is positive, while for

this term is negative,

as can be seen from the graphs in gures 3.9, 3.10 and 3.11. By considering again a limited range of temperature (from 20 to about 160 ), equation (5.22) can be linearly rewritten as follows:

LPG ∆ λLPG res (p) = ST (p) ∆ T where the term

∆ λLPG res (p)

(5.23)

is the shift of the LPG resonance wavelength of the

p−th coupled cladding mode, ∆T is the variation of the temperature along the LPG ber and S T (p) represents the linear coecient of the temperature sensitivity about the LPG in which the guided core mode coupled to the p−th coupled cladding mode. Looking at equation (5.22), the shift of the resonance wavelength due to the material dispersion eect can have either polarity and its magnitude is a function of the dierential change between the eective indices of the guided core and cladding modes. For LPGs with periodicity of magnitude of hundreds of micrometers, the material dispersion eect typically dominates the waveguide dispersion contribution to the temperature-induced shift. The strong dependence of the material dispersion eect on the order

p

of the coupled cladding

modes results in distinct shifts of each attenuation band of LPGs. Moreover, since the period of the grating

Λ

dictates the order

p

of the coupled cladding

mode, the temperature sensitivity of each attenuation band for a given optical ber can vary considerably with the grating periodicity.

Figure 5.5 depicts

the shift of the resonance wavelength of four attenuation bands (from curve A to curve D) as a function of the temperature for the same LPG (Λ

µm)

=

280

used in strain characterization [14]. The depicted spectra correspond to

temperatures of 22.7, 49.1, 74.0, 100.9, 127.3 and 149.7. The distinct spectral displacement of the four bands is clearly visible. The shift of the attenuation band related to curve A (higher order cladding mode, 1608.6 nm at 31.2 ) is about 11.8 nm from 22.7 to 149.7 . A linear t to the shift data of the resonance wavelength yields a slope of about 93 pm

−1

and that

is almost an order of magnitude higher than that observed in a ber Bragg

158


Figure 5.5: Shift in the resonance wavelengths of four attenuation bands, A−D, as a function of temperature for a LPG. The dashed line is the temperature-induced wavelength shift for a FBG fabricated at 1550 nm for comparison [14]

grating. For a complete comparison, gure 5.5 shows also the temperatureinduced shift of the resonance wavelength for a FBG at 1550 nm (curve E), which is characterized by a linear t of about 13 pm

−1 .

It is easy to ob-

serve that a FBG is less temperature sensitive than a LPG. Moreover, the non-linearity in the shift of the resonance wavelength for the LPG bands can be attributed primarily to the temperature dependence of the thermo-optic coecients of the core and the cladding. For this particular grating, the sen-


159

sitivity to temperature increases with the order of the cladding mode due to the dierent material dispersion contributions for distinct cladding modes. In general, LPGs fabricated in standard SMF-28 optical bers exhibit temperature sensitivities ranging from 30 pm

−1

to 100 pm

−1

[14].

On the

contrary, LPGs fabricated in photosensitive optical bers exhibit greater temperature sensitivities than that of fabricated in standard SMF-28 optical bers (see part II). As an example, LPGs manufactured in photosensitive B-Ge codoped optical bers have been shown to oer sensitivities of up to 2.75 nm

−1

[129].

Thus, the LPG temperature sensitivity is at least an order of

magnitude larger than the FBG temperature sensitivity. For the sake of completeness, other techniques for enhancing the temperature sensitivity (ie 19 nm

−1 )

have been reported based upon surrounding

the optical ber by a material of large thermo-optic coecient, resulting in the LPG responding to both the changes in temperature and the temperatureinduced RI change of the surrounding medium [15, 130]. Alternatively, recoating an optical ber characterized by a negative thermal expansion coecient, with a material with a positive thermo-optic coecient has been shown to permit the temperature sensitivity to be reduced up to 0.7 pm

−1

[131].

It is worthy of highlighting that, by an appropriate choice of the grating period, it is possible to balance the two dispersion contributions to the temperature sensitivity in order to obtain both a temperature-insensitive attenuation band and also attenuation bands with temperature sensitivities (positive or negative) appropriate to specic applications. Moreover, by altering the material composition of the optical ber, such that the thermo-optic coecient of the core is either large or smaller than that of the cladding, it allows us to obtain a required temperature sensitivity [97]. Therefore, the magnitude and the slope of LPG attenuation bands may be dierent if a B-Ge co-doped optical bers were used due to both a dierent material dispersion contribution of the ber core and a dierent thermal expansion eect of the ber itself.

Surrounding refractive index sensor As discussed previously, it is worthy of remembering that the sensitivity of LPGs to environmental parameters is inuenced by the period of the grating

Λ,

by the order

p

of the cladding mode to which the coupling takes place and


160

by the material composition of the optical ber.

Having said that, the last

found sensitivity characteristic of LPGs, which is also the most interesting one because of the many applications developed in dierent eld later (see section 5.2), is their sensitivity to the refractive index of the medium surrounding the ber cladding (nsur ) in the grating region. This arises from the dependence of the resonance wavelengths of each attenuation band on the effective refractive index (ERI) of the cladding modes, which depends, in turn, on the refractive index (RI) of the medium surrounding the ber cladding (see equation (3.61)) [27].

This is the physical principle that allows us to

use LPGs as RI sensors based on the change in resonance wavelength and/or transmission of the LPG loss peaks. By considering the LPG characteristic equation (3.61) and by assuming that both the grating period

ne core nsur ,

Λ

and the eective RI of the guided core mode

remain unchanged under the eect of a change in the surrounding RI the inuence of variation in the surrounding refractive index around the

ber cladding of a LPG can be mathematically expressed by means of the following nonlinear function

f (nsur )

[14, 26, 42]:

e d n λ, n , n d λLPG sur clad clad (p) res (p) f (nsur ) = = d nsur d nsur e d nclad (p) λ, nclad , nsur d λLPG res (p)

where

ne clad (p)

(5.24) is the eective RI of the

depends on the working wavelength on the cladding RI

nclad

cladding mode, which in turn

(material and waveguide dispersion),

and, as mentioned above, on the RI of the medium

surrounding the ber cladding

d ne clad (p) /d nsur

λ

p−th

nsur .

It is worthy of noticing that the term

is dierent for each cladding

p−mode

and hence the spectral

response of a long period grating depends strongly on the order

p of the coupled

cladding mode. It is important to observe that the shift in the LPG resonance wavelength may be positive or negative for a given optical ber and cladding mode, depending on the local slope of the characteristic phase-matching curve


[14].

Everything has just been said can be observed in gure 5.6. In fact, gure 5.6 shows the shifts of the resonance wavelength in four attenuation bands for a long period grating written in a standard Corning SMF-28 optical ber


161

Figure 5.6: Experimental shift of the resonance wavelength in four attenuation bands (from curve A to curve D) of a long period grating as a function of the surrounding refractive index [14]

and characterized by a grating period of 320

µm.

The lled black points are

the experimental data related to four dierent attenuation bands and hence to four dierent cladding modes. The values of the resonance wavelength of each cladding mode are 1496.6 nm (curve A), 1329.3 nm (curve B), 1243.8 nm (curve C) and 1192.1 nm (curve D), respectively. These values were measured by placing the optical ber in air, namely, when

nsur =

1 RIU. The shifts of

each resonance wavelength were also measured with respect to the locations at

nsur =

1 RIU (air). Looking at gure 5.6 it is clear that, for this particular

grating, the shift of the resonance wavelength is negative for all bands and increases with the order of the coupled cladding mode from curve D (lower


162

order cladding mode) to curve A (higher order cladding mode). It is worthy of highlighting that the largest shifts of the resonance wavelength of about

−66.9

nm (curve A) were measured for the attenuation band related to the

higher order cladding mode, as expected from the literature [27]. Anyway, the sensitivity to changes in external RI can be enhanced or reduced by manipulating the parameters of the used optical ber and by choosing the suitable grating period for coupling to specic cladding modes [14].

Patrick et al [27] found experimentally that the longest resonance wavelength, or equally the highest order attenuation bands were most sensitive to

nsur

λLPG res (p) cladding nclad .

and the largest variations of

refractive index of the ber

were seen as

nsur

approached the

The shift of the resonance wave-

length occurs because increasing the surrounding RI increases the eective RI of the coupled cladding mode as well, particularly for the higher order cladding modes which extend further into the medium surrounding the ber [17]. The sensitivity to surrounding refractive index manifests itself as a change in the value of both the resonance wavelength (see gure 5.7(a)) and the minimum transmission (see gure 5.7(b)) of the attenuation band related to the coupled cladding mode.

The gure 5.7 shows the shift of the resonance wavelength

(a) and the minimum transmission value of the attenuation band (b) related to the same coupled cladding mode as a function of the refractive index of the medium surrounding the LPG. The LPG is characterized by a grating period of 400

µm

and is written in a B-Ge co-doped optical ber with a cut-o

wavelength of 650 nm [15].

As can be seen from the same gure 5.7, when

the surrounding RI changes from

nsur =

1 RIU (air) to

nsur =

1.44 RIU,

this is a total internal reection (TIR) condition, which is best dealt with using the coupled mode theory based on a three-layer geometric model of the ber [81, 86].

Therefore, the principal eect is a blueshift (shift to shorter

wavelengths) of the resonance wavelength of the attenuation band related to the coupled cladding mode, which is particularly pronounced in the longest attenuation bands, as discussed above (see gure 5.6). In the same RI range, the minimum transmission value remains practically unchanged, or rather changes about a few dB. Between

nsur =

1.45 RIU and

nsur =

1.46 RIU, an abrupt

change in the spectral characteristics is observed, which is associated with the maximum RI sensitivity (the maximum slope of the curve in gure 5.7(a)).


163

Figure 5.7: Plot of the shift of the resonance wavelength (a) and the minimum transmission value of the related attenuation band (b) as a function of the refractive index of the medium surrounding a long period grating with a period 400

µm

written in a borongermanium co-doped optical ber [15]


164

Now, the cladding modes would be expected to no longer be discrete guided modes and, as seen, the attenuation bands in the transmission spectrum spread and the couplings nearly disappear. In fact, when

nsur = nclad ,

the cladding

appears to be of innite extent and thus supports no discrete modes.

This

means that the cladding modes are converted to radiation modes [132].

A

few dB of broadband radiation-mode coupling losses are then observed, but no distinct attenuation bands. In this RI range, the observed changes in the minimum transmission value are due to the expansion of the cladding modes as the guiding of the optical ber decreases, decreasing the coupling coecients between the core mode and cladding modes until the guiding around

nsur =

1.46 RIU is almost nonexistent (attenuation bands nearly disappear).

Finally, for

nsur > 1.46 RIU or rather when the surrounding refractive index is

higher than that of the cladding, the resonance wavelengths of the attenuation bands show a considerably reduced sensitivity (a minimum slope of the curve in gure 5.7(a)) [27, 41], but a change in the form of the transmission spectrum is observed, namely, the extinction of the attenuation bands is reduced. The reappearance of discrete attenuation bands was explained by means of the socalled

leaky modes , which exist in waveguides with an inverted RI prole.

In

fact, as the surrounding RI increases this leaky modes are better conned, increasing both the coupling coecients between the core mode and these leaky modes and the minimum transmission value [100]. From a physical point of view, the presence of attenuation bands in this situation, where the cladding is no longer acting as a guiding element, is related to the existence of attenuated cladding modes (ie leaky modes) arising from Fresnel reection, rather than the total internal reection at the cladding/surrounding interface [16].

For the sake of clarify, the last case, or rather when

nsur > nclad ,

was

comprehensively discussed by Hou et al [133]. The authors bore out that the analysis of SRI sensitivity of LPGs must be eectively performed by means

nsur < nclad , as widely explained in chapter 3. case where nsur > nclad , the authors showed that

of a three-layer model while On the other hand, for the

the two-layer model was used to calculate the cladding modes, which provided reasonably accurate values. In fact, the two-layer model basically treats the ber cladding and core as one multimode optical ber and the surrounding environment as the new cladding only in the grating region of LPG. In this

5.2. Applications of optical ber gratings for physical sensing

165

case, the cladding modes no longer experienced the TIR condition and were referred to as leaky modes.

Thus, the problem has to be treated as a two-

layer model in order to accurately calculate the cladding modes.

Anyway,

looking at gure 5.7(a), the resonance wavelength experiences a measurable shift of a few nm, which suggested that LPGs coated with a material of higher refractive index than that of the ber cladding may be used as refractive index sensors [133]. The use of coated OFGs will be discussed in section 5.3. The refractive index sensitivity of LPGs has been extensively studied in the literature to develop refractive index sensors, such as chemical concentration sensors [28, 29, 50], liquid level sensor [134].

More recently, LPGs have

been proposed as a new technological platform in the eld of biochemical sensing [40, 65]. To use LPGs as biosensors, LPGs have to be coated with selective layers and hence the analysis given in this section must be reviewed. This will be discussed in section 5.3. On the contrary, LPGs have also been fabricated in optical bers with complex structures in order to desensitize the LPG spectrum to the surrounding refractive index. As an example, LPGs fabricated in dual shaped core (DSC) dispersion-shifted optical ber exhibited an attenuation band that was insensitive to external refractive index and to mechanical damage of the ber surface [135]. The DSC bers contain an inner cladding region that has a higher refractive index than the outer cladding layer. The refractive-index-insensitive attenuation band was believed by the authors to correspond to coupling to a mode of this inner cladding.

5.2 Applications of optical ber gratings for physical sensing ptical ber gratings can oer some advantages compared with the use

O

of other technology platforms thanks to the typical properties of optical

bers such as compactness and light weight and, from a technological point of view, the fact that they are highly compatible with optoelectronic components/devices used for standard and photosensitive optical bers, since the working wavelengths generally correspond to the telecommunication windows around 1300 nm and 1500 nm. Moreover, the literature about FBGs showed that they can be also used to study the dispersive phenomena, in particular


166

for applications such as dispersion compensation, pulse shaping and for all the other applications which make use of ber and semiconductor laser components [76, 136].

In the case of LPGs, the dispersion is more of a concern

mainly because these have a broader bandwidths than FBGs even in absence of dispersion [76], but other interesting applications about LPGs can be found in this reference [136]. Broadly speaking, FBGs and LPGs are used in both the eld of telecommunications and the eld of sensors. Some examples using FBGs and LPGs are presented in subsection 5.2.1 and 5.2.2, respectively.

5.2.1 Fiber Bragg gratings FBGs have rstly be used in the eld of telecommunications and later in the eld of sensors. An excellent overview can be found in [1]. In fact, Hill and Meltz gathered in two tables of all the FBG applications. The rst table collected the most interesting applications of FBGs in the telecommunications area, whereas the second table in the area of other applications. The rst application in the eld of telecommunications was found by Hill et al [137] and regards the use of FBGs as optical lters. Due to the spectral characteristics of FBGs, they were used as narrow-bandwidth optical waveguide transmission lters.

Another typical telecommunications application regards their use as

optical add/drop multiplexer [138].

Figure 5.8 depicts the mechanism of

Figure 5.8: Schematic of an optical add/drop multiplexer based on a ber Bragg grating an optical add/drop multiplexer based on a ber Bragg grating. The optical


167

add/drop multiplexer expression refers to the specic characteristics of the multiplexing about the SDH/SONET network, which allow one to draw or enter directly a single data ow without having to demultiplexing the entire aggregate ow. In fact, looking at gure 5.8, the selected (added or dropped) data ow (red) is that is characterized by the same wavelength than that of the schematized FBG. Another classical application regards the use of FBGS as wavelength selective devices. An example is their use as wavelength division multiplexing [139]. Figure 5.9 depicts the mechanism of an optical wavelength

Figure 5.9: Schematic of an optical wavelength division multiplexing system based on a ber Bragg grating

division multiplexing system based on a ber Bragg grating. Within an optical ber network, the FBG can be used as a system to multiplex the data in transmission and to demultiplex the data in reception based on a division in wavelength.

One of the most interesting application about the FBGs in

the eld of telecommunications was undoubtedly that regards their use as dispersion compensation [140, 141, 141].

Figure 5.10 depicts the mechanism

of an optical dispersion compensation system based on a chirped ber Bragg grating (see gure 4.3). The eect of dispersion in optical bers belongs two

168


distinct temporal signal to each other. Therefore, the use of a chirped FBG allows the two signal to place at a certain distance. From a spectral point of view, there is obviously a spread of the FBG reection spectrum. In fact, the

Figure 5.10: Schematic of an optical dispersion compensation system based on a chirped ber Bragg grating

change in the grating period means that dierent wavelengths are reected in dierent places and at dierent times. In this way the eect of dispersion due to the optical ber can be strongly reduced. Other applications concern their use together with ber and semiconductor laser components, for example as pulse shaping [136] and also as cascaded Raman amplication at 1.3

µm [142].

Among the above-mentioned area of other applications, Hill and Meltz [1] talk about the use of FBGs as optical ber mode converters [143], for studying the nonlinear eects [82] and, nally, as grating-based sensors.

Optical ber sensor technology based on ber Bragg gratings has uses in a number of important application areas, ranging from structural monitoring to chemical sensing [127]. As discussed widely, any change in ber properties, such as strain, temperature or polarization, which varies the eective RI of the core mode or the grating period, causes an almost linear shift of the Bragg resonance wavelength.

Moreover, the measurand information is wavelength

encoded, thus the sensor response is practically independent from the intensity modulations that can be pertained to the optical source or to the optcial ber. These characteristics made FBGs excellent sensor elements. In addition, optical ber sensors (OFSs) can oer several advantages over the conventional


169

sensors, such as resistance to chemical agents because the glass is an inert material, linear response over several orders of magnitude and very low signal

−1 ). In fact, the optoelectronics control unit can

attenuation (about 0.3 dB km

be placed several tens of km far from the measurement point. Many examples of applications can be found in the literature and hence a complete list and description is out of the aims of the present work, but the most important elds of applications are summarized below:

structural health monitoring in civil engineering (strain, temperature and pressure sensors) [144];

cultural heritage (strain, temperature and pressure sensors) [145];

aerospace applications (strain, temperature and pressure sensors), such as the monitoring of new aerospace materials as reinforced carbon ber composites [146];

marine applications (pressure sensor), such as the monitoring of structures but also as Bragg reetors in distributed Bragg reector (DBR) laser for subsea acoustic sensing [147];

medical applications, such as the remote temperature monitoring in nuclear magnetic resonance (NMR) machines [148];

pipeline monitoring [149];

measurements on moving vehicles, such as aircrafts, trains, etc;

measurements on harsh environments, such as during nuclear fusion processes.

The list could have been very large, considering also that the FBGs can be applied to any kind of transducer, which changes its shape under the eect on a particular physical, chemical or biochemical measurand. Other interesting congurations are based on multiple in-line FBGs, which are able to be use in the eld of multi-parameters sensing. The most used congurations are based on two FBGs written in series within the same optical ber for simultaneous measurement of changes in axial strain and environmental temperature.

170


5.2.2 Long period gratings As in the case of FBGs, even the LPGs were used in the eld of telecommunications at the beginning. The two classical applications regard their use as band-rejection lters [73] and as gain-attening lters for erbium doped ber ampliers [5]. Because the spectrum of LPGs is characterized by a series of attenuation bands centered at discrete wavelengths, these bands can be used as optical wavelength-selective band-rejection lters. The only drawback can be the not-too-small value of bandwidth of the attenuation bands, typically from 10 nm to 20 nm. Thus, these optical lters may not be suciently selective. Moreover, considering both the nonuniform gain prole of the erbium doped ber ampliers (solid curve in gure 5.11) and the opposite trend of the attenuation bands of LPGs around the same wavelength range, Vengsarkar et al [5] wrote an LPG in series with an erbium doped ber amplier.

The total

Figure 5.11: Eect of gain-attening (lled circles) using LPGs on the gain of erbium doped ber ampliers (solid curve) [5] eect is the attening of the gain of the erbium doped ber amplier (lled

5.2. Applications of optical ber gratings for physical sensing circles in gure 5.11).

171

The wavelength division multiplexing channels of an

−1 ) can be accommodated within

optical ber network (each operating at Gb s

the 1530−1560 nm band of an erbium doped ber amplier. But the nonuniform gain proles of erbium doped ber ampliers gave rise to uneven gains in the dierent channels leading to unacceptable bit-error-rate performance. By writing an in-line LPG, this problem was avoided.

Later, the use of LPGs has been extended to the eld of sensors as well. Other than just discussed in section 5.1.2, the refractive index sensitivity of LPGs has been exploited to form other types of physical sensor. LPGs have been proposed to form a ow sensor to monitor the arrival of resin within a liquid composite molding system [150]. The measurement relies upon the reduction in the transmission value of the LPG attenuation band that occurs when the LPG is surrounded by a material of higher refractive index. Another interesting application reported in the literature concerns an LPG−based liquid level sensor [134].

The partial immersion of the LPG within a liquid (see

Figure 5.12: Principle of operation of the liquid level sensor based on an LPG: (a) schematic of the LPG and (b) transmission spectrum of the expected split in the LPG attenuation band [16]

gure 5.12(a)) results in each attenuation band splitting into two. One of the


172

splitted attenuation bands has a resonance wavelength corresponding to coupling to the cladding mode when the optical ber is surrounded by air (band B in the transmission spectrum depicted in gure 5.12(b)), while the other has a resonance wavelength corresponding to coupling to the same cladding mode, but when the optical ber is surrounded by the liquid sample (band A in the transmission spectrum depicted in gure 5.12(b)) characterized by a refractive index higher than the air. As expected from the theory of LPGs, the minimum transmission value of an LPG attenuation band is dependent on the length of the grating according to equation (3.78). So the relative depth of the splitted attenuation bands changes in response to a change in the liquid level.

The authors proved also that the proposed liquid level sensor has a

linear response over 60% of the grating length.

As already mentioned in section 5.1.2, the refractive index sensitivity has also been used to enhance or to reduce the temperature sensitivity of LPGs. Surrounding the LPG by a liquid with a large thermo-optic coecient results in the LPG responding to both changes in temperature and to the temperatureinduced RI change of the surrounding medium [15, 130, 131].

According to

the sign of both the thermo-optic coecient and the thermal expansion of the ber (see equation (5.22)), the total eect can be an increase or a decrease in the temperature sensitivity of LPGs. For example, recoating an LPG with a UV-curable acrylate-based polymer of refractive index approximately equal to that of the ber cladding and with a negative thermo-optic coecient, increased the sensitivity of the LPG fabricated in a conventional dispersionshifted optical ber from 50 pm

−1

to 800 pm

−1

[15].

Using a liquid

crystal material and an air-clad optical ber in which the air regions were lled by the same material, it produces a temperature sensitivity of about 2.1 nm

−1

[130].

Moreover, ultra high sensitivity of up to 19 nm

over a limited temperature range of 1

,

−1 ,

has been obtained by surrounding

the optical ber with a cargille oil of refractive index that was approximately equal to that of the ber cladding [15]. The sensor has be designed to operate at a range of temperatures by choosing an oil whose thermo-optic coecient was such that, at the required operating temperature, the refractive index was approximately equal to that of the ber cladding. On the contrary, for an LPG recoated with a material of positive thermo-optic coecient, a temperature

5.2. Applications of optical ber gratings for physical sensing sensitivity as low as 0.7 pm

−1

173

was obtained [131].

As for the LPG refractive index sensitivity, it can be seen from gure 5.7(a) that the RI sensitivity range of bare LPGs is limited from 1.4 RIU to the RI of the ber cladding. specic.

Moreover, the response of bare LPGs is not species

Nevertheless, it has been shown that bare LPGs may be used for

on-line monitoring of the concentration of aqueous solutions of materials and of materials in harsh environments for industrial production quality control. One of the rst examples of a long period grating applied to chemical sensing was related to the determination of calcium chloride, sodium chloride and ethylene glycol in solution [28]. Concentrations of these solutions have been measured with sensitivities equal to, or better than that of conventional hand-

−4 RIU). Since then, many other OFG

held Abbe refractometers (about 5 x 10

platforms have been described that are based on the measurement of the RI changes within the volume around the optical ber for the measurement of isopropyl alcohol [46] (etched FBG, see section 5.3.1), glycerine [47] (etched FBG, see section 5.3.1), sucrose [49], ethanol and glucose [49], cane sugar [50], antifreeze [27] and chloride ion [51, 52].

Moreover, the use of LPGs to

monitor the rening of kerosene, which requires that the concentration of organic aromatic compounds such as benzene and xylene has to be measured, has been proposed [29]. To demonstrate the feasibility, the concentration of a binary solution of xylene in heptane was measured with a minimum detectable volumetric concentration of about 0.04%, corresponding to a refractive index

−5 [29]. This is comparable to the accuracy of the standard

change of 6 x 10

techniques, such as liquid chromatography and UV spectroscopy. As discussed in chapter 3, the wavelength shift for a particular band of a long period grating due to axial strain or temperature is a strong function of the optical ber parameters and the order of the corresponding cladding mode. The dierential shift in two or more attenuation bands of an LPG can be utilized for multi-parameter sensing [14].

Among these multi-parameter

sensing techniques, the use of two cascaded LPGs, with dierent periods chosen such that one LPG had an attenuation band that was insensitive to temperature changes, while the other one had a band that was insensitive to refractive index variations, has been shown to allow simultaneous, independent measurement of these two parameters [151]. This potentially allows the


174

temperature-independent monitoring of chemical solutions with temperaturedependent refractive indices. Another example concern the use of two dierent attenuation bands of an LPG centered at two dierent wavelengths for simultaneous measurement of axial strain and temperature [44]. By writing a system of two independent equations related to the two dierent attenuation bands and by assuming all the four coecients of axial strain and temperature related again to the two dierent attenuation bands are known, the value of both

∆ and ∆T

can be evaluated. Although this approach is very simple, the

non-linearity in the four coecients requires at-large that they be expanded in higher order terms. Additionally, the cross-sensitivity between strain and temperature causes the linear and higher order coecients related to

∆ to be

functions of temperature [14]. If both the non-linearity and cross-sensitivity are appropriately characterized, a single LPG can be used for simultaneous strain and temperature measurements.

Among the multi-parameter sensing, some example of hybrid grating congurations have been reported in the literature.

Patrick et al [152] pro-

posed a novel sensor, which used the dierence in strain and temperature response of two in-line FBGs and an LPG to discriminate between strain- and temperature-induced shifts of the resonance wavelength. The large dierence in temperature response of the LPG compared to the FBGs made LPG's excellent candidates for dual grating sensors. The sensor conguration presented by the authors uses the advantages of the LPG sensor, while allowing the system interrogation to be performed entirely on the FBG reections. Strain and temperature were simultaneously measured with a root mean square (rms)

±9 µ and of the measured temperature from the applied temperature of ± 1.5 , respectively. deviation of the measured strain from the applied strain of

Jesus et al [43] described a ber optic sensing system for simultaneous measurement of refractive index and temperature, based on a hybrid ber Bragg grating/long period grating arrangement.

The experimental results showed

that the proposed setup had a good performance in terms of linearity and sensitivity, with a maximum sensor resolution for the refractive index of about 2 x

−5 RIU. The sensing conguration has the ability to be read-out in reection

10

and works in the telecommunications window. Moreover, the proposed sensing system has good characteristics for application in salinity measurements or for

5.3. Theory of optical ber gratings for biochemical sensing

175

detection of pollutants and other chemical substance.

5.3 Theory of optical ber gratings for biochemical sensing uch

M

research has gone into the study of antigen detection, drug recog-

nition and the development of antibodies in order to diagnose and treat

harmful illnesses. Previous to the last decade or so, most biological reactions have been monitored predominantly on a chemical basis. The Enzyme-Linked Immuno-Sorbent Assay (ELISA) is a good example.

The assay allows re-

searchers to assess whether or not a reaction is taking place and at which degree. Though the ELISA is a widely used method of antibody-antigen interaction detection, it has the drawbacks of requiring chemical treatment and manipulation of the samples and several time-consuming steps [153]. The expensive and delicate process associated with the labeling of antibodies is a concern. Polystyrene binding capacity and non-specic adsorption eects also oer drawbacks to the ELISA. Optical sensing techniques can be employed to eliminate some of these problems.

For example, optical techniques can

oer real-time results in a short period of time, sometimes eliminating the need for labeled secondary antibodies. Constructing a more desirable means of detection to yield real-time results with a minimum of preparation techniques is the motivation behind attempting to use long period gratings as ber optic biosensors. They oer the possibility to use an optical approach to detect chemical and biochemical species without resorting to luminescenceor absorption-based measurements. This distinctiveness is important and can be essential to measure chemicals and biochemicals which do not have optical properties or which interact selectively with recognition elements without producing uorescence or absorption changes. In bioassays, for example, the most diused optical approach is provided by label-based assay, which exploits the interaction between the analyte under study and a biological recognition element (BRE), labeled with uorescent or chemiluminescent labels. On the other hand, the use of labeled BREs very often implies multistep detection protocols (as in the ELISA tests or in sandwich assays), which can complicate the biochemical interaction and can cause sensor cross-sensitivities. In con-


176

trast, the label-free approach does not have this inconvenience and oers the possibility to measure the interaction between the BRE and the analyte directly and in real time, providing the possibility of also investigating dynamic interactions. In biochemical sensors, the biological recognition element capable to bind with the analyte can be used and, in this case, also high selectivity can be also reached, as in all biosensors, depending on the anity between the BRE and the investigated analyte. In the last years optical ber gratings (OFGs) have been proposed as tools for chemical and biochemical sensing [36] and many examples are described in the literature of the last years. The use of OFGs can oer some advantages compared to other ones thanks to the typical properties of optical bers such as compactness, lightweight and, from a technological point of view, to the fact that they are highly compatible with optoelectronic components/devices used for standard optical bers, since the working wavelengths are generally in correspondence of the telecommunication windows around 1.3

µm.

µm

and 1.5

Moreover, the combination of the use of optical bers with the fact that

the signal modulation is spectrally encoded oers multiplexing and remote measurement capabilities which the other technology platforms are not able to or hardly can oer. Among all the existing technology platforms measuring the RI of a surrounding medium, those based on surface plasmon resonance (SPR) are the most diused ones [32].

Other well-known and fascinating

technology platforms are based on the use of interferometers, implemented both on optical bers and planar waveguides and optical resonators, which in terms of resolution can be comparable with SPR [31]. In recent years, optical ber gratings based on both LPGs and FBGs have been proposed as tools for chemical and biochemical sensing and many examples are described in the recent literature [36, 65]. Subsection 5.3.1 describes the use of FBGs in the eld of biochemical sensing, whereas subsection 5.3.2 of this section talks about the use of LPGs in the same eld.

5.3.1 Fiber Bragg gratings Although ber Bragg gratings are unquestionably an attractive sensing platform, these are limited by either sensitivity to strain and temperature, and they are also characterized by expensive demodulation schemes [14]. This


177

type of grating is useless for the measurement of the surrounding RI (SRI) and hence for the use in the biochemical eld, since the optical radiation is strongly conned within the ber core and only a small amount of the radiation is transferred to the ber cladding and, in any case, never reaches the external environment.

The interaction of the optical radiation, which

travels along the ber core, with the external environment can be achieved by suitable modication of the FBG structure. Therefore, surrounding refractive index sensors using FBGs need either to etch or to taper the ber cladding, or to tilt the grating planes at a certain angle in order to gain access to the evanescent eld of the guided counter-propagating core mode. These two types of modied FBGs, the transmission properties of which are modulated by SRI changes, are illustrated in gure 5.13: the tilted FBG (TFBG) and the etched FBG (EFBG). The red arrows in gure 5.13 show how the interaction with the

Figure 5.13: Basic congurations of modied ber Bragg grating to be used as surrounding refractive index sensor: tilted ber Bragg grating (a) and etched ber Bragg grating (b) [17]

surrounding medium occurs. The graph on the right of each FBG delineates the transmission spectrum in the presence of a broadband source.

The red

178


curves in these graphs provide an indication of the eect of an increase of the SRI in the ber transmission spectrum. Figure 5.13(a) shows the TFBG, where the index modulation pattern is constituted by grating planes tilted by a certain angle

θ

with respect to the ber axis. Typical tilt angles are in

the range from 2° to 20°. Such tilt angles allow the coupling of the light from the fundamental guided core mode to the counter-propagating cladding modes, which are sensitive to changes of the surrounding RI [38]. Figure 5.13(b) shows the EFBG in which a partial etching or tapering of the ber cladding allows the evanescent eld to extend eectively into the surrounding medium [39]. It is clear that the maximum SRI sensitivity of EFBGs can be achieved when the ber cladding is totally etched, that is to say, when the evanescent wave interacts more with the surrounding medium.

It is worthy of noticing that

an SRI increase gives rise to a red shift of the resonance wavelength in both TFBGs and EFBGs, whereas a blue shift of the loss peaks (opposite trend) is observed for LPGs, as exactly expected from the literature. Furthermore, for all modied FBGs, the maximum sensitivity is approached when the SRI is close to that of the ber cladding, as for LPGs.

On the other hand, the

closer is the SRI to the RI of the ber cladding, the less denite is the shape of the attenuation band, with its complete disappearance for

nsur = nclad ,

which

practically corresponds to a cladding with an innite thickness. This attening of the loss peak leads to greater diculty in the evaluation of the resonance wavelength and, consequently, to worse accuracy of the measurement [26]. Finally, it is worthy of highlighting that, among the technological platforms using optical ber gratings, the EFBGs are surely the least promising, since higher sensitivities can be achieved only with larger and larger etching of the ber cladding, which implies a very high fragility of the structure.

5.3.2 Long period gratings Dierent from FBGs, standard bare LPGs can be used for sensing purposes in both the chemical and biochemical eld.

The sensing mechanism relies

upon the measurement of a change of refractive index associated with a chemical/biochemical reaction that takes place over the grating region. Therefore, a direct detection of molecular interactions can be carried out, while avoiding the use of auxiliary chemical components (

label-free approach ).

DeLisa et


179

al [65] rstly demonstrated the feasibility of using LPGs to develop a ber optic biosensor.

By means of a bio−functionalization of the ber portion

in which the grating has been inscribed, with amino, carboxylate or biotin groups, it allows to immobilize antibodies on the ber surface with a covalent bond. This in turn permits to measure the bioreaction between bound antibodies (receptor) and free antigens (ligand) as a change in refractive index that further results in a spectral shift of the LPG resonance wavelengths. The selectivity and RI sensitivity of LPG immunosensors render them ideal tools for use in medical diagnosis, environmental monitoring, bioprocessing and other applications (see section 5.4). It is quite easy to understand that the refractive index value of most chemical/biochemical solutions ranges from 1.33 RIU (refractive index of distilled water) up to about 1.4 RIU. This RI range corresponds to the minimum slope of the RI response curve of LPGs and hence the minimum SRI sensitivity of LPGs, as can be observed in gures 5.6 and 5.7. It was demonstrated that all the attenuation bands within the LPG transmission spectrum exhibit the same shape of the RI response, but the magnitude of the shift of resonance wavelength is dependent on the order

p of the corresponding coupled cladding

mode [27]. Although higher order cladding modes exhibit a greater shift of resonance wavelength than lower order cladding modes, the obtained best RI resolution in the above-mentioned RI range does not reach a value of about

−5 RIU or lower, which is necessary to develop a credible biochemical sensor

10

with performance comparable to other existing techniques (ie surface plasmon resonance). Moreover, LPGs are not chemical/biochemical species-specic and are limited to work with solutions characterized by refractive indices less than or equal to the RI of the ber cladding. Therefore, a new class of OFGs based on coated LPGs has been studied widely. Of more interest was the potential for deposition of overlay materials that exhibited variations of the their refractive index in response to changes in refractive index of the local environment. In this case, the ber cladding of an LPG is coated by a nm-thick thin-lm whose refractive index is higher than that of the cladding glass. It was observed that, for lms of RI higher than that of the cladding glass, the resonance wavelength and transmission value of the attenuation bands exhibited a very high sensitivity to the optical thickness


180

of the deposited overlay, when the thickness of the lms was of the order of a few hundred nanometers [1822, 154, 155]. For materials characterized by a RI lower than that of the cladding glass, the sensitivity to the thickness of the overlay material is considerably reduced [16]. This is quite distinct from the behavior under bulk immersion of solutions in which the highest sensitivity is observed for refractive indices lower than that of the ber cladding, as shown in gure 5.7(a). The illustrative schematic of a thin-lm coated LPG structure is shown in gure 5.14(a).

Figure 5.14(b) depicts the refractive index prole

Figure 5.14: Schematic of a thin-lm coated LPG structure (a) and the corresponding refractive index prole (b) [18]

of the coated LPG structure correspondingly. overlay,

acoat

ncoat

is the RI of the deposited

is the total radius of the coated LPG structure and

nsur

is the

RI of the surrounding medium, depicted in the gure as the RI of the air

5.3. Theory of optical ber gratings for biochemical sensing (nsur

= 1).

The thickness of the thin-lm

d

is thus

d = acoat − aclad .

181

Even if

the gure 5.14(b) is not perfectly in scale, it can be seen that the less thickness is that of the lm, whereas the largest value of the refractive index is again that of the lm (ncoat

> ncore > nclad > nsur ).

It was rstly demonstrated by Rees et al [19] that both the resonance wavelength and minimum transmission of the LPG attenuation bands exhibit a dependence on both the thickness and refractive index of an overlay material, even when the coating has a RI higher than that of the cladding glass. So the coatings may be engineered to change their optical properties in response to an external perturbation. A lot of congurations have been discussed [21], which facilitate the interaction between modes of the optical ber and the coatings, oering techniques for monitoring changes in optical properties of the coating. The two major nano−coating techniques that have been reported in the literature are unquestionably the electrostatic self−assembly (ESA) and the LangmuirBlodgett (LB) deposition. Each facilitates the deposition of a surface coating, one molecular layer at a time, providing a control over the layer thickness at nanometer scale.

Both techniques allow the formation of thin

lms at room temperature and pressure. Moreover, both techniques require careful cleaning of the ber surface having previously removed the its jacket. The LB technique is based on the fabrication of monolayer lms, which are rst oriented on a sub−phase and subsequently transferred, layer by layer, onto a solid surface (ie optical ber) at room temperature and molecule specic surface pressure. It was proved that this technique oers high resolution control over the lm thickness of about 1-3 nm per layer and hence results ideal for optical ber applications. On the other hand, the ESA technique allows the deposition of multilayered lms of magnetic, electrically conductive and nonlinear optical materials onto a substrate. This technique is based on the alternate dipping of a charged substrate into solutions of cationic and anionic polymers. The growth of the lm occurs by means of the electrostatic attraction between the opposite charges of molecules in alternate monolayers. It is clear that these two techniques oer a number of dierent features. LB lms consist of a single chemical species. This homogeneity is not available using the ESA method, because it requires alternate layers of oppositely charged materials. On the contrary, the ESA technique makes possible to incorporate


182

more than two molecules into the multilayer due to the attraction of opposite charges.

Therefore, aperiodic multilayer assemblies may be prepared, oer-

ing more versatility than the LB technique. Finally, lms constructed using the ESA technique have been shown to have good thermal and mechanical properties, whereas those constructed using the LB technique suer from the applied stress which may compromise the integrity of the LB multilayers. Reference [19] dates, for the rst time, the eect of the overlay thickness on the transmission spectrum of a LPG. Rees et al used the LB technique for controlling the overlay thickness of the deposited thin-lm.

ω−tricosenoic

The LB lm of

acid, which has a refractive index of 1.57 RIU and a molecu-

lar length of 2.6 nm, was deposited onto an optical ber containing an LPG. Figure 5.15 shows the experimental shift of the resonance wavelengths of two dierent cladding modes as a function of the overlay thickness, when the surrounding medium is air (ie

nsur = 1).

correspond to the coupling to the tively.

p=

The lled circles and lled squares 9 and

p=

11 cladding modes, respec-

From the gure some interesting features can be extracted.

Firstly,

the trend of the two resonance wavelengths is the same, but the magnitude of the shift is dependent on the order

p

of the corresponding cladding mode.

In addition, three dierent regions from A to C can be observed, which are characterized by three distinct trends of both the resonance wavelengths. For an overlay thickness lower than 250 nm (region A), the resonance wavelengths exhibited a blue shift of about 5 nm. For an overlay thickness ranging from 250 nm to 380 nm (region B), the amplitude of the attenuation bands in the ber transmission spectrum approached to zero showing that no couplings occurred, and thus no resonance wavelengths could be recorded. This range of overlay thickness denes the so-called cut-o thickness

dcut-o .

For an overlay

thickness greater than 380 nm (region C), nally, the resonance wavelengths were recorded again and exhibited a blue shift once again, but the their values were higher than originally observed in absence of the overlay material. As the lm thickness was increased further, the resonance wavelengths returned toward their original values.

The authors developed a numerical model in

order to explain the dependence of the resonance wavelengths on both the thickness and refractive index of the coating. The eective refractive indices of the cladding modes were calculated as a function of wavelength and overlay


Figure 5.15: Experimental shift of the resonance wavelengths of the (lled circles) and

183

p =

9

p = 11 (lled squares) cladding modes, plotted as a function

of the overlay thickness [19]

thickness by considering the cladding/overlay system as a stack of thin lms and employing the transfer matrix method (see section 3.3) [19], whereas the eective RI of the fundamental core mode was calculated by means of the Gloge's approach [80]. Afterwards, using the LPG characteristic equation, it was possible to obtain the value of the resonance wavelengths as a function of the overlay thickness. Some discrepancies, which arose from the approximations made and from the not-so-complete knowledge of the ber and overlay material parameters, came out but the experimental behavior was explained qualitatively, anyway. Initially, only the surrounding air inuences the eective RI of the cladding mode. As the lm thickness increases (region A), both the LB lm and the air inuence the cladding mode, increasing the average external refractive index and thus the eective RI of the cladding mode. As the average external refractive index experienced by the cladding modes increases, a blue shift in resonance wavelength occurs, as would be expected

184


from the classical theory of SRI sensitivity. In region B, the average external refractive index is approximately equal to that of the ber cladding. In this case the structure does not support guided modes and hence no attenuation bands can be observed in the ber transmission spectrum. In region C, nally, a more complex structure exists. The existence of cladding modes, when the surrounding RI is higher than that of the cladding glass, was just explained by the presence of leaky modes. As the thickness of the LB lm increases further, the resonance wavelengths would be expected to approach the value observed for an overlay of innite extent. Later, more rigorous theoretical treatments, where the high RI (HRI) coated LPGs have been modeled as four layer structure and have been treated using the CMT, conrmed the previous experimental results but provided a new interesting explanation of the physical and optical principle, which allowed to understand how the coupling between modes occurs in coated LPGs and hence how the shift of the resonance wavelengths can be evaluated. The rst comprehensive theoretical and numerical analysis was reported by Del Villar et al [20, 22, 154, 156]. Cusano et al [55, 155] studied theoretically and experimentally the responses and sensitivities of coated LPGs for chemical and biochemical applications. Using a linearly polarized (LP), weakly guiding approximation, it was demonstrated that, as the thickness of an overlay of refractive index higher than that of the ber cladding is increased, the thin overlay becomes capable of guiding one of the cladding modes. During the transition to guidance, the eective RI of the considered cladding mode varies rapidly, as evidenced by the rapid change in resonance wavelength of the attenuation bands (see gure 5.16).

The curves depicted in gure 5.16

were obtained by means of a coated LPG inscribed in a SMF-28 optical ber.

µm, cladding diameter of 125 µm, core RI of 1.5362 RIU, cladding RI of 1.5306 RIU, overlay RI of 1.67 RIU + − ([P DDA /P olyS − 119 ]), grating period of 276 µm and grating length of 25 mm. Because the RI modulation is considered sinusoidal, σ (z) = s0 = s1 = 1 The LPG parameters are: core diameter of 8.3

and the amplitude of the modulation is about 3 x 10

−4 RIU.

In the absence of losses (the imaginary part of refractive index) in the overlay, it is the cladding mode with the highest eective RI, or rather the lowest order cladding mode that is guided by the overlay. The transition is


185

Figure 5.16: Eective refractive index of cladding modes as a function of the overlay thickness [20]

also characterized by a strong reorganization of the cladding modes, as can be seen from gure 5.16. Moreover, the eective refractive indices of the cladding modes are then increased to that of their nearest lower order cladding mode in the absence of the overlay in order to cover the energy state left by their predecessors, as illustrated in the same gure.

Further increases in overlay

thickness cause this process to repeat, thus more cladding modes are guided by the overlay and a new reorganization of cladding modes takes place. The LP approximation does not predict the disappearance of the attenuation bands unless the overlay material exhibits a complex refractive index. In this case, the attenuation of the cladding modes is predicted to increase rapidly in the transition region, which reduces the coupling coecient between the core and cladding modes and, as a result, causes the extinction of the attenuation bands [156]. The attenuation bands corresponding to the coupling

186


to higher order cladding modes than those guided by the overlay, recover the PMC of the immediate lower order cladding mode.

The attenuation bands

corresponding to the coupling to cladding modes of order lower than those guided initially, suer a blue shift before recovering their original resonance wavelength. It is worthy of highlighting that, when coated LPGs are taken into account, the LPG characteristic equation can not be used to calculate accurately the value of the resonance wavelengths. However, if the modied rst-order Bragg condition (see equation (3.101)) is applied, errors are lower than 0.1% [103]. This is because the self-coupling coecients are more related to changes in the resonance wavelength of the attenuation bands, whereas the cross-coupling coecients modify the minimum transmission value of the attenuation bands. Following the above-discussed analysis, the response of the resonance wavelengths to the deposition of thin lms of dierent RI can be obtained. example is shown in gure 5.17.

An

The gure show the inuence of the overlay

Figure 5.17: Shift of the resonance wavelength as a function of the overlay thickness for dierent value of the refractive index of overlay material: lled triangles 2 RIU, lled rhombuses 1.7 RIU and lled squares 1.57 RIU [21]


187

refractive index on the sensitivity of the LPG. The lled triangles trend is obtained with a RI of the overlay of 2 RIU, the lled rhombuses of 1.7 RIU and, nally, the lled squares of 1.57 RIU. It can be seen that, as the RI of overlay material increases, the region of high sensitivity moves to lower thickness and the wavelength shift is lower. Therefore, it is also possible to predict the sensitivity of the attenuation bands to changes in the refractive index of the overlay, assuming a constant overlay thickness.

This indicates undoubtedly

the potential for developing sensors based on nanometer−scale coatings that change their refractive index in response to an external perturbation. As can be easily understood remembering the LPG characteristic equation, the immediate consequence of the shift in eective RI (see gure 5.16) is that it leads to a displacement in all the attenuation bands. Furthermore, Del Villar et al [20, 22] found that there are an optimal deposition thickness value for each cladding mode where the shift of the resonance wavelength as a function of the surrounding RI is highest. This value is known in the literature as optimum overlay thickness (OOT). Figure 5.18 shows OOT for the

p=

15 cladding mode (high order cladding mode) as a function of the overlay

refractive index.

For higher values of overlay RI, the OOT tends to lower

values because the guidance in the overlay starts sooner for the higher contrast of refractive indices between the cladding and the overlay.

The OOT

value depends not only on the overlay RI, but also on the surrounding RI. Consequently, a good choice for a high sensitive device to the surrounding RI is to stop the deposition when the ERI value of a mode is located between the ERI of the mode itself before the deposition and that of the next lower order cladding mode before the deposition. To calculate a more exact value, the modied rst-order Bragg condition (see equation (3.101)) has to be used.

By considering three dierent RI overlay materials, 1.57 RIU for

ω−tricosenoic acid, 1.62 RIU for [P DDA+ /P olyR − 47− ] and 1.67 RIU for [P DDA+ /P SS − ], Del Villar et al [20] showed that, if the overlay RI is higher, the guidance of a cladding mode starts faster, or rather the transition happens earlier, as illustrated in gure 5.19.

It was proved that there are two

important advantages for using a higher RI coating. Firstly, a lower amount of material is needed for the deposition and thus this saves much time. Secondly, the transition to guidance of a cladding mode in the overlay is faster,

188


Figure 5.18: Optimum overlay thickness for the

p=

15 cladding mode as a

function of the overlay refractive index [22]

which implies a higher variation of the eective RI of the cladding modes as a function of the surrounding refractive index and hence a higher shift of the resonance wavelengths. It is clear that, even if the OOT is not exactly xed for a cladding mode, there is a range of values that also allows high sensitivities as a function of the surrounding RI. Therefore, once the refractive index of the overlay has been determined, the versatility of this phenomenon is proved by the dependence of the OOT on a second parameter, namely,

nsur .

This allows

to design refractometers sensitive to specic ranges of surrounding refractive indices. In fact, gure 5.19 shows the design of a coated LPG to be used as a gas sensor. The OOT for the third cladding mode (p

=

5) is 278.5 nm and

the three curves have been obtained for a SRI equal to 1 RIU (RI of air and so of gases). The choice of using the third cladding mode in this analysis is to demonstrate that, even for low order cladding modes, the phenomenon is appreciable and hence the RI sensitivity can be greatly enhanced. Del Villar et al [20] found experimentally that the decrease in the optimum overlay thickness, as the SRI increases, can be explained by means of the slab waveguide theory. A second example shows how a suitably coated LPG can


Figure 5.19: Shift of the resonance wavelength in the

189

p = 5 cladding mode as

a function of the overlay thickness for dierent overlay refractive index when the coated LPG is placed in air (nsur

= 1)

[20]

be used as RI sensor with high sensitivity for the detection of oils, which are characterized by a RI around 1.468 RIU. After having calculated the OOT of 159 nm, optimized around a SRI of 1.468 RIU, the evolution of the resonance wavelength of the fth (p

= 9) cladding mode cause by a change in surrounding

RI of dierent oils is shown in gure 5.20.

Figure 5.20(a) illustrates the shift

of resonance wavelength of the fth cladding mode for an LPG where no overlay is added. Three dierent oils with refractive indices 1.461 RIU (tee), 1.481 RIU (cod) and 1.518 RIU(tung) are considered. In gure 5.20(b), the same is done for an LPG with OOT optimized for surrounding refractive index around 1.468 RIU. It can be clearly observed that the LPG with the overlay

190


Figure 5.20: LPG transmission spectra of the

p=

9 cladding mode for three

dierent surrounding refractive indices without the overlay (a) and with an overlay characterized by a thickness of 159 nm and a refractive index of 1.67 RIU [20]

5.4. Applications of optical ber gratings for biochemical sensing

191

is also highly more sensitive than the other one, in this case, where the SRI is close to that of the cladding glass.

Moreover, there is an unquestionable

improvement in the RI sensitivity of the device. In fact, between the rst and the third refractive index, there is a shift of the resonance wavelength of 22.98 nm, whereas for the LPG without overlay it is of 1.77 nm. Thus, a factor 12.98 of improvement has been obtained. In addition, a factor of 70.5 is obtained, if we only consider tee and cod oils, because their refractive indices are closer to that of the OOT has been calculated for. It is worthy of noticing that the key feature of the HRI coated LPGs relies on the possibility to tune the maximum value of the RI sensitivity over the desired SRI range by acting on both the RI and thickness of the overlay material. Moreover, the region with the highest SRI sensitivity moves towards lower surrounding refractive indices as the overlay thickness increases [155].

5.4 Applications of optical ber gratings for biochemical sensing

Ta compact analytical device incorporating a biological or biologically derived he

denition of a biosensor has been decided on by IUPAC [157] and also

published by Prof. Turner and Newman [158] who referred to a biosensor

−

as:

sensing element either integrated within or intimately associated with a physiochemical transducer.

Biosensors can be classied either on the base of the biological receptor or depending on the transducer. An electrochemical biosensor is a biosensor with an electrochemical transducer, such as ion selective, glass or gas electrodes for potentiometric measurements and metal or carbon electrodes for amperometric measurements [157].

Other types of biosensors are based on

mass sensitive transduction (piezoelectric shear and surface acoustic waves) and optical transduction (such as planar waveguide, optical ber and surface plasmon resonance) [157] (see gure 5.21). The research and technological development of optical biosensors have experienced an exponential growth during the last decade due to the potential of this technology for real time and direct detection of biomolecules or chemical substances [159161]. As stated in a review by Marazuela et al [162], the vast

192


Figure 5.21: Schematic representation of a biosensor.

The dierent bio-

recognition elements and transducers are depicted in the gure [23]

range of applications of optical biosensors partially arises from the possible use of optical bers which enable the scientist

the sample.

to bring the spectrometer to

This is further demonstrated by the huge quantity of published

works on ber optic biosensors (FOBs) which have been extensively reviewed in the last decade [161169]. Actually, several advantages of FOBs have been presented, among which the high exibility and the possibility of performing measurements in non-conventional, conned or dangerous environments: these has led to a vast area of applications in elds like environmental surveillance, chemical process analysis, food manufacturing and storage, clinical monitoring, space and aeronautics [169]. In the clinical and veterinarian eld many enzyme-based FOBs have been developed for the detection of blood glucose, some of which with a needle-type conguration [24, 170, 171] (see gure 5.22).


193

Figure 5.22: Schematic representation of (A) hybrid sensor and (B) implanted hybrid sensor [24]

Other enzyme-based FOBs have been presented for environmental applications in the detection of heavy metals or pollutants such as organophospates [172] or carbamate pesticides. FOBs based on the use of antibodies have been published as evanescent wave immunosensors, Fabry-Perot interferometric immunosensors, surface plasmon resonance immunosensors and chemiluminescencebased immunosensors for the detection of pesticides [173], viruses [174] or for the diagnosis of specic diseases [175]. Optical bers have been also coupled to nucleic acids or whole cells in the development of biosensors for the detection of mutations [176], bacteria [177], and environmental pollutants such as herbicides [178].


194

All the possible bioreceptors used in biosensors have been exploited in the most recent (2009-2011) published works on FOBs: nucleic acids, enzymes, antibodies, whole cells and biomimetic receptors.

The application of these

biosensors ranges from the biomedical eld, to the environmental or food control areas with transduction based on localized surface plasmon coupled uorescence (LSPCF), surface plasmon resonance (SPR) or evanescent wave absorbance. Very recent nucleic acids FOBs have been proposed for application for quality control in food and beverages industries [179] with chemiluminescent detection. LSPCF FOBs have been reported for application in the biomedical eld for the detection of prostate specic antigen [180], swine-origin inuenza A (H1N1) virus [181], severe acute respiratory syndrome (SARS) coronavirus [182] and alpha-fetoprotein [183]. All these biosensors were based on sandwich immunoassays and gold nanoparticles signal enhancement and could detect the target molecule at high sensitivity in complex samples such as human serum and nasal mucosa. Nanoparticles, in particular super-paramagnetic nanoparticles, were also used as signal amplication tool in a ber optic SPR biosensor for the detection of food allergens [25] (see gure 5.23). Innovative bioreceptors such as aptamers have been also coupled to optical bers for the development of

aptasensors :

in particular, a ber optic

surface plasmon resonance aptasensor have been reported for the detection of immunoglobulin E (IgE), a protein which plays an important role in many allergic reactions [184].

5.4.1 Fiber Bragg gratings Among the modied FBG structure, an interesting example has been reported for the detection of deoxyribonucleic acid (DNA) hybridization by means of an etched FBG [185]. The proposed sensor was developed by etching away the ber cladding and part of the ber core. The physical mechanism is based on detecting the change of resonance Bragg wavelength due to the changes in RI of the surrounding medium. The maximum sensitivity of about 1394 nm RIU

−1 was achieved, when the diameter of the ber core was reduced

to about 3.4

µm

and the RI of the surrounding medium was close to that of

−6 RIU.

the ber core. Moreover, the sensor achieves a RI resolution of 7.2 x 10


195

Figure 5.23: (A) Fiber optic SPR probe; (B) schematic representation of the system setup; (C) overview of the immunoassay strategies on the ber optic SPR biosensor; (D) the spectrum dips in PBS buer after 10 min incubation of the SPR ber in: a negative control sample (blue dip), a sample containing the antigen (red dip), a sample containing the antigen subsequently labeled with antibody linked nanobeads (black dip) [25]

The sensitivity at lower surrounding RI was achieved by using higher order

−1

modes excited in the Bragg grating region and a value of about 404 nm RIU

was obtained by the authors around 1.4098 RIU. Having said that, the etched core FBG sensor was further investigated to detect hybridization of DNA. Single stranded DNA oligonucleotide probes of 20 bases were immobilized on the surface of the grating using a common glutarahyldehyde chemistry. Hy-

196


bridization of the complimentary target single strand DNA oligonucleotide was monitored in situ and successfully detected.

5.4.2 Long period gratings Most of the literature about LPGs used as refractive index sensors has concentrated upon the bulk immersion of the LPG into a solution. It is attractive to consider the prospect of depositing overlay materials that exhibit changes in their refractive index and/or in their thickness in response to local environment variations.

In this way, the LPG may be also used to form a

species-specic chemical/biochemical sensor.

In practical LPG-based sensor

applications, the deposited lm serves as the sensing element by incorporating sensing chemical/biological molecules into it, whereas the LPG serves as the optical transducer for signaling the occurrence of a chemical/biological interaction event of interest. The demonstration that OFGs can be used as biosensors was given by Wang et al [65] which showed that ionic self-assembled multilayers adsorbed on LPGs work eectively as biosensors, in which the biotinstreptavidin system serves as the bioconjugate pair.

The same authors [18]

reported a guideline for building ecient LPG−based sensors for practical use. Reference [19] shows that the coupled cladding mode cuts o and turns into a leaky mode, when the LPG is coated with a thin-lm whose refractive index is higher than that of the cladding glass and its thickness is larger than a cut−o thickness

dcut-o .

This is because a leaky mode is not guided due

to the total internal reection, but exists because of Fresnel reections at the ber cladding/thin−lm interface. In such case, weak attenuation bands are obtained and the coated LPG structure is not suited for sensing purposes. Therefore, the key condition is to guarantee the existence of guided cladding modes and this can be achieved by coating the LPG with a thin−lm of a thickness smaller than

dcut-o .

LPG-based biosensors have been investigated by immobilizing antibodies on the surface of the ber and monitoring the change in refractive index that occurs when an antigen binds with the antibody [65]. This is the rst reported example of the use of an LPG to form a species-specic biochemical sensor, offering a good performance not again comparable with other techniques, which include both the surface plasmon resonance (SPR) and interferometric cong-


197

urations (ICs), but with the prospect for on-line monitoring. Moreover, the deposition of thin-lm overlays by means of the Langmuir-Blodgett technique has been proposed to develop chemically sensitive sensors based on coated LPGs [19], oering the prospect for the development of a range of new speciesspecic chemical sensors. Moreover, LPGs applied for label-free detection of specic bacteria using physically adsorbed bacteriophages were presented for the rst time by Smietana et al [62]. LPGs were used also for the measurement of DNA hybridization [63, 64] and for antibody/antigen interaction [40, 6568]. OFG and SPR can be combined, by depositing a thin gold layer on the grating surface [48]. A high sensitive biosensor based on a 20 nm gold coating applied on a TFBG has been recently proposed for real-time and label-free monitoring of both the formation of DNA monolayer in aqueous environment and complementary DNA binding [69]. Tang et al [70] proposed a new class of biosensor using an antibody-antigen binding model for dinitrophenol (DNP), relying on the modication of the grating portion of a long period ber grating with self-assembled Au colloids, which is sensitive to the RI of the colloidal gold surface and, hence, is suitable for label-free detection of biomolecular binding at the surface of Au colloids. It was widely demonstrated that, if a lm of appropriate thickness is deposited, then a small change in the surrounding refractive index causes a large shift of the resonance wavelength, giving the chance to develop highly sensitive sensors. This has been exploited by dip-coating the nanoporous crystalline from syndiotactic polystyrene (sPS) onto an LPG [186].

δ

sPS reversibly ad-

sorbs analytes of suitable size and shape, with a concomitant change in refractive index of the deposited layer. The sensor was shown to be capable of sub−ppm (parts per million) detection of chloroform in water. The authors demonstrated that an appropriate choice of the overlay thickness allows the optimization of both the response time and sensitivity of the device. Furthermore, the deposition of nanostructured lm onto concatenated or in-series LPGs has been reported [187].

The authors proved that, if these

lms are deposited on the length of the optical ber that separates the two LPGs, then they aect only the interference fringes produced by means of the interferometric mechanism, while, if these lms are deposited along the entire length of the device, then they inuence both the interference fringes and the

198


attenuation band envelope.

Part II

Flow cell for refractive index measurements: design, development and test

Chapter 6

Experimental setup for refractive index measurements The most beautiful thing we can experience is the mysterious. It is the source of all true art and science. Albert Einstein

6.1 Basic concepts about the refractive index measurements

R

efractive index (RI) measurements in liquids have been used for many years in the quantitative measurements of both optical parameters in the

physical eld and analytes in the biochemical eld.

Within the optical ap-

proach, optical ber long period gratings (LPGs) have been extensively proposed for physical, chemical and biochemical sensing. These sensors have high sensitivity to the surrounding RI (SRI), in addition to all the other benets oered by optical ber sensors. For these reasons, a number of refractometric measurement systems that make use of LPGs have been proposed in the literature [16, 27, 4043].

However, LPGs show great sensitivity not only to

the SRI, but also at the same time to temperature, strain and ber bending. The inuence of these parameters can be essential when the refractometric measurement is carried out with the investigated sample owing within a ow cell, as generally occurs whenever the measurement of the RI is carried out for chemical/biochemical sensing. The literature about LPGs shows that these devices can be used as a sensitive measure of chemical/biochemical concentration for liquids in the range of refractive index from 1.33 RIU to 1.43 RIU. Patrick et al [27] dealt rstly

202

6. Experimental setup for refractive index measurements

with a remaining technical challenge in order to realize practical and credible RI sensors for liquid samples.

This technical challenge was related to both

strain and temperature cross-sensitivities. Strain sensitivity can be addressed by mounting the LPG under tension to a material with the same coecient of thermal expansion as the optical ber, so that strain is held constant during the measurements. Moreover, by xing the optical ber upon a suitable framework, the ber bending which represents another LPG cross-sensitivity, is also avoided. In addition, it was extensively demonstrated that any changes in temperature cause also the shift of the resonance wavelengths of the LPG attenuation bands in the transmission spectrum of the ber [73,132,152] due to both the intrinsic temperature sensitivity of the LPGs and the temperaturedependent refractive index changes of the liquids, which is ascribed to the thermo-optic eect acting on the dierent solutions [26, 188]. The rst eect is most easily addressed using a simultaneous measurement technique, such as employing another optical ber grating written in series with the LPG. The best choice is unquestionably a ber Bragg grating, which is insensitive to the surrounding refractive index and can also be employed as a temperature monitor and correcting for the intrinsic temperature sensitivity of the LPG. The second eect is inherent to any RI-based sensor and thus it is required the calibration of the liquid's

d nsur /d T

(evaluation of the thermo-optic coecient

of the investigated liquid), as well as limiting the range of operating temperatures of the sensor if the mixtures have very dierent values of

d nsur /d T .

As

explained in subsection 5.1.2, because the value of the temperature sensitivity of LPGs is also dependent on thermo-optic eect acting on the dierent solutions/liquids, the temperature sensitivities of the used LPG for all the solutions, or rather the temperature sensitivities

STLPG (p)

for all the used RI values

is dierent and hence they have to be determined.

Said that, the chapter starts with the description of the proposed methodology in order to get rid of the variations coming from the sensor crosssensitivities and also shows a comprehensive block diagram of the entire system for refractometric measurements (section 6.2). The chapter carries on with an exhaustive description of the manufactured thermo-stabilized ow cell (section 6.3), which has been used for both physical and biochemical measurements. Moreover, the chapter talks about the developed system for the fabrication

6.2. Methodology of the proposed refractive index sensor

203

of the gratings (section 6.4) and the reason of our choices will be discussed. Certainly, the most attractive feature of the proposed manufacturing system is that it makes possible both the fabrication of FBGs and LPGs using the same laser source and the entire customization of the grating parameters. Finally, the used interrogation system and data processing are also explained (section 6.5) together with the uidics system and chemicals (section 6.6) used for carrying out the RI measurements.

6.2 Methodology of the proposed refractive index sensor

S

tarting from the above-mentioned technical challenge, we describe the complete design, development and test of the thermo−stabilized ow cell of

relatively low volume (tens of

µL)

for accurate RI measurements using a long

period grating. Moreover, a methodology for measuring and hence correcting all the LPG cross−sensitivity is proposed. A ber Bragg grating written on the same ber in series with the LPG and an accurate temperature measurement system are used to introduce feedback signals to eliminate or, in any case, to reduce to a minimum the interferences coming from changes in temperature and strain. In detail, the FBG is used for measuring small changes in strain and thus nely correcting them, whereas a thermocouple is used for measuring and nely correcting small changes in temperature. In fact, the inuence of the above-mentioned parameters can be essential when the refractometric measurement is carried out with the investigated sample owing within a ow cell, as generally occurs whenever the measurement of the RI is carried out in the eld of chemical/biochemical sensing. It is worthy of highlighting that the entire system is thermally stabilized as it should be done in the case of accurate RI measurements. To do this, starting from the LPG and FBG characteristic equations (see equation (3.58) and (3.57), respectively) and by making some simple mathematical manipulations, we are able to isolate the contribution of the shift of the LPG resonance wavelength only due to changes in the surrounding RI. For the FBG, we sum the two linear relations that bind the measured resonance wavelength shift (∆

λFBG res )

to a change in both the strain (∆ ), given


204

in equation (5.2), and temperature (∆

T ),

given in equation (5.6):

FBG ∆ + S FBG ∆ T ∆ λFBG res = g (∆ , ∆ T ) = S T where

SFBG

and

STFBG

(6.1)

are the constants associated with the changes in strain

and temperature, respectively (hereafter denoted as strain and temperature coecients), which can be determined experimentally. For the LPG, a dierent relation is valid.

In fact, we sum the three contributions that bind the

λLPG res (p) ) to a change in strain (∆ ), (∆ T ), given in equation (5.23), and

measured resonance wavelength shift (∆ given in equation (5.21), temperature

surrounding RI (nsur ), given in equation (5.24):

LPG LPG ∆ λLPG res (p) = g (∆ , ∆ T, nsur ) = S (p) ∆ + ST (p) ∆ T + f (nsur ) 0

where

SLPG (p)

and

STLPG (p)

(6.2)

are the LPG strain and temperature coecients, re-

spectively, of the coupled cladding mode, which can also be determined experimentally, and

f (nsur )

is the nonlinear function that expresses the inuence

of changes in the RI of the medium surrounding the ber, which is what we want to estimate. As above-mentioned, in the last equation, the eects which arise from the ber bending are disregarded, since the optical ber is suitably xed in the ow cell. After the experimental evaluation of the four coecients and by measuring both the temperature variations by means of the thermocouple and the shift of the resonance wavelengths of FBG and LPG by means of an optical spectrum analyzer (OSA), the rst term on the right side of equation (6.1) (strain dependence) can be determined and, consequently, both the two terms on the right side of equation (6.2) (strain and temperature dependences) can

f (nsur ) can be attained. It is clear f (nsur ) gives us information about only the shift of the LPG

be determined and hence the value of that the value of

resonance wavelength induced by a change in the surrounding RI. In order to obtain the value of the surrounding RI, as occurs in the case of a classical refractometer, we have rst to extrapolate the nonlinear response curve

f (nsur )

and its best tting curve. All the needed steps will be described in

the experimental section about the RI measurements (see section 7.2).

6.3. Thermo-stabilized ow cell

205

6.3 Thermo-stabilized ow cell

T

he

most attractive part of the experimental setup for refractive index

measurements is unquestionably the thermo-stabilized ow cell.

The

sketch of the ow cell and its picture are shown in gures 6.1 and 6.2, respectively.

The cell itself consists of two parts: the upper one is a 4 mm thick

Figure 6.1: Sketch of the manufactured ow cell: longitudinal cross−section (a) and top view (b) [26]

PMMA transparent layer that makes a visual inspection of the ow cell possible, and the bottom one is a 6 mm thick aluminum layer placed in thermal

206


Figure 6.2: A picture of the developed ow cell [26]

contact with a thermo-electric cooler (TEC) element that is composed of a series of three Peltier cells. A second aluminum bar is mounted on the bottom of the Peltier cells in order to increase their eciency. The whole system is mounted on an extruded aluminum heat sink. The ow cell is 80 mm long, 15 mm wide and 10 mm high. The ow channel is realized by means of a 1 mm wide, 0.5 mm deep and 50 mm long rectangular section groove that is built on the PMMA and aluminum pieces.

A gasket

obtained from a specially shaped Paralm® sheet is interposed between the two parts in order to assure the water-proong of the ow cell. The resulting volume of the ow channel is 50

µL. In addition, a deep v−groove of about 0.4

mm is engraved on the ends of the PMMA layer in order to locate the optical

6.3. Thermo-stabilized ow cell

207

ber. The ber with its jacket is glued to the v−groove edges using an UV optical exible adhesive (Norland 65), which, after the UV polymerization, guarantees a safe sealing of the ow cell. In this way, the bare portion of the optical ber, where the two gratings have been inscribed, is exactly placed at the middle of the ow channel.

In fact, the microuidic theory states

that the liquids owing inside a microuidic system travel by means of a laminar ow. This means that there will be more friction along the walls of the channel, whereas the liquids will travel more regularly at the middle of the ow channel, where the optical ber is placed. Two stainless−steel tubes (1.6 mm outer diameter and 1 mm inner diameter) located on the upper part of the PMMA layer serve as the inlet and outlet of the ow cell. The temperature stabilization section of the ow cell makes use of a thermistor, inserted into the aluminum bottom part as close as possible to the ow channel (the green wire in gure 6.3), which acts as a feedback element on the Peltier elements that are driven by a suitable controller (ILX Lightwave LDC−3722B TEC controller).

The temperature of the ow cell is

measured by a thermocouple connected to a thermometric measuring unit (Lutron TM−917) and placed inside the PMMA layer as close as possible to the ow channel (the blue wire in gure 6.3). The raw temperature data are acquired by a PC via the RS−232 serial interface, with a resolution of

±0.01

and sampling time of 2 s. The stabilization eect due to the use of the Peltier cells can be observed in gure 6.4.

In order to prove the stabilization eect

due to the use of the Peltier cells, we measured the shift of the LPG resonance wavelength when the optical ber was placed inside the ow cell and the environmental temperature was about 20. The ow channel was empty, or rather in air. The interrogation system, which allows us to measure the shift of the resonance wavelengths of both the gratings, will be described in section 6.5. Moreover, we test the thermal stabilization using an LPG instead of an FBG because an LPG is more sensitive to temperature changes (see gure 5.5). From the gure 6.4, it can clearly be seen that the LPG resonance wavelength exhibited a large blueshift until the stabilization system was switched on (after about 20 minutes). By setting the controller at 23 , the LPG resonance wavelength does not shown a visible shift or thermal drifts. This was further demonstrated by means of long-term measurements, when the ow cell was

208


Figure 6.3: A side-view picture of the ow cell

lled with distilled water (see subsection 7.1.3).

Notwithstanding the fact that the TEC control system makes it possible to work at constant temperature, the continuous measurement of the temperature of the ow cell is necessary both to control possible drifts induced by environmental temperature changes during long−term measurements and to take into account the eects induced by pumping uids at dierent temperatures within the ow channel. Moreover, the continuous measurement of the temperature is also necessary for the described methodology in order to allow the ne temperature correction of the sensor response.

6.4. Manufacturing of the gratings

209

Figure 6.4: Stabilization eect on the LPG resonance wavelength by means of the Peltier cells

6.4 Manufacturing of the gratings

A

s introduced in section 1, we studied and developed during my PhD time a sensor made up of a hybrid conguration of optical ber gratings which

consisted of two dierent in-line OFGs. The former was a long period grating, which was able to sense changes in surrounding refractive index, whereas the latter was a ber Bragg grating, which was used to compensate the eects on the sensor response due to possible changes in strain and temperature induced on the ber. That we had in mind, it is the development of a system for grating fabrication that could allow us to use it for both types of gratings (FBGs and LPGs) with simply small changes only. This features together with the pos-


210

sibility of customizing both the optical and physical properties of the grating represents unquestionably an important issue, thus one of the contributions. So the developed manufacturing system makes it possible to write both FBGs and LPGs with the same facilities. Having said that and looking at the differences of the manufacturing techniques about FBGs (see the last paragraph of subsection 4.2.3) and LPGs (see the last paragraph of subsection 4.3.2), we made some observations and decided to use the following manufactur-

phase mask technique for ber Bragg gratings, whereas the point-to-point technique with excimer KrF laser for long period gratings. ing techniques: the

The reason of these choices are a lot. Regarding the FBGs, the phase mask technique is unquestionably the most full-grown and suitable method to the current state of the art. It is also true that the equipment needed is expensive and the phase masks at our disposal were limited, but it was exactly what we needed in any case.

In fact, we already had an ultraviolet laser source and

phase masks at our disposal made possible to write FBGs, which the values of resonance wavelengths belonged to the wavelength range of the optical source used. Regarding the LPGs, the point-to-point technique with an excimer KrF (λ

=

248 nm) laser was the best choice because it allowed us to use the same

laser source for LPGs inscription by means of the use of the classical physical mechanism based on the excitation of the singlet-singlet transition band (near 242 nm) of the germanium-oxygen-vacancy defects. This method is suitable as well, because it also allowed us to customize greatly the LPGs.

More-

over, using a photochemical technique, we were suciently sure not to change the geometrical and optical characteristics of the ber cladding and hence to avoid couplings to antisymmetric cladding modes. The main reason was that we wanted a transmission spectrum as clean as possible in order to avoid the interference problem of the loss peaks during measurements. Therefore, we had to use a photosensitive optical ber. We used the BGe co-doped step-index single-mode Fibercore PS1250/1500 ber, which is characterized by the following parameters

1:

refractive index of the ber core (λ

refractive index of the ber cladding (λ

=

1550 nm): 1.4508 RIU;

=

1550 nm): 1.4441 RIU;

1 Data available on line at the following website www.fibercore.com/LinkClick.aspx?

fileticket=DyYyL9DYexEid=506


211

numerical aperture (λ

diameter of the ber core: 6.5

diameter of the ber: 125.94

cut-o wavelength: 1194 nm;

attenuation (λ

composition of the ber core: pure fused silica (SiO2 ), germanium oxide

GeO2

=

=

1550 nm): 0.14;

µm;

µm;

1550 nm): 121.11 dB km

and boron oxide

B2 O3

−1 ;

in dierent unknown percentage ratios;

composition of the ber cladding: pure fused silica (SiO2 );

composition of the ber jacket: acrylic polymer coating.

The Fibercore Company provided also the curve of the RI prole of the ber used, which is reported in the gure 6.5. The shown RI prole is the typical

Figure 6.5: Refractive index prole of B-Ge co-doped step-index single-mode Fibercore PS1250/1500 ber


212

RIP of a B-Ge co-doped step-index single-mode optical ber, that is to say, it is characterized by a dip centered along the ber axis (position of 0

µm).

This

characteristic shape results from the use of double doping with germanium and boron. It is worthy of noticing that the values along the y-axes, the refractive index dierence on the left and the refractive index on the right, are the values at the wavelength of 653.7 nm (visible spectrum). The schematic of the manufacturing setup for FBGs is shown in gure 6.6. The laser source used is the Lambda Physik Compex 110 excimer laser.

It

Figure 6.6: Schematic of the manufacturing setup for FBGs. SLD, superluminescent light diode

is a gas laser operating with a mixture of two gases, which do not bound chemically in normal condition. But if the two gases are appropriately excited, they bind to form a dimer (hence the term English

excimer

excited dimer, or rather excited dimers).

that comes from the

The mixtures used to obtain

6.4. Manufacturing of the gratings dierent emission wavelengths are:

ArF

(193 nm), Krypton-Fluorine

nm) and Xenon-Fluorine

XeF

213

Fluorine

KrF

F2

(157 nm), Argon-Fluorine

(248 nm), Xenon-Chlorine

XeCl

(308

(351 nm). Since it was chosen for the gratings

manufacturing to use B-Ge co-doped step-index single-mode bers, which have the maximum absorbance (see gure 4.11) at a wavelength around 242 nm, we chose the KrF mixture. Here are the technical specications of the KrF excimer laser:

peak wavelength: 248 nm;

maximum energy per pulse: 300 mJ;

maximum pulse repetition frequency: 100 Hz;

duration of pulses: 30 ns;

beam spot size: 24 x 10 mm ;

beam spot divergence: 3 mrad in vertical direction, 1mrad in horizontal

2

direction. The laser was set to operate at constant high-voltage mode (ie 21-24 kV) with a maximum value of energy per pulse of about 250 mJ. As can be also seen in the picture 6.7, which depicts our manufacturing setup for FBGs, the UV beam after undergoing a double reection in two mirrors passes through a square

2 and is focused by a cylindrical lens on the

slit of dimensions 10 x 10 mm

rectangular phase mask, which is xed on a suitable aluminum framework. The photosensitive optical ber, on which the grating will be inscribed, is placed behind the framework (see gure 6.7). Before placing the ber in the suitable framework in physical contact with the phase mask, it is necessary to remove the protective coating (or simply jacket) because is not transparent to UV light. The jacket removal, which has to be made only on the portion of the ber where the grating will be formed (in our case, about 3 cm), is made manually with a special mechanical device or by immersing the ber portion in trichlorethylene, which after a few minutes softens the jacket and allows us to remove it with a simple shift of the ngers. The necessary condition to write a FBG eciently is the correct positioning of ber with respect to the phase mask: the optical ber must be perfectly in contact with the phase mask. To

214


Figure 6.7: Photograph of our manufacturing setup for FBGs

make it easier, we have recourse to the use of a manual translation stage. One end of the ber is initially blocked by means of a xed clamping point on the framework, while the other end is blocked by means of a moving clamping point on a second framework above of which is placed the manual translation


215

stage. In order to satisfy the above-mentioned condition, the optical ber has to be set at the right axial strain. This is obtained by means of the manual translation stage together with a force sensor, placed in physical contact with the manual translation stage itself, which measures the applied axial strain as a voltage value. At this point, the ber is stretched by means of the manual translation stage, until it is behind the phase mask. When the force sensor gives a voltage value of about 10 mV, we are sure that the optical ber is set at a sucient axial strain to write the FBG eciently.

Therefore, the

uncoated portion of the ber is perfectly placed in front of the phase mask and thus in contact with it. The ber clamping points and the ber positioning mechanism are shown in the photograph 6.8.

During the process of FBGs

inscription, the laser was set to operate at a pulse repetition frequency of 50 Hz. Furthermore, by varying the distance between the focusing lens and the phase mask is possible to change the intensity of radiation incident on the ber. Typically, we used a distance of 11 cm in order to obtain a uence per

−2 . We used a phase mask manufactured by Lasiris

pulse of about 450 mJ cm

Inc. and designed to work at a wavelength of 248 nm, which is characterized by a grating pitch period

Λpm

of 1059.9 nm that, in turn, corresponds to a grating

ΛF BG of about 530 nm.

The total time, which is used for writing a FBG

with reectivity of about 90%, is about 1 minute that, in turn, corresponds to a total number of about 3000 laser shots. The very short time for FBGs writing is certainly to be ascribed to the very high photosensitivity of the used optical ber. All the manufacturing process of FBGs inscription is monitored in realtime by means of both an optical source and an optical spectrum analyzer (OSA). Remembering that a FBG can be also interrogated in reection mode as depicted in gure 6.6, the FBG is interrogated in transmission mode because we are interested in the monitoring of the value of loss peak and hence of the FBG reectivity. In this way, we can know both the value of the resonance wavelength and the intensity of loss peak in every moment and hence we can stop the writing process when we want to do it. Otherwise, it is difcult to evaluate the loss peak and hence the reectivity. The used optical source is a broadband SLD-1550-DIP pigtailed. It is a superluminescent light emitting diode (LED), or rather superluminescent diode (SLD) manufactured


216

Figure 6.8: Detail of the ber clamping points and the ber positioning mechanism of our manufacturing setup for FBGs

by Fermionics Lasertech, which has the following characteristics:

peak wavelength: 1550 nm;

bandwidth (FWHM): 44.4 nm;

maximum output optical power: 0.5 mW.

The used OSA is an Anritsu MS9030A/MS9701B. It is made up of two distinct units, the former is the control and display electronic unit (MS9030A),


217

whereas the latter is the optical unit (MS9701B). The most important component of the optical unit is certainly the monochromator, which is made up of a diractive optic component (D in gure 6.9), that divides the dierent spectral components of the incident radiation, and several mirrors (C and E in gure 6.9), that carry on the light of interest wavelength to the photodetector. A schematic of a typical monochromator is shown in gure 6.9. The used OSA

Figure 6.9: Schematic of a typical monochromator placed inside an optical spectrum analyzer for the spectral analysis of an optical signal has the following characteristics:

input wavelength range: 350 nm - 1750 nm;

input optical power range: -80 dBm - +10 dBm;

optical power accuracy:

maximum optical resolution: 0.1 nm.

±1.5

dB;

By using the same photosensitive Fibercore PS1250/1500 optical ber, the same broadband optical source, the same OSA and the same KrF excimer

218


laser previously described, we have to make some little changes to the FBGs manufacturing setup in order to write LPGs. Compared to the FBGs manufacturing setup depicted in gure 6.6, the schematic of the manufacturing setup for LPGs includes both an adjustable micrometric slit to insert after the cylindrical lens and a dierent framework for the optical ber without any phase mask. In fact, we replace the framework used for FBGs clamping and positioning mechanism of the ber (see gure 6.8) with another framework specically designed for LPGs clamping mechanism. This detail is shown in gure 6.10. Moreover, the KrF excimer laser was set to operate at constant energy mode, namely, a value of energy per pulse of about 170 mJ. As for FBGs fabrication, the UV beam after undergoing a double reection in two mirrors passes through the same square slit and is focused by a cylindrical lens on the adjustable micrometric slit. Behind the micrometric slit, the photosensitive optical ber is xed on two clamping points placed on a bar of aluminum, which is connected to a computer-controlled motorized translation stage Burleigh 6000 (see gure 6.10).

Both the motorized translation stage

and the laser action are controlled and synchronized by a personal computer with an ad hoc developed NI CVI program and a digital input/output board (Eagle period

µ-DAQ USB-96C), which makes it possible to choose ΛLP G and the number of laser shots for each step.

both the grating This is a point-

to-point technique because the optical ber is moved of the desired period step-by-step. Thus the uncoated portion of the ber is placed in front of the adjustable micrometric slit. The length of the micrometric slit is set to the half of the desired grating period in order to obtain a square wave modulation of the core RI with a duty cycle of 50%. The schematic of the manufacturing setup for LPGs is shown in gure 6.11.

Referring to gure 6.11, the UV laser

beam lights the optical ber changing the core RI to a width of motorized translation stage is moved by a pitch equal to a grating with a period of

ΛLP G = Lb = 2 w.

2 w,

w.

Then the

thus obtaining

As for FBGs, the grating in-

scription is monitored throughout the writing process: one end of the ber is connected to the broadband laser source and the transmission spectrum of the ber is real-time displayed on the OSA. This methodology makes it possible to see step-by-step the formation of the grating attenuation bands in the desired wavelength range belonging to the input wavelength range of the


219

Figure 6.10: Detail of the ber clamping points and the ber positioning mechanism of our manufacturing setup for LPGs

OSA. During the process of LPGs inscription, the laser was set to operate at a pulse repetition frequency of 50 Hz. For LPGs, we used a distance between the focusing cylindrical lens and the optical ber of 9 cm in order to obtain a

−2 . We set the length of the micrometric

uence per pulse of about 300 mJ cm slit at a value of about 307.5 riod

ΛLP G

of about 615

µm.

µm

that, in turn, corresponds to a grating pe-

The total time, which is used for writing a LPG

with a transmission value of the loss peak of about -15 dB and a length of


220

Figure 6.11: Detail of the schematic of the manufacturing setup for LPGs

about 2.46 cm, is about 20 minutes. We set 1500 laser shots for each step and, considering a total number of 40 grating planes, we achieve a total number of laser shots of about 60000. It is worthy of noting that the value of uence is lower than that reported in table 4.1, regarding the same technique at the same wavelength (λ

= 248 nm),

due to the higher photosensitivity of the used

optical ber. An advantage of this method with respect to non-UV method is that gratings show changes in the refractive index of the ber core only. In fact, the ber cladding, made up of of

SiO2 ,

is not sensitive to the UV wavelength of

the laser source and, most of all, the ber itself does not undergo a geometric and/or structural deformation as can be seen in gure 6.12. In order to prove the feasibility and eectiveness of the developed manufacturing system of LPGs, two dierent tests have been performed and the


221

Figure 6.12: Photograph taken with transmission optic microscope Nikon Optiphot of a LPG written by means of the point-to-point technique with KrF excimer laser

nal comparison is shown. The tests included the real-time recording of the ber transmission spectrum by means of an OSA during the manufacture of the LPG and hence the real-time monitoring of the LPG attenuation bands in the wavelength range of interest from 1450 nm to 1650 nm. In both tests, we used the above-mentioned point-to-point technique with the grating period xed at a value of 615

µm,

whereas the optical resolution of the used OSA

was set at a value of 0.5 nm. In the rst test, the length of the grating was set at 30.75 mm, thus the number of steps was 50. The test was to perform multiple scans along the entire length of the grating for a total number of scans of 22. Moreover, the laser shots for each step was set at 100, except for the last two scans in which the value was 250. Therefore, the total number of laser shots was about 125000. Figure 6.13 shows the recorded transmission spectra of the manufactured LPG at dierent scans. All the spectra have been

222


normalized with respect to the source spectrum (not shown).

In the gure,

Figure 6.13: Transmission spectra of the manufactured LPG at dierent scans. Each curve is labeled with a dierent color (see the label in the graph)

two distinct attenuation bands can be observed, the former around 1500 nm and the latter beyond 1550 nm. The rst attenuation band is characterized by a resonance wavelength of 1507.6 nm and a transmission value of -12.65 dB that were obtained during the last laser scan (black curve). The second attenuation band is characterized by a resonance wavelength of 1565.2 nm and a transmission value of -22.66 dB that were obtained during the twelfth


223

laser scan (violet curve). It is clear that the second attenuation band reaches its maximum transmission value, or rather its maximum coupling eciency at the twelfth laser scan and follows a rapid decrease after this condition, as expected from the theory. On the contrary, the rst attenuation band does not reach its maximum coupling eciency. Remembering equations (3.78) and (3.79), both the maximum transmission value and coupling eciency depend on the grating length and the coupling factor of the cladding mode. In this test, the grating length was kept at a xed value, thus the trend showed in the gure is explained by means of a change of the coupling factor of the cladding mode, which is dierent for each mode. Because the test have been performed by means of multiple scans, the change in the induced-RI of the ber core

DC

spatially averaged over the grating length (ncore ) is surely the main contribution to the shift of the LPG resonance wavelength showed in gure 6.13 (see section 4.1). This value, in turn, aects the induced modulation of the ber core RI (∆ncore ) that increases during each scan. In general, both the shift of the LPG resonance wavelength and the variation of the transmission value during the manufacturing process are explained by an increase of

∆ncore ,

as

discussed in section 4.1. In the second test, instead, the length of the grating was variable, thus the number of steps is variable too. The test was to perform a single scans increasing the grating length at each step. The value of these steps was equal to the grating period for a total number of steps of 95, which in turn corresponds to a grating length of 58.425 mm. Moreover, the number of laser shots for each step has been increased up to 1500. Figure 6.14 shows the recorded transmission spectra of the manufactured LPG at dierent steps. As before, all the spectra have been normalized with respect to the source spectrum.

In the gure,

we have taken into account the two attenuation bands that are relate to the same two cladding modes. The rst attenuation band is now characterized by a resonance wavelength of 1499.6 nm and a transmission value of -17.84 dB that were obtained in the 65−th step, or rather for a grating length of 39.975 mm (violet curve). The second attenuation band is now characterized by a resonance wavelength of 1570 nm and a transmission value of -20.77 dB that were obtained in the 45−th step, or rather for a grating length of 27.675 mm (red curve). Moreover, the rst attenuation band, which is related to a lower

224


Figure 6.14: Transmission spectra of the manufactured LPG at dierent steps. Each curve is labeled with a dierent color (see the label in the graph)

order cladding mode than the second attenuation band, reaches its maximum transmission value (or the maximum coupling eciency) for a grating length greater than the second attenuation band, as expected from the theory. Therefore, it is clear that the second attenuation band at its maximum transmission value (or at its maximum coupling eciency) is achieved with a total number of laser shots (67500) lower than the rst attenuation band at its maximum transmission value (97500). On the contrary, in this second measure, the shift


225

of the LPG resonance wavelength is not clearly visible, whereas the maximum transmission value follows the same previously-discussed trend. This means that, when the grating length is a variable parameter, the maximum coupling eciency follows the same above-mentioned laws, whereas the simultaneous variation of both

nDC core

AC

and the induced-RI modulation of the ber core (ncore )

produces a not-so-appreciable change of the resonance wavelength. In fact, the term

nAC core

depends strongly on the length of the grating, as detailed in equa-

tion (3.39). In any case, the main contribution to the grating inscription is related to an average change of

∆ncore

that increases during each incremental

step (see again section 4.1). In order to give a sensible comparison between the two distinct approaches, it is obvious that the manufactured LPGs must have the same parameters, such as the length of the grating (and thus the number of steps) and the total number of laser shots for each steps (and thus the total number of laser shots). In this way, the value of

∆ncore

will be the same.

To do this, we xed the

following grating parameters:

grating period: 615

grating length: 30.75 mm;

total number of steps: 50;

total number of laser shots: 75000.

µm;

This means that the rst approach has been characterized by 15 scans of 100 laser shots for each step, whereas the second approach by a one scan of 1500 laser shots for each step. rst test as

shots.

For the sake of simplicity, we refer to the

many scans-few shots, whereas the second test as one scan-many

The results are detailed in gure 6.15.

Figure 6.15 shows the obtained

transmission spectra by means of the two distinct manufacturing processes. As regards the rst attenuation band, the obtained results are the following:

dierence of the resonance wavelength: 1.2 nm;

dierence of the transmission value: -0.43 dB.

As regards the second attenuation band, we obtained:


226

Figure 6.15: Comparison between the two distinct manufacturing approaches. The red curve refers to the rst approach (many scans-few shots), whereas the blue curve refers to the second approach (one scan-many shots)

dierence of the resonance wavelength: 0.4 nm;

dierence of the transmission value: 2.2 dB.

As can be seen, the small dierence in these two parameter for both the attenuation bands proves the quality and feasibility of the developed manufacturing system of OFGs.


227

As above-mentioned, we developed a hybrid cascaded conguration of OFGs made up of a LPG in series with a FBG [26].

By using the two

previously-described manufacturing techniques about the two dierent gratings, we obtain the transmission spectrum of the ber measured by means of the same OSA used during the gratings fabrication. The fabrication parameters used for the two gratings are the following:

Fiber Bragg grating

grating period

ΛFBG :

grating length

L:

529.95 nm;

1 cm.

Long period grating

grating period

number of grating planes: 40;

grating length

ΛLPG : L:

615

µm;

2.46 cm.

The transmission spectrum of the ber is shown in gure 6.16. It is worthy of noticing that transmission spectrum of the ber has been normalized with respect to the source spectrum. From the transmission spectrum showed in gure 6.16, some interesting optical parameters about the two gratings can be achieved:

Fiber Bragg grating

λFBG res :

resonance wavelength

eective RI of ber core


transmission: about -10 dB;

reectivity

R:

1534.2 nm;

ne core :

1.4475 RIU (see equation (2.7));

about 90%.

Long period grating

λLPG res (p) :

resonance wavelength

order of coupled cladding mode

1567 nm;

p:

7 (see gure 3.9);


228

Figure 6.16: Transmission spectrum of the ber with the FBG loss peak on the left and the LPG loss peak on the right. The green-highlighted distance between the two resonance bands is about 33 nm


transmission: about -15 dB.

The LPG optical parameters can also be prior estimated by means of the theoretical phase-matching curves, once the grating period has been chosen. Therefore, using the curves depicted in gure 3.9, the red line takes into account the selected grating period (ie 615

µm) and intersects ve curves that

are related to ve dierent PMCs of the cladding modes. Among these curves, the one whose value of the resonance wavelength (ie about 1570 nm) belongs to the wavelength range of the used optical source, is that corresponds to the fourth cladding mode (p

=

7) as highlighted by the green line.

Thus,

gure 6.17 demonstrated the feasibility and accuracy of the proposed manu-


229

Figure 6.17: Theoretical prediction of the LPG optical parameters

facturing technique of LPGs. Moreover, it is very important to note that the proposed grating manufacturing setup makes it possible to avoid any pre- and post-manufacturing operation, for example hydrogen loading of the ber, grating annealing, or more because of the high photosensitivity of the used optical ber. Finally, a key point of the properties of the transmission spectrum of the ber is given by the fact that the attenuation bands of both the FBG and LPG must be suciently separated, in order to avoid any interference problem during the RI measurements, assuming a decreasing of the LPG resonance wavelength, or rather a blueshift of the LPG resonance wavelength up to about 20 nm following a RI increase as it is reasonable to expect [27].

The achievement

of the FBG and LPG resonance wavelengths centered at 1534.2 nm and 1567 nm, respectively, assure that this point is satised (see gure 6.16).


230

6.5 Interrogation system and data processing

T

o complete the description of the experimental setup, the last part pertains to the system for both the grating interrogation and processing of

the data. In particular, the section that concerns the data processing, which is a key feature in the case of wavelength-based measurement, was totally designed and developed during my research. The optical ber containing the gratings is rstly spliced and then connectorized on both ends with FC/PC connectors. A broadband superluminescent diode (SLD, INPHENIX IPSDD1503) is used as the optical source and the transmission spectrum of the ber in the wavelength range of interest of both the FBG and LPG attenuation bands is recorded by means of an optical spectrum analyzer (OSA) with an optical resolution of 0.1 nm (Anritsu MS9030A and MS9701B). The OSA is connected to the computer via a GPIB interface and is controlled by means of an ad hoc developed NI CVI program. In order to measure the shift of the resonance wavelength of both the gratings, the developed software routine for each measurement step, rst for the LPG and then for the FBG, performs the following steps:

it centers at the corresponding resonance wavelength that is 1533−1534 nm for the FBG and 15601570 nm for the LPG;

it xes the wavelength range of interest, or rather the the

λ−span

that

is 2 nm for the FBG and 20 nm for the LPG;

it records the transmission spectrum of the ber;

it extrapolates and saves the minimum value of the resonance wavelength by means of a suitable data tting.

The total acquisition time of each measurement step is about 23 s.

This

not-so-small value could be represent a constraint in the case of biochemical sensing, where the dynamics of the reaction are usually very quick (tens of seconds). Therefore, this feature is certainly an issue to solve in the future. In order to obtain the best performance in terms of tting goodness, two dierent tting functions for the attenuation bands of the two gratings were used: a

Lorentzian tting function hLor (λ) for the LPG and a Gaussian tting

function

hGau (λ)

for the FBG. Their expressions are the following:

6.5. Interrogation system and data processing hLor (λ) = a0 +

231

a1 (λ − a2 )2 + a23

(λ − a2 )2 2 a23 hGau (λ) = a0 + a1 e

for LPGs

(6.3)

for FBGs

(6.4)

−

where

aj

(for

j = 0, 1, 2, 3)

are the four tting parameters. It is worth notic-

ing that the tting parameter

a2

corresponding grating, ie

or

λLPG res

is simply the resonance wavelength of the

λFBG res .

At the beginning, the initial value of

the four tting parameters must be entered, or rather the starting conditions must be specied into the developed program. Therefore, we found the initial values of the tting parameters, which are dierent between the two gratings, and these values are gathered in table 6.1.

Table 6.1: Used initial values of the tting parameters of the two gratings.

a0

a1

a2

a3

LPG

-3.53

-296

1576.28

31.5

FBG

-28.3

-10

1533.16

-200

For the sake of completeness, gure 6.18 shows the front panel of the developed NI CVI program.

It consists of some indicators, controls and graphs.

First of all, we have to enter the tting parameters for both the gratings. Then we can chosen the

λ−span,

the optical resolution of the OSA and the

number of averages for each measurement step. Lastly, it is possible to start the continuous recording of the transmission spectrum of both the gratings by pushing the green button saving. At this stage, following the above-discussed software routine, the two upper graphs account for the transmission spectrum of both the gratings (FBG on the left and LPG on the right) in the selected wavelength range. The yellow curves are the acquired raw data, whereas the

232


Figure 6.18: Front panel of the developed NI CVI program for the real time monitoring of the attenuation bands of the two gratings

green curves are the corresponding tting curves of FBG and LPG (see equations (6.4) and (6.3)).

By glancing at these two graphs, it can clearly be

observed that the two tting functions work properly. The two graphs at the bottom account for the time evolution of the resonance wavelength of both the gratings (FBG on the left and LPG on the right, again), which is simply

6.6. Fluidics system and chemicals the plot of the tting parameter

233

a2 ,

as explained previously. In this way, it

is possible to see in real-time the changes of both the resonance wavelengths. Moreover, at the top right of gure 6.18, the last four numbers in the box give the measured value of temperature of the ow cell. This last value together with the resonance wavelengths of FBG and LPG are saved into a single text le (.txt), which is used for further post-processing of the data. Finally, the experimental setup consists also of a peristaltic pump (Gilson MINIPULS 3). The ow cell is connected to the peristaltic pump by means of F117938 polyvinyl chloride (PVC) tubing (internal diameter: 1.02 mm), which makes it possible to pump the appropriate solution into the ow cell. The peristaltic pump allows us to vary the ow rate at the desired value. So the description of each device that belongs to the entire experimental setup for refractive index measurements has been completed.

Figure 6.19 shows

a comprehensive block diagram of the developed experimental setup for RI measurements.

6.6 Fluidics system and chemicals n order to characterized the proposed RI sensor, the solutions at dierent

I

refractive indices were prepared by mixing glycerol (RPE-ACS Carlo Erba

AnalytiCals®) and water in dierent volumetric ratios. The RI changed from the 1.334 RIU of pure distilled water up to 1.467 RIU of the last test solution. The RI of each solution has been measured prior by means of a hand−held refractometer (Atago R-5000) which works at the sodium D line (nD or

λ=

−3 refractive index unit (RIU). During 589.29 nm) with a resolution of 10 these measurements, the room temperature was monitored and kept constant at 23.0

±0.1.

During the refractive index measurements, the ow rate of

−1 .

the liquid pumped into the ow cell is kept constant at 0.5 mL min

The protocol followed for measuring the resonance wavelengths of the two gratings in the dierent solutions is summarized here as follows:

ow rate of about 0.5 mL min

halting of the peristaltic pump and acquisition of FBG and LPG minima

−1 for approximately 4 min;

extrapolated by the properly data tting functions for about 10 min.

234


Figure 6.19: Comprehensive block diagram of the refractive index measurements

It is worth observing that the value of the ow rate, when the liquids were pumped into the ow cell, was greater than that discussed above as long as the ow channel was completely lled with the investigated sample. In this way, it has been reduced to a minimum the problem of air bubbles that were formed along the ow channel.

Chapter 7

Compensated refractive index measurement for mixtures It is a miracle that curiosity survives formal education. Albert Einstein

the measurement of the RI of dierent glycerolwater mixtures is reported in order to both conrm the correct functioning and obtain the metrological parameters of the proposed system, including the RI sensitivity and resolution

7.1 Characterization of the sensor's cross-sensitivities 7.1.1 Strain characterization 7.1.2 Temperature characterization 7.1.3 Long-term stability of the sensor

7.2 Refractive index measurement (Sensorgram) (Response curve) (Sensitivity and Resolution)

Chapter 8

Preliminary biochemical measurement on antibody-antigen bioassay Knowledge is limited. Albert Einstein

8.1 An overview about antibody-antigen bioassay 8.2 Materials and methods 8.2.1 Reagents All the following chemicals were purchased from Sigma (Sigma-Aldrich S.r.l., Milan, Italy): ethanol (EtOH), bovine serum albumin (BSA), phosphatebuered saline (40 mM PBS, pH 7.4).

The methacrylic acid/methacrylate

copolymer (Eudragit L100) was purchased from Degussa, Röhm Pharma Polymers, Evonik Degussa GmbH, Düsseldorf, Germany.

The mouse IgG, goat

anti-mouse IgG and Cy5-labelled goat anti-mouse-IgG were purchased from Zymed Laboratories, Invitrogen Immunodetection, Milan, Italy. 1-Ethyl-3-[3dimethylaminopropyl] carbodiimide hydrochloride (EDC) and N-hydroxysuccinimide (NHS) were purchased from Pierce, Rockford, Illinois, USA. Mouse monoclonal antibody, anti-PSA (prostate-specic antigen), clone A67-B/E3, was kindly furnished by EXBIO Praha, Czech Republic.

8.2.2 Chemical treatment of the sensor and immunoassay LPG surfaces were functionalized by immersion in 2 mM Eudragit L100 in ethanol for 1 minute and then waiting about 15 minutes in air, until the complete solvent evaporation occurred. The polymeric deposition gives carboxylic

8. Preliminary biochemical measurement on antibody-antigen bioassay

238

functional groups (-COOH) to the surfaces, useful for antibody immobilization. Once the LPGs were functionalized, bers were collocated into the ow cell and all the following steps were performed in uidic condition at dier-

−1 for cross-linkers activation with EDC+NHS, −1 surface passivation with BSA and all the washings in PBS, and 25 µL min

ent ow rate of 250

µL

min

for mouse IgG antibody, anti-PSA antibody and all the concentration of goat anti-mouse IgG antigen. The activation of -COOH groups was carried out by means of EDC (2 mM) and NHS (5 mM) for 30 minutes. Immediately after, 1 mg L

−1 mouse IgG in PBS was used for covalent immobilization of antibodies

on the LPG. After 1 hour a washing step with PBS buer was performed. The surface passivation was carried out with 3% BSA in PBS for 15 minutes. The specicity of the sensor was tested introducing in the ow cell a solution of

−1 of anti-PSA antibody (a non-specic antigen for

PBS containing 10 mg L

the immobilized antibody). Immunoassays were then performed with dierent concentrations of goat anti-mouse IgG (from 0.1 mg L

−1 to 500 mg L−1 )

following the developed protocol, with 15 minutes of incubation time for the antigen and 5 minutes for PBS washing step. In order to demonstrate the ecacy of the novel functionalization chemistry using Eudragit L100 besides the commonly used silanization procedure [189], 1 mg L

−1 mouse IgG in PBS was

let ow directly on the LPG without any previous treatment. The established immunoassay protocol was then performed using 10 mg L

−1 goat anti-mouse

IgG in PBS as antigen solution. Although the LPGs are used for label-free applications, an immunoassay using labeled goat anti-mouse IgG was performed in order to verify the antibody/antigen interaction occurred along the ber.

The immobilization of

mouse IgG was obtained using the previously described protocol and 10 mg

−1 goat anti-mouse IgG labeled with Cy5, in PBS buer, was let ow for 15

L

minutes. After a washing step of 5 minutes in PBS a uorescence intensity measurement was performed.

8.3 Biochemical measurement on an antibody-antigen bioassay (Sensorgram) (Response curve) (Sensitivity and LOD)

Part III

Conclusions

Chapter 9

Conclusions

Anyone who has never made a mistake has never tried anything new. Albert Einstein

9.1 Summary and contributions 9.2 Tracks for future works

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Index

β -plot, 21 ω−tricosenoic

Bacteriophage, 5 acid, 182

Band-rejection lter, 170 Benzene, 173

Abbe number, 52 Abbe refractometer, 173 Absorption-based measurement, 175 Accurate refractive index measurement, 203 Acquisition time, 230 Acrylate-based polymer, 172 Aerospace application, 169 Air-clad optical ber, 172 Amino group, 179 Amperometric measurement, 191 Amplitude mask, 104 Amplitude mask technique, 101 Antibody, 5, 179 Antibody detection, 175 Antibody-antigen interaction, 175 Antifreeze, 4, 173 Antigen, 5, 179 Antigen detection, 175 Aptamer, 194 Argon ion laser, 88 Atomic-force microscope, 116 Azimuthal order, 31

Bessel function, 31 Bio-functionalization, 179 Bioassay, 5 Biochemical sensing, 176 Biological recognition element, 4, 175 Biological sensing, 2 Biological sensing element, 191 Biomedical eld, 194 Bioprocessing, 179 Bioreceptor, 194 Biosensor, 191 Biotin, 5 Biotin group, 179 Birefringence, 128 Blazed FBG, 86 Blood glucose detection, 192 Boundary condition, 57

Calcium chloride, 4 Cane sugar, 4, 173 Carboxylate group, 179 Cargille oil, 172 Cascaded Raman amplication, 168

Bacteria, 5

Chemical process analysis, 192

Bacteria detection, 193

Chemical sensing, 2, 176

268

INDEX

Chemiluminescence, 175

DNA oligonucleotide, 196

Chemiluminescence-based immunosensor,

Drug recognition, 175

193 Chirped FBG, 86

Dual resonant peaks, 56 Dual shaped core, 165

Chloride ion, 4, 173 Chloroform, 4, 197 Cladding mode coupling, 29 Clinical monitoring, 192 CO2 laser, 118 Coated OFG, 4 Colloidal gold nanoparticle, 5 Complex coupled mode theory, 67 Complimentary target, 196 Constructive interference, 17 Cooling rate, 123 Core-mode core-mode coupling constant, 40 Counter-propagating mode, 13 Coupled mode theory, 28 Coupling coecient, 30 Coupling constant, 39 Coupling factor, 64 Covalent bond, 179 Cross-sensitivity, 2, 202 Cultural heritage, 169

Eective refractive index, 21 Electric eld, 16 Electric eld vector, 30 Electrochemical micromachining, 3 Electromagnetic interference, 2 Electromagnetic wave, 16 Electrostatic self−assembly, 181 Energy band-gap, 102 Environmental monitoring, 179 Environmental surveillance, 192 Enzyme-Linked Immuno-Sorbent Assay, 175 Etched ber Bragg grating, 177 Ethanol, 4 Ethylene glycol, 4 Evanescent wave, 15, 178 Evanescent wave immunosensor, 193 Extrinsic optical ber sensor, 12 Fabry-Perot interferometric immunosensor, 193

Cut-o thickness, 182

FBG characteristic equation, 23

Cut-o wavelength, 107

FBG detuning parameter, 44 FC/PC connector, 230

Deoxyribonucleic acid, 194

Fiber bending, 2

Dierential eective refractive index, 65

Fiber Bragg grating, 5

Diraction grating, 16

Fiber cladding, 15

Diraction order, 19

Fiber core, 14

Dinitrophenol, 5

Fiber glass densication, 118

Dip-coating, 197

Fiber optic biosensor, 192

Dispersion compensation, 166

Fiber tapering, 125

Dispersion relation, 30

Fictive temperature, 123

Distributed Bragg reector, 169

Finite dierence, 68

DNA, 5

Finite element, 67

DNA hybridization, 194

Finite element method, 28, 79

INDEX

269

tting function, 230

Induced-index change, 84

Fitting goodness, 230

Intensity, 36

Flow cell, 5

Interferometric conguration, 2, 197

Flow rate, 233

Internal writing technique, 88

Fluorescence, 175

Intrinsic optical ber sensor, 11

Food manufacturing and storage, 192

Ion implantation, 130

Forward-propagating mode, 15

Isopropyl alcohol, 4

Fresnel equation, 70

IUPAC, 191

Fresnel reection, 164 Front panel, 231

Kerosene, 173

Full width at half maximum, 60

Kramers-Kronig principle, 103 Kronecker delta function, 40

Gain-attening lter for erbium doped ber ampliers, 170

Label-based assay, 175

Galerkin procedure, 67

Label-free, 1, 176

Gaussian tting function, 230

Laminar ow, 207

Geometrical optics, 13

LangmuirBlodgett, 181

Germanium dioxide, 11

Langmuir-Blodgett technique, 197

Germanium-oxygen-decient center, 107

Laser, 11

Glucose, 4, 173

Leaky mode, 68, 164

Glutarahyldehyde chemistry, 195

Ligand, 179

Glycerine, 4

Light emitting diode, 215

gold nanoparticle, 194

Limit of detection, 5

GPIB interface, 230

Linearly polarized, 31

Grating equation, 19

Liquid chromatography, 173

Grating period, 13

Liquid crystal material, 172 Local densication, 116

Heat sink, 206 Heating-cooling process, 123

Localized surface plasmon coupled uorescence, 194

Heavy metal detection, 193

Long period grating, 5

Heptane, 173

Long−term measurement, 208

Herbicide detection, 193

Longitudinal coupling coecient, 39

High refractive index, 184

Lorentzian tting function, 230

Hill grating, 90

Low volume, 203

Hybrid coupled mode theory, 67

Low-order, 36

Hydrogen, 4

LPG characteristic equation, 24 LPG detuning parameter, 46

Immunoglobulin detection, 194

Luminescence-based measurement, 175

Immunosensor, 179 Index perturbation, 39

Magnetic eld vector, 30

270

INDEX

Marine application, 169

Overlay refractive index, 181

Material dispersion, 52, 141, 150

Overlay thickness, 181

Maxwell's equation, 30 Medical application, 169

Peltier cell, 206

Medical diagnosis, 179

Perfectly matched layer, 67

Microuidic system, 5

Perfectly reecting boundary condition, 67

Mode conversion, 27 Mode equation, 51

Peristaltic pump, 233

Modied Bessel function, 31

Pesticide detection, 193

Modied phase mask method, 96

pH, 4

Molecular length, 182

Phase mask, 94

Multi-parameter sensing, 173

Phase mask method, 96

Mutation detection, 193

Phase mask technique, 91 Phase-matching condition, 14

Nano−coating technique, 181

Photochemical approach, 100

Nanostructured lm, 197

Photoelastic eect, 133

Narrow-bandwidth optical waveguide trans- Photonic crystal, 3 mission lter, 166

Photonic crystal ber, 79

Neumann function, 34

photosensitivity, 89

NI CVI program, 230

Physical eld, 140

Non-coated OFG, 4

Physiochemical transducer, 191

Non-photochemical approach, 101

Piezoelectric shear, 191

Non-specic adsorption, 175

Pipeline monitoring, 169

Normalized eective refractive index, 31

Planar waveguide, 191

Nuclear magnetic resonance, 169

Pockel's coecient, 142

Numerical aperture, 31

Point-to-point technique, 101

Oil detection, 189 Oligonucleotide, 195 Optical add/drop multiplexer, 166 Optical ber, 11 Optical ber grating, 2 Optical ber mode converter, 168 Optical ber sensor, 2, 11 Optical lter, 166

Pollutant detection, 193 Polymer, 4 Potentiometric measurement, 191 Pressure, 2 Propagation constant, 21, 30 Prostate specic antigen, 194 Pulse shaping, 166 PVC tubing, 233

Optical resolution, 217

Quality control in beverage, 194

Optical resonating structure, 2

Quality control in food, 194

Optical spectrum analyzer, 215, 230 Optimum overlay thickness, 187

Radian frequency, 30

Organic aromatic compound, 173

Radiation mode, 164

INDEX

271

Radiation mode coupling, 29

Streptavidin, 5

Radio frequency interference, 2

Structural health monitoring, 169

Rayleigh length, 116

Sucrose, 4

Receptor, 179

Super-paramagnetic nanoparticle, 194

Reection grating, 13

Superluminescent diode, 215, 230

Refractive index, 1

Surface acoustic waves, 191

Refractive index prole, 84

Surface measurement, 3

Refractive index sensitivity, 179

Surface plasmon resonance, 1, 176, 196

Refractometric measurement, 3

Surrounding refractive index, 2, 148

Residual stress relief, 118

Swine-origin inuenza A, 194

Resolution, 2

Syndiotactic polystyrene, 197

Resonance wavelength, 29 Root mean square deviation, 174 RS−232 serial interface, 207

Sandwich immunoassay, 194 Selectivity, 4, 179 Sellmeier equation, 52 Semiconductor laser component, 166 Sensitivity, 2 Severe acute respiratory syndrome, 194 Silica, 11 Single mode ber, 12 Single stranded DNA, 195 Slab waveguide theory, 188 Snell's law, 13 Sodium chloride, 4 Sodium D line, 233 Softening temperature, 123 Sol-gel, 4 Source-tunable interferometer technique, 94 Space and aeronautics, 192 Species-specic sensor, 196 Spectral range, 56 Splicing machine, 122

TEC control system, 208 Temperature, 2 Temperature gradient, 125 Temperature measurement system, 203 Thermal expansion coecient, 144 Thermistor, 207 Thermo−stabilized ow cell, 203 Thermo-electric cooler, 206 Thermo-optic coecient, 144 Thermocouple, 203 Thermometric measuring unit, 207 Tilted ber Bragg grating, 177 Total excitation energy, 103 Total internal reection, 103 Transfer matrix method, 28 Translation stage, 107 Transmission grating, 15 Transparent inux boundary condition, 67 Transverse coupling coecient, 39 Transverse distribution, 36 Transverse holographic technique, 92 Turn around point, 55 Two-beam interferometer technique, 91 Two-layer model, 164

SPR immunosensor, 193 Step-index, 27

Uniform FBG, 86

Strain, 2

UV spectroscopy, 173

272

V-number, 31 Vacuum electric permittivity, 30 Vacuum magnetic permeability, 30 Vapor, 4 Virus detection, 193 Volatile organic compound, 4 Volume measurement, 3 Waveguide dispersion, 52, 149, 150 Wavelength division multiplexing, 167 Wavelength selective device, 167 Weakly guiding approximation, 28 Xylene, 4, 173

INDEX

Publications List

Il tutto è maggiore della somma delle parti Aristotele Metasica

In press (1)

CHIAVAIOLI F, MUGNAINI M, TRONO C, BALDINI F, and BRENCI M,

CASCADED LPG AND FBG INTEGRATED IN A MINIATURIZED FLOW CELL FOR COMPENSATED REFRACTOMETRIC MEASUREMENT, In:

(A. D'Amico et al. Eds.) Lecture Notes in Electrical Engineering: Sensors and Mi-

crosystems: AISEM 2011 Proceedings, vol.

109, NEW YORK: SPRINGER SCI-

ENCE+BUSINESS MEDIA, ISBN: 9781461409342, doi: 10.1007/978-1-4614-09359_41, 2012.

2012 (2)

BALDINI F, BRENCI M, CHIAVAIOLI F, GIANNETTI A, and TRONO C,

OPTICAL FIBRE GRATINGS AS TOOLS FOR CHEMICAL AND BIO-

274

INDEX

CHEMICAL SENSING, Analytical and Bioanalytical Chemistry (Springer Berlin

/ Heidelberg), vol. 402 (1), p. 109116, ISSN: 1618-2642, doi: 10.1007/s00216-0115492-3, 2012.

2011 (3)

BALDINI F, BRENCI M, CHIAVAIOLI F, GIANNETTI A, and TRONO C,

OPTICAL FIBER REFRACTOMETER BASED ON A LONG PERIOD GRATING AND AN ACCURATE CROSS-SENSITIVITIES COMPENSATION SYSTEM INTEGRATED INTO A THERMO-STABILIZED FLOW CELL, In:

4th EOS Topical Meeting on Optical Microsystems (OµS'11), Capri

(NA) - Italy, September 26 - 28, paper 4555, 2011.

(4) CHIAVAIOLI F, MUGNAINI M, BALDINI F, BRENCI M, GIANNETTI A, and TRONO C, RIFRATTOMETRO IN FIBRA OTTICA BASATO SU RETICOLO A PASSO LUNGO CON SISTEMA DI AUTOCOMPENSAZIONE DELLE CROSS SENSIBILITA', In: Atti del XXVIII Congresso Nazionale del

Gruppo Misure Elettriche ed Elettroniche, Palazzo della Borsa - Sala delle Grida Via XX Settembre 44 - Genova (GE), 12 - 14 Settembre, 2011.

(5)

TRONO C, BALDINI F, BRENCI M, CHIAVAIOLI F, and MUGNAINI M,

FLOW CELL FOR STRAIN- AND TEMPERATURE-COMPENSATED REFRACTIVE INDEX MEASUREMENTS BY MEANS OF CASCADED OPTICAL FIBRE LONG PERIOD AND BRAGG GRATINGS, Measurement

Science & Technology (IOP Publishing), vol. 22 (7), p. 075204, ISSN: 0957-0233, doi: 10.1088/0957-0233/22/7/075204, 2011.

(6) TRONO C, BALDINI F, BRENCI M, CHIAVAIOLI F and FALCIAI R, FLOW CELL WITH HYBRID LPG AND FBG OPTICAL FIBER SENSOR FOR REFRACTOMETRIC MEASUREMENTS, In:

Proceedings of 21st Interna-

INDEX

275

tional Conference on Optical Fiber Sensors, Ottawa - Canada, May 15 - 19, vol. 7753, p. 775392, doi: 10.1117/12.885126, 2011.

(7)

TRONO C, BALDINI F, BRENCI M and CHIAVAIOLI F, LONG PERIOD

GRATING-BASED OPTICAL FIBRE SENSOR WITH INTERNAL OPTICAL FEEDBACK FOR THE RELIABLE MEASUREMENT OF REFRACTIVE INDEX IN LIQUID SAMPLES, In:

Atti del XIII Convegno Nazionale

delle Tecnologie Fotoniche, Palazzo Ducale - Genova (GE), 9 - 11 Maggio, 2011.

(8)

TRONO C, BALDINI F, BRENCI M, CHIAVAIOLI F, FALCIAI R, GIAN-

NETTI A and MUGNAINI M, LONG PERIOD AND FIBER BRAGG GRATINGS WRITTEN WITHIN THE SAME FIBER FOR SENSING PURPOSES,

In: Proceedings of SPIE Photonics West 2011, Integrated Optics: Devices, Materials,

and Technologies XV, The Moscone Center - San Francisco, California, USA, January 22 - 27, vol. 7941, p. 794112, doi: 10.1117/12.873796, 2011.

2010 (9)

CHIAVAIOLI F, MUGNAINI M, BALDINI F, BRENCI M, GIANNETTI A and

TRONO C, SENSORE DI INDICE DI RIFRAZIONE IN FIBRA OTTICA BASATO SU RETICOLI A PASSO LUNGO, In: Atti del XXVII Congresso

Nazionale del Gruppo Misure Elettriche ed Elettroniche, Centro Congressi Hotel Summit - Gaeta (LT), 13 - 15 Settembre, 2010.

2009

276

(10)

INDEX

FORT A, CHIAVAIOLI F, LOTTI C, MUGNAINI M, ROCCHI S and VIG-

NOLI V, A LABORATORY IMPEDANCE METER FOR ELECTROCHEMICAL SENSORS, In:

AIP Conference Proceedings, vol.

1137, p.

303-305, doi:

10.1063/1.3156532, 2009.

(11)

FORT A, CHIAVAIOLI F, LOTTI C, MUGNAINI M, ROCCHI S and VIG-

NOLI V, IMPEDENZIMETRO DA LABORATORIO PER LA CARATTERIZZAZIONE DI SENSORI ELETTROCHIMICI, In: Atti del XXVI Congresso

GMEE Gruppo Misure Elettriche ed Elettroniche, Salerno, 16 - 19 Settembre, 2009.

Design, Development and Test of a Refractometer

Design, Development and Test of a Refractometer

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