sensors Article
Investigation of A Slow-Light Enhanced Near-Infrared Absorption Spectroscopic Gas Sensor, Based on Hollow-Core Photonic Band-Gap Fiber Zhi-Fa Wu, Chuan-Tao Zheng *, Zhi-Wei Liu, Dan Yao, Wen-Xue Zheng, Yi-Ding Wang, Fei Wang * and Da-Ming Zhang State Key Laboratory of Integrated Optoelectronics, College of Electronic Science and Engineering, 2699 Qianjin Street, Jilin University, Changchun 130012, China;
[email protected] (Z.-F.W);
[email protected] (Z.-W.L.);
[email protected] (D.Y.);
[email protected] (W.-X.Z.);
[email protected] (Y.-D.W.);
[email protected] (D.-M.Z.) * Correspondence:
[email protected] (C.-T.Z.);
[email protected] (F.W.); Tel.: +86-137-5609-0979 (C.-T.Z.) Received: 3 May 2018; Accepted: 2 July 2018; Published: 7 July 2018
Abstract: Generic modeling and analysis of a slow-light enhanced absorption spectroscopic gas sensor was proposed, using a mode-tuned, hollow-core, photonic band-gap fiber (HC-PBF) as an absorption gas cell. Mode characteristics of the un-infiltrated and infiltrated HC-PBF and gas absorption enhancement of the infiltrated HC-PBF were analyzed. A general rule of microfluidic parameters for targeting different gas species in the near-infrared was obtained. Ammonia (NH3 ) was used as an example to explore the effects of slow light on gas detection. The second harmonic (2f ) signal and Allan deviation were theoretically investigated based on the derived formulations. Keywords: photonic band-gap fiber; infrared absorption spectroscopy; gas sensor; slow light
1. Introduction The sensitive and selective detection of trace chemicals is important for environmental, safety, and industrial process monitoring, as well as in national security applications. Infrared absorption spectroscopy, which relies on the absorption lines of a gas molecule for identifying and detecting trace chemicals, is suitable for gas detection [1,2]. Conventional absorption spectroscopic sensor systems [3–5], such as cavity-enhanced absorption spectroscopy, are ultrasensitive, but are large and have a heavy tabletop instrument that requires a large gas cell with a long absorption path length. Recently, there has been an increasing emphasis on the miniaturization of chemical analysis systems and optics, such as lab-on-a-chip microsystems [6–8] and fiber optic sensors [9,10]. In particular, miniaturized gas sensors based on photonic hollow-core crystal (PHC) waveguides are receiving attention for achieving superior performance in optical signal processing and sensing applications [11–13]. Intuitively, slow-light propagation offers photons more time and increases the effective optical length for interacting with a host medium (e.g., gas molecules) [14,15]. Infrared absorption spectroscopy is based on the absorption of a gas molecule on an infrared light with a specific wavelength. Different molecules have different absorption wavelengths, leading to the unique selectivity of the technique. Therefore, this technique is particularly suitable for the detection of gas mixtures. Silicon PHC slot waveguide gas sensors based on the Beer-Lambert law have been demonstrated [7,11]. Besides, a hollow-core photonic band-gap fiber (HC-PBF) allows the confinement of an optical mode and chemical materials simultaneously within the hollow core and provides an ideal platform for strong light-matter interactions over a long distance [15]. Thus, there are a wide variety of gas sensors based on HC-PBFs for the detection of different gas species or for the Sensors 2018, 18, 2192; doi:10.3390/s18072192
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application different signal processing techniques. ordetection HC-PBF of sensors have unique are a wideofvariety of gas sensors based on HC-PBFs PHC for the different gas speciesdispersive or for properties that allow for the control and manipulation of light-matter interactions on the length scale the application of different signal processing techniques. PHC or HC-PBF sensors have unique of the light wavelength, byallow infiltrating into selected holes of interactions PHC devices, dispersive properties that for the optical control fluids and manipulation of air light-matter on which the length scale of the by infiltrating fluids into selected air holes of PHC devices, makes it possible to light tunewavelength, and reconfigure photonicoptical devices suitable for various applications. which makes possible tune and reconfigure devices applications. In view of itthe abovetoconsiderations, as thephotonic main focus andsuitable noveltyforofvarious the paper, we propose In view of the above considerations, as the main focus and novelty of the paper, we propose a a generic design and analysis of a slow-light enhanced absorption spectroscopic gas sensor based design of a slow-light enhanced absorption gas the sensor based on of on generic HC-PBF. The and ideaanalysis and simulation of selective infiltration of spectroscopic HC-PBF to tune wavelength HC-PBF. The idea and simulation of selective infiltration of HC-PBF to tune the wavelength of the for the maximum enhancement factor for specific modes are proposed. The microfluidic parameters maximum enhancement factor for specific modes are proposed. The microfluidic parameters forthe targeting different gas species are obtained. Ammonia (NH3 ) is used as an example to explore targeting different gas species are obtained. Ammonia (NH3) is used as an example to explore the effects of slow light on gas detection as a reference in the design and development of such kind of effects of slow light on gas detection as a reference in the design and development of such kind of gas gas sensors. sensors.
2. Modeling of the Hollow-Core Photonic Band-Gap Fiber-Based Spectroscopic Gas Sensor 2. Modeling of the Hollow-Core Photonic Band-Gap Fiber-Based Spectroscopic Gas Sensor
A simplified schematic of an HC-PBF-based spectroscopic gas sensor is shown in Figure 1a, A simplified schematic of an HC-PBF-based spectroscopic gas sensor is shown in Figure 1a, which includes a tunable distributed feedback laser (DFBL), two pieces of single-mode fiber (SMF), which includes a tunable distributed feedback laser (DFBL), two pieces of single-mode fiber (SMF), a a HC-PBF an infrared infrared detector detector(Det), (Det),a apre-amplifier pre-amplifier (kR), and a lock-in amplifier HC-PBF for for gas gas sensing, sensing, an (kR), and a lock-in amplifier (Lock-in). Figure 1b,c(1b,1c) show show the two-dimensional (2-D)(2-D) cross-section viewview of an withwith a lattice (Lock-in). Figures the two-dimensional cross-section ofHC-PBF an HC-PBF a constant a, an air hole diameter of d = 0.9a, and a hollow core diameter of D = 2.52a. The lattice lattice constant a, an air hole diameter of d = 0.9 a , and a hollow core diameter of D 2.52 a . The of lattice air holes inholes the simulation is definite, which is similar shownininthethe scanning of air in the simulation is definite, which is similartotothe thestructure structure shown scanning electron microscope (SEM) image of the Figure 1d, commercially available from NKT electron microscope (SEM) image of fiber the in fiber in Figure 1d, commercially available fromPhotonics NKT (Birkerød, Denmark). gray circles represent the hollow holesairand core, the blue Photonics (Birkerød, The Denmark). The gray circles represent theair hollow holes andwhile core, while the regions blue regions the represent the chalcogenide glasswith (ChG) with a refractive linear refractive 0 = 2.8. represent chalcogenide glass (ChG) a linear indexindex of n0 of =n 2.8. Gas in DFBL
SMF
Gas out
HC-PBF
(a) us(t)
SMF
Det
kR
Lock -in
A2f(t) infiltrating optical fluids
d =0.9a
a
D
(b)
(c)
(d)
Figure 1. (a) Schematic of a hollow-core photonic band-gap fiber (HC-PBF)-based spectroscopic gas
Figure 1. (a) of show a hollow-core photonic band-gap (HC-PBF)-based spectroscopic sensor. TheSchematic sub-figures (b) the cross-section structure fiber by un-infiltrating optical fluids to thegas sensor. The sub-figures show (b) the cross-section structure by un-infiltrating optical fluids HC-PBF, and (c) the cross-section structure by infiltrating optical fluids into the selected air holestoofthe HC-PBF, and (c) the cross-section structure by infiltrating optical fluids into the selected air holes of the the HC-PBF. (d) Scanning electron microscope (SEM) image of the HC-PBF commercially available HC-PBF. (d) Scanning electron microscope (SEM) image of the HC-PBF commercially available from from NKT optics. NKT optics. The principle of infrared absorption spectroscopy is based on the Beer-Lambert law [4,5], given by:The principle of infrared absorption spectroscopy is based on the Beer-Lambert law [4,5], given by:
𝐼(𝜆) = 𝐼 (𝜆)exp[− 𝛾(𝜆)𝛼(𝜆)𝐶𝐿],
I (λ) = I0 (λ) exp[−γ(λ)α(λ)CL],
(1)
(1)
where I0 is the incident light intensity; 𝛼(λ) is the gas absorption coefficient at the wavelength of λ; C is Itheis gas is the optical length; and coefficient γ is a wavelength-dependent, where the concentration; incident lightLintensity; α(λ) interaction is the gas absorption at the wavelength of 0 medium-specific absorption enhancement factor, due to slow-light effect in dispersive structures. In λ; C is the gas concentration; L is the optical interaction length; and γ is a wavelength-dependent, conventional free-space systems, γ = 1. For PHC devices, the enhancement factor γ is
medium-specific absorption enhancement factor, due to slow-light effect in dispersive structures. ⁄ In conventional free-space systems, γ = 1. 𝛾For PHC the enhancement factor γ is =𝑓 × devices, , (2)
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γ= f×
c/n , vg
(2)
where f is a filling factor denoting the relative fraction of the optical field, c is the light wave velocity in free space, and vg = dω dβ = c/ng is the light wave group velocity. From Equation (2), the enhancement factor can obviously be increased by either a small vg or a high f. Due to the use of high-frequency wavelength modulation for 1/f noise suppression, and a lock-in amplifier for further noise suppression, wavelength modulation spectroscopy (WMS) is more sensitive than the direct absorption spectroscopy (DAS) technique. Therefore, the WMS technique is usually adopted in an infrared gas sensor system. In this work, WMS is used as an example, to show how this enhancement will affect the second harmonic signal. This technique requires that the emitting wavelength of the laser must be stabilized, in order to be the peak absorption wavelength for a certain gas molecule. A periodic saw-tooth signal is used to scan the absorption line, which can be expressed in one period as: Asaw usaw (t) = Asaw + (t − Tsaw ), 0 ≤ t ≤ Tsaw , (3) Tsaw where Asaw and Tsaw are the amplitude and period of the sawtooth signal, respectively. Also, a sinewave signal, expressed as: Asin usin (t) = sin(ωsin t), (4) 2 is used to modulate the laser, where Asin and ω sin are the amplitude and the angular frequency of the sinewave signal, respectively. Thus, the total driving signal of the DFBL is us (t) = usaw (t) + usin (t).
(5)
Under the operation of u(t), the variation of the emitting wavelength leads to a change of the absorption coefficient α(t), expressed as [5]: α(t) =
α0
1+
2 , υ0 + δu(t) − υg /γ0
(6)
where υ0 is the central emitting wavenumber (determined by the laser operating temperature), υg is the central absorption wavenumber of the targeted gas molecule, α0 is the gas absorption coefficient at υ0 , γ0 is the half-width of the absorption peak at υ0 , and δ is a light modulation coefficient. The laser power can be expressed as Equation (7): Pt (t) = KEO Gu(t),
(7)
where G is a voltage-to-current conversion coefficient of the laser driver, and KEO is a voltage-to-optical conversion coefficient of the laser. The SMF will couple with the HC-PBF for gas sensing. Let the normalized mode field distribution of the SMF be ESMF . The mode coupling coefficient η m between SMF and the m-th guided mode of the HC-PBF can be determined by Equation (8): s
E∗ Em dxdy ηm = s SMF PBF . Em 2 dxdy
(8)
PBF
Then, with two coupling effects between the SMF and the HC-PBF, the input power to the second SMF without gas absorption is given by Equation (9): 2 Pt,PBF (t) = Pt (t)∑ ηm . i
(9)
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Pr t Pt t m2 exp m t t CL ,
(10) i Considering a slow-light induced gas absorption loss, the input power to the second SMF is where m t is a time‐dependent enhancement factor of the m‐th HC‐PBF mode. The detector signal 2 Pr (t) = Pt (t)∑ ηm exp[−γm (t)α(t)CL], (10) from the pre‐amplifier can be expressed as: i
ud (t ) kRK ) m2of exp m tHC-PBF t CLmode. OE K EO Gus (tfactor (11) , The detector signal where γm (t) is a time-dependent enhancement them-th i from the pre-amplifier can be expressed as: where kR is the gain of the pre‐amplifier, and KOE is the optical‐to‐electrical conversion coefficient of 2 ud (t) we = kRK KEO Gus (t)∑ ηlock‐in γm (t)α(t)to CLextract (11) ], m exp[− the infrared detector. Next, use OE an orthogonal amplifier the 2f signal from i
ud (t ) , as:
where kR is the gain of the pre-amplifier, and KOE is the optical-to-electrical conversion coefficient 2 2 (12) of the infrared detector. Next, we use to extract the 2f signal from , A2fan A2f , lock-in + A2f , amplifier t orthogonal ud (t), as: r t t an where A2f , t ud ( )sin 2A sin(t)d= , AA2f , t 2+ A ud ( )2 ,cos 2sin d and Tint 2 is (12) t Tint2 t Tint2 2 f ,k 2f 2 f ,⊥
integral time factor, determined by the cutoff frequency of the related low‐pass filter. Rt Rt where A2 f ,⊥ (t) = t−T ud (τ ) sin(2ωsin τ )dτ, A2 f ,k (t) = t−T ud (τ ) cos(2ωsin τ )dτ and Tint2 is an int2 int2 integral time factor, determined by the cutoff frequency of the related low-pass filter. 3. Mode Analysis of Hollow‐Core Photonic Band‐Gap Fiber 3. Mode Analysis of Hollow-Core Photonic Band-Gap Fiber 3.1. Uninfiltrated Hollow‐Core Photonic Band‐Gap Fiber Mode Analysis 3.1. Uninfiltrated Hollow-Core Photonic Band-Gap Fiber Mode Analysis Based on the commercial software Comsol 5.0, by using the finite element method (FEM)‐based plane wave expansion code to solve the Maxwell’s equations, it is feasible to obtain the photonic band Based on the commercial software Comsol 5.0, by using the finite element method (FEM)-based structure for the un‐infiltrated PBF. The gray region extending over the normalized frequency range plane wave expansion code to solve the Maxwell’s equations, it is feasible to obtain the photonic band of 0.4877 ≤ a/λ ≤ 0.51105 represents the photonic band gap (PBG) region of the HC‐PBF. Six modes structure for the un-infiltrated PBF. The gray region extending over the normalized frequency range of were found to be confined along the fiber hollow core, as shown in Figure 2(a1, b1, and c1), as well 0.4877 ≤ a/λ ≤ 0.51105 represents the photonic band gap (PBG) region of the HC-PBF. Six modes were as Figure Among modes, modes and 6 3a–c) cannot be confined found to be3a–c. confined alongthese the fiber hollow core,4, as5, shown in(Figure Figure 2(a1,b1,c1), as well as Figurewhen 3a–c. propagation constant β0, indicating that they do not possess a slow‐light property. As constant seen in Among these modes, modes 4, 5, and 6 (Figure 3a–c) cannot be confined when propagation Figure 2(a1, b1, and c1), the three black curves, indicated by triangles in the PBG area, represent the β →0, indicating that they do not possess a slow-light property. As seen in Figure 2(a1,b1,c1), the three dispersion of by the three guided optical for zero propagation constant black curves,relation indicated triangles in the PBG area, modes represent thethe dispersion relation of the three (βα/2π = 0). Figure 2(a2, b2, and c2) show the group index n g of the three modes, which will reach a guided optical modes for the zero propagation constant (βα/2π = 0). Figure 2(a2,b2,c2) show the peak propagation constant β0. group index n of the three modes, which will reach a peak propagation constant β→0. g
0.52
(a1)
mode 1, nf=1.0
10
mode 1, nf=1.2
0.51
(a2) mode 1, nf=1.0 mode 1, nf=1.1 mode 1, nf=1.2
ng
a/2c = a/
mode 1, nf=1.1
2
0.50
10
1
0.49 0.00
0.05
0.10
0.15
a / 2
0.20
0.25
0.485 0.490 0.495 0.500 0.505 0.510 0.515
a/2c=a/
Figure 2. Cont. Figure 2. Cont.
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(b2)
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0.51
mode 2, n =1.1
f mode 2, nf=1.1
ngng
0.51
mode 2, nf=1.0 0.50 mode 2, nf=1.0 0.50 mode 2, nf=1.1 mode 2, nf=1.1 mode mode2,2,nnf=1.2 =1.2 0.49 f 0.49 0.00 0.00 0.05 0.05 0.10 0.10 0.15 0.15 0.20 0.20 0.25 0.25
mode 2, n =1.2
1
10 1
(c1)(c1) 0.52 0.52
0.495 0.500 0.505 0.5050.510 0.5100.515 0.5150.520 0.520 0.525 0.495 0.500 0.525
/2πc= c=aa//λ ωaa/2
(c2) (c2) 22
10 10
mode mode3,3,nf=1.0 n =1.0
0.51 0.51
f
0.49
0.49
0.00
0.05
0.05
0.10
0.10
mode3,3,nn=1.0 =1.0 mode f f mode3,3,nn=1.1 =1.1 f mode f mode 3, nf=1.2 mode 3, nf=1.2
0.15
0.15
a/2 βa/2π
0.20
0.20
mode mode3,3,nf=1.1 n =1.1
nngg
0.50 0.50
0.00
f mode 2, nf=1.2
10
βa/2 π a/2
ωa/2πc=a/λ a/2c=a/
(b2)
2
0.25
0.25
f
mode mode3,3,nf=1.2 n =1.2 f
10 10
1
1
0.506 0.508 0.510 0.512 0.514 0.516 0.518
0.506 0.508 0.510 0.512 0.514 0.516 0.518
a/2c=a/ ωa/2πc=a/λ
Figure Photonicband bandgap gapand and group group index (a1,(a1,a2) a2) mode 1, (b1, b2) mode 2, 2, Figure 2. 2. Photonic indexof ofinfiltrated infiltratedHC-PBF; HC-PBF; mode 1, (b1,b2) mode Figure 2. Photonic band gap distributions and group index of infiltrated HC-PBF; (a1, a2)HC-PBF mode 1,with (b1, slow-light b2) mode 2, and (c1, c2) mode 3. Field of guided optical modes 1–3 in the and (c1,c2) mode 3. Field distributions of guided optical modes 1–3 in the HC-PBF with slow-light andeffect (c1, c2) mode 3. Field Figures distributions optical modes 1–3 in the HC-PBF with slow-light also shown a1, b1, of andguided c1, respectively. effect areare also shown ininFigures a1, b1, and c1, respectively. effect are also shown in Figures a1, b1, and c1, respectively.
Figure 3. Field distributions of guided optical modes 4–6 in the HC-PBF without slow-light effect are shown in(a) Figures (a), (b), and (c), respectively. (b) (c)
Figure 3.3.Field distributions of optical modes 4–6 in 3.2. Infiltrated Hollow-Core Photonic Band-Gap Fiber Mode Figure Field distributions ofguided guided optical modes 4–6Analysis inthe theHC-PBF HC-PBFwithout withoutslow-light slow-lighteffect effectare are shown in Figures (a), (b), and (c), respectively. shown in Figures (a), (b), and (c), respectively. Optical fluids with different indices (nf = 1.0, 1.1, 1.2) were infiltrated into the selected green air holes, which can be realized by Band-Gap using the Fiber selective infiltration 3.2. Infiltrated Hollow-Core Photonic Mode Analysis methods presented in [17,18]. The 3.2.dispersion Infiltratedrelations Hollow-Core Band-Gap Mode and Photonic the group index ofFiber modes 1, 2,Analysis and 3 for infiltrating fluids with different Optical fluids with different indices (nfin= 1.0, 1.1,2a–c. 1.2) were infiltrated region into the selected air indices were calculated, and are shown Figure The slow-light to green a long Optical fluids with different indices (nf = 1.0, 1.1, 1.2) were infiltrated intoshifted the selected green holes, which can be realizedthebyrefractive using the selective infiltration methods presented in [17,18]. The wavelength by increasing index of optical fluids. At the band edge, the group indices air holes, which can be realized by using the selective infiltration methods presented in [16,17]. dispersion relations the group index group of modes 1, 2,was andfar 3 for infiltrating fluids different sharply;and correspondingly, velocity the speed of with light in free Theincreased dispersion relations and the groupthe index of modes 1, 2, and 3less forthan infiltrating fluids with different space,were and acalculated, large groupand velocity dispersion Mode 1 got completely out of the indices are shown in (GVD) Figureoccurred. 2a–c. The slow-light region shifted to PBG a long indices were calculated, and are shown in Figure 2a–c. The slow-light region shifted to a long region with and thus only modes 2 and fluids. 3 are considered. For edge, a giventhe fluid, however, wavelength byinfiltrating increasingfluids, the refractive index of optical At the band group indices wavelength by increasing the refractive index of optical fluids. At the band edge, the group indices the wavelength experienced bythe mode 2 wasvelocity significantly larger that of speed mode 3.ofThis results increased sharply;shift correspondingly, group was far lessthan than the light in free
increased sharply; correspondingly, the group velocity was far less than the speed of light in free space, and a large group velocity dispersion (GVD) occurred. Mode 1 got completely out of the PBG space, and a large group velocity dispersion (GVD) occurred. Mode 1 got completely out of the PBG region with infiltrating fluids, and thus only modes 2 and 3 are considered. For a given fluid, however,
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region with infiltrating fluids, and thus only modes 2 and 3 are considered. For a given fluid, however, the wavelength shift experienced by mode 2 was significantly larger than that of mode 3. This results from the fact that the electrical field intensity of mode 2 in the selected air holes with infiltrated fluids was stronger than that of mode 3. Different degrees of shift led to different degrees of wavelength Sensors 2018, 18, x 6 of 10 tuning: mode 2 is suitable for coarse tuning, and mode 3 is suitable for fine tuning of a slow-light region. Without thethe need to change the structural parameters of theair fiber, guided modes of an from the fact that electrical field intensity of mode 2 in the selected holesthe with infiltrated fluids appropriately designed slow-light regime by use of selectively infiltrated HC-PBF can be tuned to was stronger than that of mode 3. Different degrees of shift led to different degrees of wavelengththe absorption line of2 aistarget gasfor species desired formode maximizing the gas tuning: mode suitable coarseas tuning, and 3 is suitable for absorption. fine tuning of a slow-light region. Without the need to change the structural parameters of the fiber, the guided modes of an
3.3.appropriately Slow-Light Effect Analysis designed slow-light regime by use of selectively infiltrated HC-PBF can be tuned to the
absorption line of targetwith gas a species as desired for maximizing the gas aabsorption. The HC-PBF is afilled homogeneously distributed gas with complex refractive index of
n = n0 + n00 = 1 + n00 (n0 = 1), where the imaginary part n” is an extinction coefficient that relates to 3.3. Slow-Light Effect Analysis fiber absorption loss. The relationship between the extinction coefficient n00 and the gas absorption The HC-PBF with a homogeneously distributed gas with a complex refractive index of loss coefficient αg (λ)isisfilled as follows: 𝑛 = 𝑛 + 𝑛 = 1 + 𝑛 (𝑛 = 1), where the imaginary part n’’ is an extinction coefficient that relates to 4π 00 coefficient 𝑛 and the gas absorption fiber absorption loss. The relationship between the00 extinction n . (13) αg (λ) = 2kn = λ loss coefficient 𝛼 (𝜆) is as follows: 4𝜋 By using finite element method (FEM) to numerically 𝛼 (𝜆) = 2𝑘𝑛 = solve 𝑛 .the wave equation:
(13)
𝜆
2
00 = (n0the + in ) , equation: ∇method × (∇ ×(FEM) E) − Kto02 εnumerically By using finite element wave γ E = 0, ε γ solve
(14) (14)
∇ × (∇ × 𝐸) − 𝐾 𝜀 𝐸 = 0, 𝜀 = (𝑛 + 𝑖𝑛 ) ,
we can calculate the complex propagation constants β = β0 + iβ00 and obtain the absorption loss of can calculate the complex propagation constants = 𝛽 + i𝛽 propagation and obtain the absorption an we infiltrated HC-PBF. The relationships between the𝛽 complex constants β =loss β0 +ofiβ00 an infiltrated HC-PBF. The relationships between the complex propagation constants and the normalized frequency α/λ for mode 3 of the un-infiltrated and infiltrated HC-PBF are shown 𝛽 = 𝛽4.+From i𝛽 and the 4a, normalized frequency 𝛼⁄𝜆 for mode 3 of the un-infiltrated and infiltrated in Figure Figure the dispersion departed significantly from the ideal lossless case in the 0 HC-PBF are shown in Figure 4. From Figure 4a, the dispersion departed significantly from the assumed slow-light regime near β → 0 . The dispersion relation curve dropped sharply when ideal β0 → 0 , lossless case in the assumed slow-light regime near 𝛽 → 0. The dispersion relation curve dropped even for a lossless, un-infiltrated HC-PBF. Figure 4b shows that the HC-PBF with fluid infiltration sharply when 𝛽 → 0, even for a lossless, un-infiltrated HC-PBF. Figure 4b shows that the HC-PBF exhibited a lower optical loss, resulting from a smaller light-gas interaction area (except for the green with fluid infiltration exhibited a lower optical loss, resulting from a smaller light-gas interaction area air holes). With an increase of the extinction coefficient, the degrees of curvature of β0 and β00 became (except for the green air holes). With an increase of the extinction coefficient, the degrees of curvature flatter, and the two curves became the same value for the same nf , with an increasingly complex of 𝛽 and 𝛽 became flatter, and the two curves became the same value for the same 𝑛 , with an propagation constant β. Furthermore, for the infiltrated structure, both β0 and β00 curves shifted to increasingly complex propagation constant β. Furthermore, for the infiltrated structure, both 𝛽 and a lower frequency. calculation, the influences of infiltrated liquid loss can be 𝛽 curves shifted Through to a lowertheoretical frequency. Through theoretical calculation, the influences of infiltrated neglected, due to a very small overlap area of the four liquid holes with the six guided modes liquid loss can be neglected, due to a very small overlap area of the four liquid holes with the in sixthe HC-PBF, such a structure to be such suitable for practical operation. guidedwhich modesenables in the HC-PBF, which enables a structure to be suitable for practical operation. 0.512
(a) mode 3
0.508 0.504
nf=1,n''=0.001 nf=1,n''=0.005 nf=1,n''=0.01
0.500
nf=1.2,n''=0.001 nf=1.2,n''=0.005 nf=1.2,n''=0.01
0.496 0.00
0.04
0.08
'a/2
0.12
a/2c=a/
a/2c=a/
0.512
(b) mode 3 nf=1,n''=0.001
0.508
nf=1,n''=0.005 nf=1,n''=0.01 nf=1.2,n''=0.001
0.504
nf=1.2,n''=0.005 nf=1.2,n''=0.01
0.500 0.496 0.00
0.04
0.08
0.12
0.16
''a/2
Figure 4. Complex propagation constants versus the normalized frequency 𝛼 𝜆 for mode 3 of the Figure 4. Complex propagation constants versus the normalized frequency α/λ for mode 3 of the un-infiltrated and infiltrated HC-PBF of Figure 1, (a) β’, and (b) β’’. Optical fluids (𝑛 = 1.0, 1.2) are un-infiltrated and infiltrated HC-PBF of Figure 1, (a) β0 , and (b) β”. Optical fluids (nf = 1.0, 1.2) are infiltrated into the selected air holes (Figure 1). Other un-infiltrated air holes and the core are filled infiltrated into the selected air holes (Figure 1). Other un-infiltrated air holes and the core are filled with gas, with a complex refractive index of 𝑛 = 𝑛 + 𝑛 = 1 + 𝑛 and 𝑛 = 0.001, 0.005, 0.01. with gas, with a complex refractive index of n = n0 + n00 = 1 + n00 and n00 = 0.001, 0.005, 0.01. ⁄
Our focus is to explore to what extent a large group index will enhance light-matter interactions, and to investigate the absorbance enhancement factor γ in Equation (2). The group index ng can be derived from the real part β’, and the filling factor f can be calculated from the modal optical electrical field distributions. However, γ can also be calculated based on Equation (15), as
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Our focus is to explore to what extent a large group index will enhance light-matter interactions, and to investigate the absorbance enhancement factor γ in Equation (2). The group index ng can be Sensors 2018, 18, x 7 of 10 derived from the real part β0 , and the filling factor f can be calculated from the modal optical electrical field distributions. However, γ can also be calculated based on Equation (15), as
𝛾γ==
𝛽 00 − 𝛽 (𝑛 = 0) β − β00 (n00 = 0) n00 𝑛
(15)
(15)
Figure 5 shows the corresponding absorption enhancement factor γ along with the group index Figure 5 shows the corresponding absorption enhancement factor γ along with the group index ng. The variation of of γ is similar isaasaturated saturated value ng, compared to the curve of ng . The variation γ is similarto tonngg.. There There is value forfor γ orγnor g , compared to the curve of ng ng ininFigure fora alossless lossless structure. Under certain conditions for 𝑛 is, athere is a maximum γ at a Figure 22 for structure. Under certain conditions for n00 , there maximum γ at a specific specific wavelength. The weaker the absorption intrinsic absorption gasthe is, absorption the largerenhancement the absorption wavelength. The weaker the intrinsic of the gas is,ofthethe larger enhancement factor that can be achieved. Hence, HC-PBF with a slow-light effect exhibits a superior factor that can be achieved. Hence, HC-PBF with a slow-light effect exhibits a superior performance performance for the detection weakly absorbing For moderesults 2, similar can be obtained. for the detection of weaklyof absorbing trace gases.trace For gases. mode 2, similar canresults be obtained. 0.510
0.512
(a) m ode 3
0.508
0.508
0.504
wa/2c=a/
a/2c=a/
0.506
n f=1,n''=0.001 n f=1,n''=0.005
0.502
0.504 n f=1,n''=0.001
0.500
n f=1,n''=0.005
n f=1,n''=0.01
n f=1,n''=0.01
n f=1.2,n''=0.001
0.500 0.498
(b) mode 3
0.496
n f=1.2,n''=0.001
n f=1.2,n''=0.005
n f=1.2,n''=0.005
n f=1.2,n''=0.01
0
10 20
30
40 50 60
ng
70 80
90
0.492
n f=1.2,n''=0.01
0
2
4
6
8
10
12
14
16
Figure 5. For mode 3, curves ofof (a)(a)group and (b) (b)absorption absorptionenhancement enhancement factor 𝛾 versus Figure 5. For mode 3, curves groupindex index 𝑛 ng,, and factor γ versus
the normalized frequency. the normalized frequency.
4. Slow-Light Enhanced Gas Sensing Analysis 4. Slow-Light Enhanced Gas SensingPerformance Performance Analysis Mode Tuning Near-InfraredGas GasSensing Sensing 4.1. 4.1. Mode Tuning forfor Near-Infrared For practical applications, it is important to tune the slow-light region of a fiber mode to a specific
For practical applications, it is important to tune the slow-light region of a fiber mode to a specific gas absorption line. A general rule should be applied, in order to obtain an enhanced absorption gas absorption line. A general rule should be applied, in order to obtain an enhanced absorption wavelength (i.e., the wavelength corresponding to the peak ng or γ). Figure 6a,b shows the relationship wavelength (i.e., the wavelength corresponding to the peak ng or γ). Figure 6a,b shows the between the enhanced absorption wavelength and the refractive index of the liquid for modes 2 and relationship between theanenhanced wavelength and wavelength the refractive index of the 1.51 liquid 3, respectively. With increasingabsorption liquid index, the enhanced increased from to for modes 2 and 3, respectively. With an increasing liquid index, the enhanced wavelength increased 1.59 µm for mode 2, so that several gas species could be detected, e.g., CO at 1.56 µm, C2 H2 and NH3 fromat1.51 to 1.59 mode so that several gas couldwavelength be detected, CO atover 1.56aµm, 1.53 µm, andµm CO2for at 1.57 µm.2,However, for mode 3, species the enhanced onlye.g., increased C2Hsmall 2 and range, NH3 ati.e., 1.53 µm, andtoCO 2 atµm, 1.57which µm. However, foramode 3, the enhanced from 1.523 1.535 is suitable for fine wavelength tuning.wavelength only increased over a small range, i.e., from 1.523 to 1.535 µm, which is suitable for a fine wavelength tuning. 4.2. NH3 Absorption Enhancement Analysis 1.59 NH3
was used as an example to explore the effects of 1.54 slow light on gas detection. An absorption line
1.58
Wavelength (m)
Wavelength (m)
(b) mode 3 (a) mode 2 located at 1.53168 µm was selected as the target line, with an absorption coefficient of 2.45332 × 10−4 m−1
and an extinction coefficient of 2.925 × 10−5 . The mode coupling coefficients between the SMF mode 1.57 HC-PBF modes 1−6 were calculated to be 0.31, 0.32, 0.33, 0.71, 0.42, and 0.44, respectively, by and using 1.56 COMSOL software. To target the selected NH3 line and obtain the slow-light effect for mode 2 1.53 at 1.53168 µm, the refractive index of the liquid was determined to be 1.095. With these parameters, 1.55 the absorption enhancement factor, as well as the absorption spectra of NH3 , is shown in Figure 7a. It was 1.54 1.53 1.52
1.0
1.1
1.2
1.3
1.4
Liquid refractive index n
1.5
1.52
1.0
1.1
1.2
1.3
1.4
Liquid refractive index n
1.5
4.1. Mode Tuning for Near-Infrared Gas Sensing For practical applications, it is important to tune the slow-light region of a fiber mode to a specific gas absorption line. A general rule should be applied, in order to obtain an enhanced absorption wavelength (i.e., the wavelength corresponding to the peak ng or γ). Figure 6a,b shows8 of the Sensors 2018, 18, 2192 10 relationship between the enhanced absorption wavelength and the refractive index of the liquid for modes 2 and 3, respectively. With an increasing liquid index, the enhanced wavelength increased found that the peakµm of for the mode enhancement curve strictly to be thedetected, absorption line at at 1.53168 µm. from 1.51 to 1.59 2, so that several gascorresponds species could e.g., CO 1.56 µm, The factor and absorption is shown in Figure 7b. C2Hrelationship 2 and NH3 atbetween 1.53 µm,the andenhancement CO2 at 1.57 µm. However, for modewavelength 3, the enhanced wavelength only Only modes 1–3,a especially mode 2, have an enhanced absorption effect. for a fine wavelength tuning. increased over small range, i.e., from 1.523 to 1.535 µm, which is suitable 1.54
(a) mode 2
1.58
(b) mode 3
Wavelength (m)
Wavelength (m)
1.59
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4.2. NH3 Absorption Enhancement Analysis 1.56
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1.53 NH3 was used as an example to explore the effects of slow light on gas detection. An absorption line located at 1.53168 µm was selected as the target line, with an absorption coefficient of 1.54 × 10−4 m−1 and an extinction coefficient of 2.925 × 10−5. The mode coupling coefficients between 2.45332 the1.53 SMF mode and HC-PBF modes 1−6 were calculated to be 0.31, 0.32, 0.33, 0.71, 0.42, and 0.44, respectively, by using COMSOL software. To target the selected NH3 line and obtain the slow-light 1.52 1.52 effect for 1.0 mode 1.1 2 at 1.53168 µm, refractive to be 1.095. With 1.0 was 1.1determined 1.2 1.3 1.4 1.5 1.2 1.3 the 1.4 1.5 index of the liquid Liquid refractive index n Liquid refractive index n these parameters, the absorption enhancement factor, as well as the absorption spectra of NH 3, is shown in Figure 7a. It was found thatthe theenhanced peak of the enhancement curveand strictly corresponds toofthe Figure 6. The relationship between absorption wavelength the refractive index Figure 6. The between the enhanced absorption wavelength and the refractive index of absorption line relationship at 1.53168 The relationship the infiltrated liquid for (a)µm. mode 2 and (b) mode 3.between the enhancement factor and absorption the infiltrated liquidinfor (a) mode 2 and (b) mode 3. mode 2, have an enhanced absorption effect. wavelength is shown Figure 7b. Only modes 1−3, especially
20
(a)
0.00025
Enhancement curve Absorption spectrum L = 1m, C = 10 ppm, P = 1atm, T = 300 K
0.00020
15 0.00015 10
0.00010 0.00005
5
Absorbance -ln(I/I0)
Enhancement Factor
1.55
0.00000 0 1.526 1.527 1.528 1.529 1.530 1.531 1.532 1.533 Wavelength m 24
Enhancement factor ()
(b)
mode2 mode3 mode1 4,5,6
20 16 12 8 4 0
1.526
1.528
1.530
1.532
1.534
Wavelength m Figure 7. (a) Absorption spectrum of 1 ppm NH3 with a 1 m absorption length; curve of the
Figure 7. (a) Absorption spectrum of 1 ppm NH3 with a 1 m absorption length; curve of the enhancement factor γ for mode 3 versus the operating wavelength λ. (b) The relationship between enhancement factor γ for mode 3 versus the operating wavelength λ. (b) The relationship between the the absorption wavelength of NH3 and the enhancement factor for modes 1−6. absorption wavelength of NH3 and the enhancement factor for modes 1−6.
As a comparison, under the cases of using the slow-light effect and without using such an effect, theAs extracted second under harmonic signals are shown in Figure 8a, where a 1 ppmusing NH3 such with an a 1effect, m a comparison, the (2f) cases of using the slow-light effect and without used in the 2f signal amplitude is enhanced by three theabsorption extracted length secondwas harmonic (2f )calculation. signals areThe shown in Figure 8a, where a 1 ppm NH3times with via a1m the use oflength such an effect. When a white Gaussian noise (with aamplitude signal-to-noise ratio of 30by dB)three was added absorption was used in the calculation. The 2f signal is enhanced times via theofsensor system, Allanadeviation plots fornoise the two cases were as shown ratio in Figure Allan theinuse such an effect.the When white Gaussian (with a signal-to-noise of 308b. dB)The was added deviation was found to decrease from 0.04 ppm to 0.012 ppm by slow light-induced absorption enhancement, indicating a sensitivity enhancement by such an effect. Though PBF mode 2 has an enhancement factor of up to 20, the total enhancement factor is only 3, due to the inefficient coupling between the SMF mode and PBF mode 2, as well as the small gas absorption of other PBF modes.
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in the sensor system, the Allan deviation plots for the two cases were as shown in Figure 8b. The Allan deviation was found to decrease from 0.04 ppm to 0.012 ppm by slow light-induced absorption enhancement, indicating a sensitivity enhancement by such an effect. Though PBF mode 2 has an enhancement factor of up to 20, the total enhancement factor is only 3, due to the inefficient coupling between Sensors 2018,the 18, xSMF mode and PBF mode 2, as well as the small gas absorption of other PBF modes.9 of 10
2f Signal (a.u.)
0.008
0.004
0.000
-0.004 0.00
-1
10
(a)
Using slow light effect Using no slow light effect
Allan deviation (ppm)
0.012
0.02
0.04
0.06
Time (s)
0.08
0.10
(b)
-2
10
-3
10
Using no slow light effect Using slow light effect -4
10
-1
10
0
10
1
10
Averaging Time (s)
2
10
Figure the slow-light slow-light effect effectand andwithout withoutusing usingsuch sucheffect. effect. Figure8.8.(a) (a)The Theextracted extracted2f 2f signals, signals, both both using using the (b) effectand andwithout withoutusing usingsuch suchananeffect. effect. (b)Allan Allandeviation deviationplots plotsusing using the the slow-light slow-light effect
5.5.Conclusions Conclusions AAgeneric slow-light enhanced enhancedabsorption absorptionspectroscopic spectroscopicgas gassensor sensor genericmodeling modelingand and analysis analysis of of aa slow-light using HC-PBFwas wasreported. reported. tuning HC-PBF mode dispersion a slowusingaamode-tuned mode-tuned HC-PBF ByBy tuning thethe HC-PBF mode dispersion curve,curve, a slow-light light effect was achieved. The slow-light region can be tuned to an absorption line of a target gas effect was achieved. The slow-light region can be tuned to an absorption line of a target gas species for species for absorption enhancement. A general rule of microfluidic parameters targeting different absorption enhancement. A general rule of microfluidic parameters for targeting for different gas species gas species was obtained. The change in the 2f signal and the sensitivity enhancement resulting from was obtained. The change in the 2f signal and the sensitivity enhancement resulting from the slow the slow light effect were also investigated a test The reported theoretical results light effect were also investigated for NH3 for as aNH test3 as trace gas.trace The gas. reported theoretical results will be will be useful in the development other HC-PBF-based gas sensors. useful in the development of otherofHC-PBF-based gas sensors. Author F.W.;Software, Software,D.Y. D.Y.and andW.-X.Z.; W.-X.Z.;Validation, Validation, AuthorContributions: Contributions:Conceptualization, Conceptualization,D.-M.Z.; D.-M.Z.; Methodology, Methodology, F.W.; Y.-D.W.; Analysis,Z.-W.L.; Z.-W.L.; Investigation, Z.-F.W. and C.-T.Z. Resources, Data W.-X.Z.; Curation, Y.-D.W.; Formal Formal Analysis, Investigation, Z.-F.W. and C.-T.Z. Resources, Y.-D.W.;Y.-D.W.; Data Curation, Writing-Original Draft Preparation, Z.-F.W. and W.X.Z.; Editing, C.-T.Z.; Visualization, F.W.; W.-X.Z.; Writing-Original Draft Preparation, Z.-F.W.Writing-Review and W.X.Z.; &Writing-Review & Editing, C.-T.Z.; Supervision, D.-M.Z.; Project Administration, Y.-D.W.; Funding Acquisition, C.-T.Z., Y.-D.W. and F.W. C.-T.Z., Y.Visualization, F.W.; Supervision, D.-M.Z.; Project Administration, Y.-D.W.; Funding Acquisition, D.W. and F.W. Funding: This research was funded by the National Natural Science Foundation of China (Nos. 61775079, 61475061, 61627823), National Key R&D Program of China (Nos. 2016YFD0700101, 2016YFC0303902), the Industrial Innovation Program This of Jilinresearch Province,was China (No. 2017C027), and the Natural National Science Science Foundation ERC MIRTHE award Funding: funded by the National Foundation(NSF) of China (Nos. 61775079, and Robert Welch Foundation (No. C-0586). 61475061, 61627823), National Key R&D Program of China (Nos. 2016YFD0700101, 2016YFC0303902), the Conflicts Innovation of Interest: Program The authors no conflict of interest. Industrial of declare Jilin Province, China (No. 2017C027), and the National Science Foundation (NSF) ERC MIRTHE award and Robert Welch Foundation (No. C-0586).
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