Reflection spectra of etched FBGs under the ... - OSA Publishing

Reflection spectra of etched FBGs under the influence of axial contraction and stress-induced index change Hang-Zhou Yang,1,2 Kok-Sing Lim,1,* Xue-Guang Qiao,2 Wu-Yi Chong,1 Yew-Ken Cheong,1 Weng-Hong Lim,1 Wei-Sin Lim,1 and Harith Ahmad1 1

Photonics Research Centre, Dept. of Physics, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia 2 Dept. of Physics, Northwest University, Xi’an, Shaanxi 710069, China 2 [email protected] * [email protected]

Abstract: We present a new theoretical model for the broadband reflection spectra of etched FBGs which includes the effects of axial contraction and stress-induced index change. The reflection spectra of the etched FBGs with several different taper profiles are simulated based on the proposed model. In our observation, decaying exponential profile produces a broadband reflection spectrum with good uniformity over the range of 1540-1560 nm. An etched FBG with similar taper profile is fabricated and the experimental result shows good agreement with the theoretical model. ©2013 Optical Society of America OCIS codes: (060.0060) Fiber optics and optical communications; (060.3735) Fiber Bragg gratings; (230.1150) All-optical devices.

References and links 1. 2.

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K. O. Hill and G. Meltz, “Fiber Bragg grating technology fundamentals and overview,” J. Lightwave Technol. 15(8), 1263–1276 (1997). C. Li, N. Chen, Z. Chen, and T. Wang, “Fully distributed chirped FBG sensor and application in laser-induced interstitial thermotherapy,” Communications and Photonics Conference and Exhibition (ACP), 2009 Asia, vol.2009-Supplement, 1,6, 2–6 (2009). Y. Takubo and S. Yamashita, “High-speed dispersion-tuned wavelength-swept fiber laser using a reflective SOA and a chirped FBG,” Opt. Express 21(4), 5130–5139 (2013). K. C. Byron, K. Sugden, T. Bricheno, and I. Bennion, “Fabrication of chirped Bragg gratings in photosensitive fiber,” Electron. Lett. 29(18), 1659–1660 (1993). F. X. Kärtner, N. Matuschek, T. Schibli, U. Keller, H. A. Haus, C. Heine, R. Morf, V. Scheuer, M. Tilsch, and T. Tschudi, “Design and fabrication of double-chirped mirrors,” Opt. Lett. 22(11), 831–833 (1997). C. Lu, J. Cui, and Y. Cui, “Reflection spectra of fiber Bragg gratings with random fluctuations,” Opt. Fiber Technol. 14(2), 97–101 (2008). J. Mora, J. Villatoro, A. Dıez, J. L. Cruz, and M. V. Andres, “Tunable chirp in Bragg gratings written in tapered core fibers,” Opt. Commun. 210(1-2), 51–55 (2002). J. Mora, A. Diez, M. V. Andres, P. Y. Fonjallaz, and M. Popov, “Tunable dispersion compensator based on a fiber Bragg grating written in a tapered fiber,” IEEE Photon. Technol. Lett. 16(12), 2631–2633 (2004). N. Q. Ngo, S. Y. Li, R. T. Zheng, S. C. Tjin, and P. Shum, “Electrically tunable dispersion compensator with fixed center wavelength using fiber Bragg grating,” J. Lightwave Technol. 21(6), 1568–1575 (2003). J. L. Cruz, L. Dong, S. Barcelos, and L. Reekie, “Fiber Bragg gratings with various chirp profiles made in etched tapers,” Appl. Opt. 35(34), 6781–6787 (1996). L. Dong, J. L. Cruz, L. Reekie, and J. A. Tucknott, “Fabrication of chirped fiber gratings using etched tapers,” Electron. Lett. 31(11), 908–909 (1995). X. Dong, P. Shum, N. Ngo, C. Chan, J. Ng, and C. Zhao, “A largely tunable CFBG-based dispersion compensator with fixed center wavelength,” Opt. Express 11(22), 2970–2974 (2003). Z. Li, Z. Chen, V. K. S. Hsiao, J. Y. Tang, F. Zhao, and S. J. Jiang, “Optically tunable chirped fiber Bragg grating,” Opt. Express 20(10), 10827–10832 (2012). M. G. Sceats, G. R. Atkins, and S. B. Poole, “Photolytic index changes in optical fibers,” Annu. Rev. Mater. Sci. 23(1), 381–410 (1993). K. S. Lim, H. Z. Yang, W. Y. Chong, Y. K. Cheong, C. H. Lim, N. M. Ali, and H. Ahmad, “Axial contraction in etched optical fiber due to internal stress reduction,” Opt. Express 21(3), 2551–2562 (2013).

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Received 16 Apr 2013; revised 26 May 2013; accepted 10 Jun 2013; published 14 Jun 2013 17 June 2013 | Vol. 21, No. 12 | DOI:10.1364/OE.21.014808 | OPTICS EXPRESS 14808

16. A. N. Chryssis, S. M. Lee, S. B. Lee, S. S. Saini, and M. Dagenais, “High sensitivity evanescent field fiber Bragg grating sensor,” IEEE Photon. Technol. Lett. 17(6), 1253–1255 (2005). 17. W. Liang, Y. Huang, Y. Xu, R. K. Lee, and A. Yariv, “Highly sensitive fiber Bragg grating refractive index sensors,” Appl. Phys. Lett. 86(15), 151122 (2005). 18. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997). 19. T. Erdogan, “Cladding-mode resonances in short-and long-period fiber grating filters,” J. Opt. Soc. Am. A 14(8), 1760–1773 (1997).

1. Introduction Fiber Bragg Gratings (FBG) technology provides an incredible in-fiber platform for many applications, for instance laser technology, optical sensing and optical communication system [1]. To meet the various requirements of these applications, different grating structures have been suggested and demonstrated. Chirped grating is one of the grating structures in which its optical properties and applications have been intensively investigated in the past few years [2, 3]. Broadband gratings can be formed in a fiber through a number of ways. The commonly used technique is to inscribe a chirped grating with varying period along the fiber. The variation of grating period can be linear [4], quadratic [5], or randomly distributed along the fiber [6]. Besides, uniform period grating written in a tapered fiber can also produce broadband gratings. The tapered fibers are fabricated based on heating and stretching method, in which the fiber cladding and core diameters vary longitudinally along the fiber axis. The effective refractive index of the fiber is a function of cladding and core diameter. As a result, a broad reflection spectrum is achieved in tapered FBGs [7, 8]. This technique offers infinite possibility in the design of broadband grating through modification of the fiber diameter. Chemical etching using hydrofluoric acid (HF) is one of the most effective approaches in shaping the structure of the fiber to achieve the desired broadband spectra [9, 10]. Etched FBGs with uniform grating period but varying fiber radius produce broadband reflection spectra similar to that of varying grating period chirped FBG. The patterns of the reflection spectra depend on the fiber radius profile. Accurate control of the profile can be achieved by controlling the immersed fiber length in the etchant solution [11]. Broadband gratings have been frequently used as a dispersion compensator for the application of optical communication. To optimize the network performance for high speed communication, dynamic network reconfiguration and dispersion management using tunable dispersion compensator are suggested. Several techniques have been proposed to dynamically control the reflection spectra and dispersion profile of the broadband FBG, for example mechanical tuning taper shape cantilever supported FBG [12], electrically tunable FBG with thin metal film coating integrated with negative thermal expansion ceramic [9] and optical tuning using photoresponsive liquid crystal coated FBG [13]. The thermoelastic stresses in the optical fibers are the products of core-cladding thermal expansion coefficient difference [14]. As a result, a significant index difference as large as 103 is induced in the fiber core due to stress-optic effect. These stresses are released when the fiber diameter is reduced during the process of chemical etching. This leads to the phenomenon of axial contraction and stress-induced index change which cause significant alterations to the properties of the optical fibers and FBGs in terms of V-number, effective refractive index and Bragg wavelength [15]. In the previous studies of etched FBGs [10, 16, 17], the grating period and core refractive index are assumed to be constant and the aforementioned effects were never considered in their analysis. In this work, we proposed a mathematical model to describe the relation between the taper profiles of an etched FBG with its corresponding broadband reflection spectra. The effects of axial contraction and stress induced index change along the tapered etched FBG region are considered in the simulation. The modelling result is found to be in agreement with experimental observations.

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2. Stress-optic effect and axial contraction in etched FBG The Bragg wavelength λB of the etched FBG is governed by the effective refractive index neff(ξ, nam) and grating period Λξ. The relation can be expressed as [18],

B ( , nam )  2neff ( , nam )( )

(1)

The effective refractive index, neff of the etched FBG is a function of fiber radius and ambient refractive index which can be well characterized using the three layered model [19]. Figure 1(a) shows the theoretical curves of effective refractive index as a function of fiber radius, ξ. Assume a fiber core radius of 3.5 µm, the effective refractive index of the fiber remains the same at ~1.445 in the range between 10 µm to 62.5 µm. Significant decrement in effective refractive index can be observed when the fiber radius is below 5µm, which is very close to the core-cladding boundary of the fiber. The effective index eventually approaches the refractive index of the ambient medium, nam when the fiber radius is smaller than 1µm.

Fig. 1. (a) The neff varied with the fiber radius ξ in various nam of ambient materials. (b) The ∆neff varied with the nam in different fiber radius.

The difference in effective refractive index ∆neff after the fiber radius is reduced from the original radius b to a smaller radius of ξ, in an ambient medium with refractive index of nam is expressed as

neff ( , nam )  neff ( , nam )  neff (b, nam )

(2)

where neff(ξ) is the effective refractive index of the etched fiber at a fiber radius of ξ, 0    b . The difference is larger in the lower RI medium and the maximum magnitude is achieved at nam = 1. At smaller fiber radius, the evanescent field is stronger and thus it is more sensitive to the variation in ambient RI as illustrated by the characteristic curves in Fig. 1(b). Assume that the grating period is constant, these characteristic curves can be linearly translated as wavelength shift of a uniformly etched FBG in a function of fiber radii and ambient RI. In a previous work [15], the investigation has indicated that fibers with high axial tensile stress in the core experience stress relaxation and axial contraction when the fiber radius is reduced during the etching process. As a result of internal stress reduction, the core refractive index increases with reducing fiber radius and the relationship between stress induced index change and varying fiber radius is described as

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  2   a2 a2   1    2  2  b  (C1  3C2 )  E  T      2    n( )      2  1    a2  2   2       1 1  b2    2     2   a      

 a (3)

 a

1  1  2  , E is the Young’s modulus, a and b are the radii of the core and 1  cladding respectively, α1 and α2 are the thermal expansion coefficients for core glass and cladding glass respectively, ν is the poisson ratio, γ is the profile parameter, C1 and C2 are stress-optic coefficients. The axial contraction engenders changes in the grating period Λ(ξ) with varying fiber radius. The relation is given by where  

( )  0 1   ( ) 

(4)

where Λ0 is the period of an original FBG and

  1   T    ( )    1    

 2   a2  2     1   1       0  a   2   b2    2   a  

 b2  a   2  1     b 

2

 2  1     2 

(5)

a  b

ε(ξ) is the axial contraction along the etched fiber [15]. Significant changes are observed when the fiber radius approaches the core-cladding boundary. 3. Theoretical modelling and analysis To include all the aforementioned effects in the analysis and modelling of broadband FBGs, the following expressions are formulated. The ac-component of coupling coefficient, κ is assumed to be independent from the varying fiber radius and the expression is the same as that of an original FBG.

   n 1

(6)

where δn is the UV-induced index change in the fiber which can be estimated from the Bragg wavelength shift during UV writing process and υ is the fringe visibility of the index change. The stress-induced index change n( ) and effective refractive index difference

neff ( , nam ) are considered as a part of dc component of the coupling coefficient, ζ. The modified dc-component of coupling coefficient for the etched FBG is described as

 ( )  2 1 ( n  neff ( )  n( ))

(7)

The grating period varies with fiber radius (Refer Eq. (4)) and thus the detuning of δ can be expressed as a function of ξ

 ( ) 

2 neff







 0 1   ( ) 

(8)

The output spectrum can be simulated using Transfer Matrix Method (TMM) where each local section of the etched FBG is described by a matrix Fi and the resultant output spectrum is given by the product of all matrices Fi as shown in Eq. (10).

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ˆ    i sin h( B z )  cos h( B z )  i  sin h( B z )  B B  Fi     ˆ  i sin h( B z ) cos h( B z )  i sin h( B z )     B B    RM     FM  FM 1  SM 

Fi

 R0   f F1     11  S0   f 21

f12   R0    f 22   S0 

(9)

(10)

1/2

where ∆z is the length of every section,  B   2  ˆ 2 ( )  , ˆ( )   ( )   ( ) is a general dc self-coupling coefficient, M is the total number of sections, R0 = 1 and S0 = 0 are the initial complex amplitudes of forward and backward propagation light waves, respectively.

Fig. 2. (a) Graph of radius profile and (b) neff variation along the etched FBG. (c) Reflection spectra of etched FBG of different taper profiles, simulated based on conventional model (dotted) and proposed model (solid).

Figure 2(a) show the taper profiles of a 1 cm long etched FBG of different shapes, namely linear, reciprocal and decaying exponential. The effective refractive index, neff is almost the same for fiber radius larger than 18 μm. Therefore, fiber radius in the range between 17 μm and 2.2 μm is selected to ensure significant variation in neff along the etched FBG. At ξ = 2.2 µm, the calculated neff is ~1.428, a difference of 0.018 if compared with that of an unetched

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fiber. Besides, the estimated stress-induced index increment is 1.8 × 103 and the grating period is reduced by 0.17% from its original value at this radius. As shown in Fig. 2(b), reciprocal taper profile (red) has a large variation in neff at the beginning of the taper, in the region of 0.0 - 0.2 cm. Linear profile (green) has a large neff variation in the region of 0.8 - 1.0 cm. The neff variation of decaying exponential profile (blue) is slow and takes place in the center region (0.2 - 0.8 cm) of the etched FBG. Each taper profile exhibits distinct curve characteristic in neff and these characteristics have a different influence on the produced reflection spectra. Figure 2(c) shows the reflection spectrum (solid) for each taper profile simulated based on the proposed mathematical model from Eqs. (2)-(10). In the modeling, an apodized grating structure with a FWHM grating strength of 0.8 cm is assumed. For an unetched FBG, the Bragg wavelength is located at 1561 nm with a small bandwidth of ~0.3 nm (shown as grey dash curve in Fig. 2(a)). The spectral bandwidth is broadened up to ~20 nm after the FBG is etched. The reflection curve is extended to a shorter wavelength, covering from 1540 nm to 1560 nm in air (nam = 1). Ideally, decaying exponential profile can produce reflection spectra with good uniformity of ~2 dB fluctuation in reflectivity. The major factors that contribute to the flat-top reflection spectrum are the slow varying neff and this variation occurs over a long distance (0.2-0.8cm) along the etched FBG. The reflection spectra (dotted) are also simulated based on conventional model in which the effects of axial contraction and stress-induced index change in the etched fiber are not considered. These spectra share similar spectral characteristics with that of the proposed model except for the bandwidth. The spectral bandwidth produced by the conventional model is smaller by 0.8 nm and the difference can be clearly seen within the vicinity of 1540 nm in the spectrum of Fig. 2(c). The spectral bandwidth of the etched FBG can be estimated using this expression

  n ( )  n(min )     B (b, nam )  (min )  1   ( min )   eff min    neff (b)    

(11)

where ξmin is the minimum fiber radius of the etched FBG. ∆neff (ξmin) is the key parameter in controlling the spectral bandwidth. 4. FBG preparation and experiment Type I grating with a length of 2.0 cm is inscribed in hydrogenated B/Ge co-doped photosensitivity fiber (Fibercore Ltd: PS1250/1500). The fiber is hydrogenated for 10 days under a pressure of 13.8 MPa at room temperature. A continuous-wave (CW) frequencydoubled argon ion laser operating at wavelength of 244 nm with an average output power of ~28 mW is used in conjunction with a phase mask with a period of 1072.6 nm in the FBG writing. The fabricated gratings with a transmission dip of ~35 dB are treated with a total UV fluence of ~18.0 J/cm2. After storing the FBG in the lab for hydrogen out-diffusing in room condition for two weeks, the grating strength decayed to ~26 dB. The calculated index modulation for the FBGs with such reflectivity is 1.7 × 10 4. For the ease of study, Type I grating is used in this work because of its inherit properties that the dominant effect for refractive index change is the change of color-center. Considering the low UV fluence, the UV-induced stress in the fiber is negligible. Buffered Oxide Etchant (BOE) solution with the volume ratio of NH 4F solution (40% in water) and HF solution (48% in water) is used to etch the fiber on the location where grating is inscribed. To accurately control the taper profiles, a method proposed by Cruz et al. [10] is used in our experiment. After achieving the desired etched radius, the etched FBG was rinsed with de-ionized water to remove the residual etchant. The radius of the etched FBG is measured using an optical microscope. Figures 3(a) and 3(b) show the microscope image of the transition and taper end of an etched FBG.

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Fig. 3. Microscope images of the (a) transition and (b) taper end of the etched FBG.

During the fabrication, amplified spontaneous emission (ASE) from an erbium doped fiber amplifier (EDFA) is used as a broadband light source. The ASE source is launched into a circulator before the light source enters the FBGs which are placed in the HF solution. The reflection spectrum of the FBG is circulated to an optical spectrum analyzer (OSA, Ando AQ6331) for measurement at a resolution of 0.05 nm. The output spectra of an etched FBG at different conditions are as presented in Fig. 4. From original reflection spectrum (black) with a bandwidth of 0.6 nm, the bandwidth is expanded and extended towards the shorter wavelength direction during the process of etching in BOE solution. The green curve in Fig. 4 is the expanded reflection spectrum of the etched FBG in BOE solution right before the etching process was terminated. The bandwidth is larger when the etched FBG is placed in air (red). This can be easily explained using ∆neff curves in Fig. 1(b). The ∆neff is larger when the etched FBG is in the air.

Fig. 4. The spectra of the FBG before etching (black), under etching in BOE solution (green) and after etching (red).

In the experiment, several liquids of different RIs are employed in the characterization of the etched FBG, namely methanol, water, acetone and IPA which RIs are 1.326, 1.331, 1.355 and 1.374 respectively. The output spectra of etched FBG in the mediums of different RIs are as presented in Fig. 5(a). The broadest reflection spectrum is given by RI = 1.000 (black curve), which is ~20.08nm when the etched FBG is in the air. The spectral bandwidth reduces with increasing RI and the smallest spectral bandwidth is observed in the medium of RI = 1.374(blue curve). The peak reflectivity at 1561nm is contributed by the unetched part of the FBG and it is unaffected by the medium of different RI. However, the reflectivity of the extended part of the spectrum varies with the changing RI. In our observation, the reflectivity is lower with larger spectral bandwidth. This phenomenon can be attributed to the dispersing Bragg wavelengths of different parts of the etched FBG. The total reflected power is almost the same for different RI. The reflectivity of the broadband spectrum can be enhanced by using longer FBGs. Figure 5(b) shows the output spectra of the etched FBG simulated based on the proposed model. Similar spectral bandwidths and reflection curves characteristics are observed in the simulation results. For ease of comparison, the spectral bandwidths acquired from experimental and simulation results are tabulated in Table 1. The comparison indicates that both experimental data and simulation results are in good agreement.

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Fig. 5. Comparison between (a) experimental and (b) simulation results for the etched FBG in mediums of different RIs. The spectral bandwidth varies with different RI. Table 1. Bandwidth comparison between experimental and simulation results. RI 1.000 1.313 1.322 1.347 1.365

Experiment (nm) 20.08 14.94 14.72 13.80 12.84

Simulation (nm) 20.00 15.00 14.72 13.74 12.88

5. Conclusion A broadband FBG is achieved through fiber shape modification based on chemical etching method. Taking into consideration the effects of axial contraction and stress-induced index change in etched FBG, a new mathematical model is formulated. In the simulation, the calculated reflection spectra are slightly larger in bandwidth if compared with that of convention model. This discrepancy grows larger with decreasing fiber radius. The spectral change of FBG at different etched stages have been observed and decaying exponential profile has exhibited a broad reflection spectrum with good uniformity. An etched FBG with decaying exponential taper profile has been fabricated and the produced reflection spectrum agrees well with the simulation results. The advantages of the proposed etched FBG include its short grating length, broad reflection spectrum while sharing similar functionalities of chirped FBG of varying grating period. It has the potential in applications including tunable dispersion compensation and refractive index sensing. Acknowledgments We would like to thank the University of Malaya and MOHE for providing the HIR Grant (UM.C/625/1/HIR/MOHE/SCI/29) and UMRG Grant (RP019-2012C) for funding this project. The project is also partially supported by the National Natural Science Foundation of China (Nos. 60727004, 61077060), National High Technology Research and Development Program 863 (Nos. 2007AA03Z413, 2009AA06Z203), Ministry of Education Project of Science and Technology Innovation (No. Z08119), Ministry of Science and Technology Project of International Cooperation (No. 2008CR1063) and Shaanxi Province Project of Science and Technology Innovation (Nos. 2009ZKC01-19, 2008ZDGC-14).

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