I. INTRODUCTION. ρ(z) = q(z) tanh ( q(z) ) (1)

Transcription

1 3924 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 23, NO. 11, NOVEMBER 2005 Iterative Layer-Peeling Algorithm for Designing Fiber Bragg Gratings With Fabrication Constraints Yueh Ouyang, Yunlong Sheng, Fellow, OSA, Martin Bernier, and Gilles Paul-Hus Abstract We demonstrate the iterative layer-peeling algorithm (LPA) for designing fiber Bragg gratings (FBGs). The algorithm includes explicit fabrication and spectrum constraints in the iterations. The inverse layer peeling, which is two orders of magnitude faster than the traditional transfer-matrix method, is used for grating analysis. We are able to remove all phase shifts in a minimum-dispersion passband filter. The new grating is easier to fabricate with less fabrication errors. Experimental results confirm the designed performance. Index Terms Dispersion-free fiber Bragg grating (FBG), iterative layer-peeling algorithm (LPA), optical communications, optimization, wavelength-division multiplexing (WDM) passband filter. I. INTRODUCTION A FIBER Bragg grating (FBG) can be synthesized for a given spectrum using inverse-scattering methods [1] [5]. The algorithms include the integral-equation approach, such as the Gel fand Levitan Marchenko method [2], [3], and the differential approach, such as the layer-peeling algorithm (LPA) [4], [5]. The LPA reconstructs the FBG layer by layer in a recursive manner based on the causality rule. Synthesis of the FBGs by the LPA is an important progress. The discrete LPA is simple, computationally efficient, and accurate [5]. However, in many cases, the FBGs synthesized by the LPA typically have a long tap with many small-amplitude oscillations and π-phase shifts, which are difficult to fabricate with precision. In this paper, we present an approach for designing FBGs using the iterative LPA. Different from the existing iterative Gel fand Levitan Marchenk methods [3] and LPA that are implemented with iterations [6], the proposed design method is a numerical optimization, which iterates the synthesis of the grating with the LPA and the analysis of the grating with a fast inverse LPA. In this scheme, a variety of explicit constraints can be applied to the grating profile and to its spectrum. In this paper, we apply fabrication constraints to the FBG profile for improving its manufacturability. The designed FBGs still satisfy the requested spectral specifications but are easier to fabricate with less fabrication errors than those synthesized directly by a single LPA. Iterative inverse scattering has been used by several authors in FBG designs [7] [12]. In this paper, Manuscript received February 23, 2005; revised May 27, Y. Ouyang is with the Department of Physics, Chinese Military Academy, Fengshan Koahsiung, Taiwan 830, R.O.C. ( sam@cc.cma.edu.tw). Y. Sheng, M. Bernier, and G. Paul-Hus are with the Center for Optics, Photonics, and Laser (COPL), Department of Physics, Physical Engineering, and Optics, University Laval, Sainte-Foy, QC, G1K 7P4, Canada ( sheng@phy.ulaval.ca; martin.bernier.1@ulaval.ca; gpaulhs@phy.ulaval.ca). Digital Object Identifier /JLT we demonstrate and discuss the concrete steps of the constraintapplication procedure in the iterative LPA. We introduce an inverse LPA that is much faster than the conventional transfermatrix method for the FBG analysis. We also show a sample design of a bandpass FBG with minimum dispersion. In contrast with a recent design of dispersion-free FBGs [13], our design with the iterative LPA uses the fabrication constraints to exclude all the phase shifts, so that the designed FBG can be fabricated with a conventional high-quality holographic phase mask without requiring custom-made phase masks. As a tradeoff, the FBG s dispersion is slightly increased. The designed FBG has been fabricated to confirm the designed performance. Experimental results will be shown. Note that the phase shifts can also be introduced with a piezo-dithering phase-mask technique in the scanning-beam writing system without the need for custom phase masks. II. LPA AND INVERSE LPA The discrete LPA has been described in detail in [5]. For synthesizing the FBG from a given reflection spectrum, the FBG is divided into thin discrete layers of thickness, such that each layer can be considered as a uniform grating. The grating layers are further approximated as the discrete reflectors, which are equally spaced by and have complex-valued reflection coefficients ρ(z) independent of the frequency, so that [4] ρ(z) = q(z) tanh ( q(z) ) (1) q(z) where q(z) is the coupling coefficient at the point z of the target grating to be synthesized. Equation (1) is obtained from the conventional transfer matrix of a grating layer by taking the limit q while keeping the product q constant. As a consequence of the discretization, the transfer matrix of the grating layer is approximated as a product of two matrices T ρ T, where T ρ is the transfer matrix of the discrete reflector and T describes the pure propagation over a distance. The local complex-valued reflection spectrum of the layer is defined as r j (β) =u j (β)/v j (β), where β is the detuning, u j (β) and v j (β) are the forward- and backward-propagating fields, respectively, at the front end of the jth layer. The LPA is based on the causality rule: The local reflection spectrum of the first layer at the front end of the grating r 1 (β) r(z = 0,β)=H R (β) (2) is determined by the leading piece of the impulse response of the FBG, because this piece of light does not have the time /$ IEEE

2 OUYANG et al.: LAYER-PEELING ALGORITHM FOR DESIGNING FBGs WITH FABRICATION CONSTRAINTS 3925 to penetrate into the second layer, where H R (β) is the target reflection spectrum. The impulse response h(z) is the Fourier transform of the H R (β). At the time t = 0 and for the first layer z = 0, we have h 1 (0) = π π 2 π 2 r 1 (β)dβ (3) so that the reflection coefficient of the first-layer reflector ρ 1 = h 1 (0). Thus, from (1) (3), we can obtain the coupling coefficient of the first layer q(z) with z = 0as q(z) q(z) tanh ( q(z) ) = 1 N 1 r(z,n β) (4) N n=0 where the discrete form of (3) is used. After the first layer is computed, it can be peeled off. We then compute the second layer in the same way as the first layer is computed. Only the local reflection spectrum of the next layer should be calculated with the relation [5] q(z) r(z,β)+ j2β q(z) tanh ( q(z) ) r(z +,β)=e 1 + q(z) q(z) tanh ( q(z) ) r(z,β) (5) which is obtained by the field-transferring relation from the layer j to layer j + 1 ( ) ( ) uj+1 uj =(T ) j (T ρ ) j. (6) v j+1 v j Repeating the two steps described by (4) and (5) layer by layer, we can compute the coupling coefficient of the entire grating, and complete the synthesis procedure of the LPA. Given the coupling coefficient q(z) of an FBG, its reflection spectrum can be calculated with the traditional transfer-matrix method. We use the inverse LPA for the FBG analysis in the iterative LPA. The inverse LPA is the exact inverse procedure of the LPA. As the discrete LPA is computationally efficient and the local reflection spectrum of each layer is determined with satisfactory precision, we can use the same division to layers of the FBG and the same discretization of the layer s transfer matrices, as that used in the LPA, to compute the local reflection spectrum of the FBG layer by layer from the coupling coefficient q(z) given by (5), which can be rewritten as r(z,β) = ej2β r(z +,β) q(z) q(z) tanh ( q(z) ) (7) 1 ej2β q(z) tanh ( q(z) ) r(z +,β). q(z) We start from the last layer at the rear end of the FBG with z = L, where L is the grating length. The boundary condition is that the local reflection of the last layer r(l, β) =0. For the given coupling coefficient q(z), the local reflection spectrum r(z,β) in z can be calculated from that of the next layer, r(z +,β) in z + using (7). We perform the calculation Fig. 1. Iterative LPA. for the local reflection spectrum recursively, layer by layer, from the rear end to the front end of the grating with (7). In the front layer, the local reflection spectrum r(0,β) is equal to that of the entire FBG, which is H R (β). The inverse discrete LPA is faster than the traditional transfer-matrix method by two orders of magnitude for analyzing the FBG, and gives essentially the same spectrum as that given by the traditional method. The inverse LPA is a key element in the iterative LPA for the computational efficiency of the design. The FBG is an IIR filter [14]. Synthesizing the FBG by the LPA is an approximation. The LPA is based on the causality, so that one has to truncate the grating length and shift it spatially, such that the impulse response h(t) =0 for t<0 in a physically realizable FIR filter [4] [6]. III. ITERATIVE LPA The synthesis of the FBG using the LPA and the analysis of the FBG using the inverse LPA can be iterated in a loop. Compared with ad hoc search or parameter-scanning optimizations, the iterative LPA is more efficient, because in the iterations, the search in the parameter space could move along the direction of the error reduction [15]. Moreover, appropriate constraints can be applied to the grating profile and to its spectrum, respectively. The iterative LPA design with explicit constraints in both the grating and the spectrum spaces can consist of the following steps. 1) Apply the physically realizable condition to the given target spectrum. 2) Synthesize the grating by the LPA. 3) Apply the fabrication constraints to the grating profile. 4) Compute the spectrum of the modified grating using the fast inverse LPA. 5) Apply the spectrum constraints to the grating spectrum. 6) Iterate steps 1) to 5) until the grating satisfies the fabrication constraints and its spectrum satisfies the target spectral specifications. The block diagram of the iterative design is illustrated in Fig. 1. If the input output relation between the FBG coupling coefficient and its spectrum would be the Fourier transform, then the proposed LPA will be equivalent to the generalized Gerchberg Saxton (GS) algorithm for phase retrieval, which uses the iterative Fourier transform and applies the constraints to the intensities of the image and its Fourier transform [16]. The iterative LPA is the generalized GS, in the sense that the

3 3926 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 23, NO. 11, NOVEMBER 2005 TABLE I CHARACTERISTICS OF OPTIMAL SPECTRA FOR A GRATING WITH DIFFERENT LOB NUMBERS constraints are applied to both the complex-valued coupling coefficient, including the phase shifts, and the complex-valued spectrum, including the dispersion. It has been proven that the generalized GS algorithm is an error-reduction algorithm and does converge, in the sense that the error monotonically decreases during the iterations [15]. The Fourier transform is linear, but the Riccati equation governing the relation between the coupling coefficient and the spectrum is nonlinear, so that the error reduction of the proposed iterative LPA is ensured only for weak FBGs. For strong FBGs, the iterative LPA can converge, in the sense that although the error does not decrease monotonically, it tends towards a stable value asymptotically with the iterations, as shown in the experiments in next sections and in [7] [10]. The iterative LPA simply fails to work in some implementations. The key for the success of the iterative LPA is to provide a high number of degrees of freedom and to apply the constraints gradually by small steps. The mathematical study of the convergence of the iterative LPA is, however, out of the scope of this paper. A. Constraints on Grating The fabrication constraints are applied to the grating coupling coefficient q(z) in the space domain to improve grating manufacturability. The fabrication constraints on the FBG profile can include removing small oscillations, scaling the FBG, and some specific demands, such as removing phase shifts in the FBG. Removing small oscillations in the coupling coefficient can shorten the grating and avoid small apodization lobes, which are difficult to fabricate accurately. Truncating the grating length is also necessary for the FBG to be physically realizable. One method is first smoothing the grating by a big window and then truncating the grating length, where the smoothed coupling coefficients are below a threshold value. However, this thresholding can leave a part of the lobes in the grating profile, violating grating apodization. Another method is to retain only a given number of main lobes of the FBG profile and remove all other smaller lobes. We tested this method that retains one to six lobs of the grating, respectively, in our design example. The results are shown in Table I. The designs that retain two and three lobes in the grating produced slightly better performance. We choose to fabricate the two-lobe design as shown in detail in Section V. Removing small oscillations cuts the grating length and, as a consequence, broadens the spectrum. We then use a scaling of the grating by stretching out the grating with a scale parameter a, which is equal to the ratio of the requested bandwidth over the actual bandwidth of the grating. We only scaled the last output grating from the iterative LPA. Scaling the grating during the iterations could lead to a divergence of the iterations, according to our experiment. The iterative LPA can also handle some specific constraints on the gratings. For instance, we can remove all the phase shifts in the grating complex-valued coupling coefficient. Obviously, this constraint can greatly facilitate the fabrication. For this purpose, three methods to constrain the negative parts of the coupling coefficients were tested: inverting their sign, setting them to zero, and reducing their value to zero gradually in the iterations. In the last method, we multiplied the negative parts of coupling coefficients by a constant, (1/2 N ) < 1, where N is the number of iterations. The impact of removing the negative parts of the coupling coefficient on the FBG spectrum can be analyzed as follows: the coupling coefficient q is rewritten as a summation of q + + q, which are the positive and negative parts of q, respectively. Thus, q consists of asymptotically decreasing sidelobes on both sides of the maximum, as shown in Fig. 2(b). Forcing q to zero, or inverting its sign, is equivalent to adding an FBG of q,or2 q, to the FBG of q +. If the FBG spectrum would be the Fourier transform of q, then from the linearity of the Fourier transform, we have the spectrum Q = Q + + Q, where the Fourier transform Q of q is close to a sinusoidal function, contributing to the sidelobes in the FBG spectrum, as shown in Fig. 2(c). Therefore, we prefer to gradually reduce the q to zero in the iterations, which results in a small distortion in the spectrum, which would then be corrected in each iteration by the spectral constraints, as described in Section III-B.

4 OUYANG et al.: LAYER-PEELING ALGORITHM FOR DESIGNING FBGs WITH FABRICATION CONSTRAINTS 3927 Fig. 3. Figures of merit. (a) Isolation. (b) BWU. (c) GDR in the 1-dB passband. (d) Dispersion in the 0.5-dB passband. bands from 0.2 to 0.4 nm and from 0.2 to 0.4 nm. The complex-valued spectrum in these bands is a free parameter. Fig. 2. Coupling coefficient (left) and the spectrum (right) of the reflectivity and group delay computed with the transfer-matrix method. (a) Origin grating. (b) Negative part of the grating. (c) Original grating with the negative part inversed to positive. B. Constraints on Spectrum The application of the fabrication constraints to the grating would worsen its spectrum. We then applied the constraints to the spectrum of the modified grating. The application of the spectral constraints is for satisfying the target spectral specifications, while leaving some degrees of freedom for the iterative LPA to converge to a solution with minimum and acceptable errors. The FBG spectrum is, in general, complex valued; we apply the constraints to both the reflectivity and the dispersion of the gratings. In the design example for the bandpass filter with minimum dispersion, the application of the spectral constraint in each iteration consists of three steps. 1) Put the reflectivity in the 0.4-nm passband to the target value of Keep its variation, but limit the variation amplitude within the 0.1-dB range. 2) Put the reflectivity out of the passband of 0.8 nm below 30 db. 3) Limit the local dispersion within the flat-top passband of 1 dbto40ps/nm. The specific target value of the dispersion, 40 ps/nm, was determined empirically. A target value smaller than 40 ps/nm did not result in a lower dispersion in the final solution of the iterations. We did not apply any constraints in the remaining C. Figures of Merit Four figures of merit are used for characterizing the performance of the designed passband filters: the stopband isolation, the bandwidth-utilization (BWU) factor, which is the ratio between the 1-dB reflection bandwidth and the 30-dB bandwidth [2], the rms value of the group-delay ripple (GDR) in the 1-dB flat-top passband, and the maximum dispersion in the 0.5-dB bandwidth. Fig. 3 shows that the values of the figures of merit fluctuate in the first few iterations, but asymptomatically converge to their respective stable values with the iterations. The dispersion increases dramatically from the initial solution in the first iterations. This is the price paid for applying the fabrication constraints, which reduce the negative part of the coupling coefficient and finally remove the phase shifts. After the 25th iteration, the decrease of the isolation is accompanied by a slight increase of the dispersion, as shown in Fig. 3. There is a tradeoff between the isolation and the dispersion. The iterations are stopped when the tradeoff among the figures of merit is satisfactory. IV. DESIGN EXAMPLE As an example, we design a bandpass filter with the iterative LPA. The design target is a 100-GHz wavelength-divisionmultiplexing (WDM) bandpass FBG with a reflectivity of 99%, an isolation of 30 db, and a minimum dispersion in an as-large-as-possible flat-top passband. In the discrete LPA, the sampling interval was of 0.1 mm in the grating and nm in the detuning space. At the Nyquist rate, this sampling rate corresponds to a bandwidth of 8.2 nm in the wavelength and a grating length of 500 mm, respectively. In each iteration, we cut the grating length to 80 mm for satisfying the physical-realizability condition. In addition, we shift the

5 3928 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 23, NO. 11, NOVEMBER 2005 Fig. 5. Coupling coefficient for low-dispersion passband filter with two lobs after 40 iterations. Fig. 4. Bandpass filter designed by a single LPA. (a) Apodization of the 80-mm length. (b) Spectrum. FBG coupling-coefficient profile in the space, such that the main lobe of the profile is in the middle of the 80-mm window. The shift is implemented by multiplying a constant phase to the FBG spectrum. Note that the physical length of the designed FBG can be shorter than the 80-mm window size. We chose the ideal square spectrum of the 0.8-nm passband and zero dispersion as the initial solution. Fig. 4 shows the coupling coefficient of the grating synthesized by a single LPA. The hard cut of the grating caused high-amplitude sidelobes and high GDR in the spectrum. The Gibbs ringing noise can be seen in both amplitude and group-delay curves. Moreover, the grating profile is an asymmetric sinclike function with a large number of asymptotically decreasing oscillations along the grating length. This profile is typical for the outputs of the LPA. Fabrication of such an FBG with a large number of π-phase shifts and fine-tuned apodization is difficult to realize with precision. In our design with the iterative LPA, we cut small oscillations along the fiber length and removed all the phase shifts in the grating, so that the new passband FBGs could be written with the conventional holographic phase mask, which contains no phase shifts. According to the tradeoffs among the figures of merit shown in Fig. 3, we stopped the iterations when the isolation is below 30 db after 40 iterations. The designed grating is 11.7-mm long with two lobs, but contains no phase shift, as shown in Fig. 5, which is easier to fabricate than that directly synthesized with a single LPA shown in Fig. 4. In the 0.5-dB passband of 0.31-nm width, the maximum dispersion is 76 ps/nm and the rms value of the GDR is 0.2 ps. The 30-dB bandwidth is 0.77 nm and the BWU is 45%. The dispersion is a little higher than that of the dispersion-free bandpass FBG designed by the LPA in [6]. This is the price paid for removing the phase shifts in the FBG. However, this dispersion could be acceptable in many applications. Moreover, the new FBG is easier and cheaper to manufacture. The fabricated FBG can have less fabrication errors and better performance compared with the other designs. The designed FBG shown in Fig. 5 has been fabricated in H 2 -loaded Ge-doped Corning SMF28 fiber using an Excimer laser and a holographic uniform phase mask at the central wavelength of nm. We use amplitude masks to control the index modulation related to the designed coupling-coefficient profile. Experimental and simulation results for the designed grating are illustrated in Fig. 6. The fabricated FBG shows the isolation of 25 db, the 0.5-dB bandwidth of 0.32 nm, and the maximum dispersion in the 0.5-dB passband below 92 ps/nm. This presents a good agreement with the designed values. Note that the experimental FBG has a slightly higher dispersion than the designed value. On the other hand, some of our designs can give a slightly higher performance than that of the fabricated FBG. V. C ONCLUSION We have demonstrated the iterative layer-peeling algorithm (LPA) for designing the bandpass fiber Bragg grating (FBG). We used the inverse LPA as an analysis tool to speed up the iterations. We have analyzed the impact of the applied constraint to

6 OUYANG et al.: LAYER-PEELING ALGORITHM FOR DESIGNING FBGs WITH FABRICATION CONSTRAINTS 3929 Fig. 6. Reflectivity spectrum and group delay for the grating shown in Fig. 5; experiment versus simulation. the grating and to its spectrum. The convergence of the iterative LPA can be ensured only for weak gratings. As the Racatii equation is nonlinear, errors can increase in some iterations, but in most cases, finally converge asymptotically to stable values. The iteration is stopped when the isolation, dispersion, and flat-top bandwidth are traded-off to the acceptable values. The design of the passband wavelength-division-multiplexing (WDM) filter of minimum dispersion is much easier to fabricate than that synthesized by the conventional LPA. ACKNOWLEDGMENT The authors would like to acknowledge one of the reviewers, who pointed out that the inverse LPA has been presented in pages of the Ph.D. thesis of J. Skaar. REFERENCES [1] K. A. Winick and J. E. Roman, Design of corrugated waveguide filters by Fourier-transform techniques, IEEE J. Quantum Electron., vol. 26, no. 11, pp , Nov [2] G. H. Song and S. Y. Shin, Design of corrugated wave guided filter by the Gel fand Levitan Marchenko inverse-scattering method, J. Opt. Soc. Amer. A, vol. 2, no. 11, pp , Nov [3] E. Preal, J. Camany, and J. Marti, Iterative solution to the Gel fand Levitan Marchenko couple equations and application to synthesis of fiber gratings, IEEE J. Quantum Electron., vol. 32, no. 12, pp , Dec [4] R. Feced, M. N. Zervas, and M. A. Muriel, An efficient inverse scattering algorithm for the design of nonuniform fiber Bragg grating, IEEE J. Quantum Electron., vol. 35, no. 8, pp , Aug [5] J. Skaar, L. Wang, and T. Erdogan, On the synthesis of fiber Bragg grating by lay peeling, IEEE J. Quantum Electron., vol. 37, no. 2, pp , Feb [6] J. Skaar and O. H. Waagaard, Design and characterization of finite length fiber gratings, IEEE J. Quantum Electron., vol. 39, no. 10, pp , Oct [7] H. Li, T. Kumagai, and K. Ogusu, Advanced design of a multichannel fiber Bragg grating based on a layer-peeling method, J. Opt. Soc. Amer. B, vol. 21, no. 11, pp , Nov [8] K. Kolossovski, R. A. Sammut, A. V. Buryak, and D. Y. Stepanov, Three-step design optimization for multi-channel fiber Bragg gratings, Opt. Express, vol. 11, no. 9, pp , May [9] Y. Ouyang and Y. Sheng, Design fiber Bragg grating using iterative layerpeeling algorithm, presented at the Optical Fiber Communication (OFC), Los Angeles, CA, 2004, Paper MF32. [10] A. V. Buryak, Iterative scheme for the mixed scattering problem, in Bragg gratings, photosensitivity, and poling in glass waveguides, in OSA Tech. Dig. Series, Washington, DC, 2003, pp [11] J. Skaar and H. E. Engan, Distributed intragrating sensing using phase retrieval, in Proc. SPIE 13th Int. Conf. Optical Fiber Sensors (OFS), Kuongju, South Korea, 1999, vol. 3746, pp [12] J. Skaar, Iterative design of antireflection coatings based on the direct and inverse scattering transform, Opt. Commun., vol. 232, no. 1 6, pp , Mar [13] K. Aksnes and J. Skaar, Design of short fiber Bragg grating by use of optimization, Appl. Opt., vol. 43, no. 11, pp , Apr [14] G. Lenz, B. J. Eggleton, C. K. Madsen, C. R. Giles, and R. E. Slusher, Optimal dispersion of optical filters for WDM systems, IEEE Photon. Technol. Lett., vol. 10, no. 4, pp , Apr [15] J. R. Fienup, Iterative method applied to image reconstruction and to computer-generated holograms, Opt. Eng., vol. 19, no. 3, pp , Mar [16] R. W. Gerchberg and W. O. Saxton, A practical algorithm for the determination of phase from image and diffraction plane pictures, Optik, vol. 35, no. 2, pp , [17] M. Ibsen, P. Petropoulos, M. N. Zervas, and R. Feced, Dispersion-free fibre Bragg gratings, presented at the Optical Fiber Communication (OFC), Anaheim, CA, 2001, Paper-MC1. Yueh Ouyang received the M.S. degree in physics from Chung Cheng Institute of Technology, Taoyuan, Taiwan, R.O.C., in 1989 and the Ph.D. degree from the Institute of Optical Science, National Central University, Taoyuan, in He worked as a Research Assistant at the Centre d Optique, Photonique, et Laser, Laval University, QC, Canada, from 2001 to He is now teaching in the Department of Physics, Chinese Military Academy, Fengshan Kaohsiung, Taiwan. His current research interests are fiber-bragg-grating (FBG) design, optical-information processing, and pattern recognition. Yunlong Sheng received the B.S. degree from the University of Science and Technology of China, Anhui, China, in He received the M.Sc., Doctor, and Doctor ès Science Physique degrees from the Université de Franche-Comté, Besançon, France, in 1980, 1982, and 1986, respectively. Since 1985, he has been with the Center for Optics, Photonics, and Lasers, Laval University, Sainte-Foy, QC, Canada, and is now a Full Professor. His research interests involve diffractive optics, fiber Bragg gratings (FBGs), nanooptics optical-signal processing, pattern recognition, and image fusion. He has authored and coauthored more than 180 technical papers, books, and book chapters, and holds two patents on FBG fabrication. Dr. Sheng is a Fellow of the Optical Society of America (OSA) and the International Society for Optical Engineering (SPIE). Martin Bernier received the B.Ing. degree in physics from Laval University, Sainte-Foy, QC, Canada, in Currently, he is pursuing the M.Sc. degree at the Centre d Optique, Photonique, et Laser at Laval University. His research interests involve fiber Bragg gratings (FBGs) and diffractive optics. He also held a technical position at Institut National d Optique, QC, Canada, from 1999 to 2001, and worked, among other things, on the development of holographic phase-mask technology.

7 3930 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 23, NO. 11, NOVEMBER 2005 Gilles Paul-Hus received the M.Sc. degree in physics from Laval University, Sainte-Foy, QC, Canada, in He was an invited scholar within the context of the German Academic Exchange Service from 1995 to 1997 at Dresden University of Technology, Dresden, Germany. From 1998 to 2002, he was with JDS Uniphase and Alcatel Optronics in Ottawa/Gatineau, Canada, where he was involved in the development of fiber- Bragg-grating (FBG) technology. Since 2002, he has been a Research Assistant of the Centre d Optique, Photonique, et Laser at Laval University, where he is in charge of the nanophotonics infrastructure. In addition, he has worked with graduate students on the development of a passive optical component.