Design Fiber Bragg Grating using Iterative Layer-Peeling Algorithm Yeuh OuYang and Yunlong Sheng Center for optics, Photonics and Lasers Department of Physics, Physical Engineering and Optics Laval University,
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Abstract: We apply the fabrication constraint in the iterative layer-peeling algorithm, such that the new designed passband WDM grating is easier to fabricate and show better performance than that synthesized by the conventional layer-peeling algorithm. 2004 Optical Society of America OCIS codes: (060.2340) Fiber Optics Components, (230.1480) Bragg reflector, (060.4510) Optical Communications.
1. Introduction The inverse scattering layer-peeling algorithm (LPA) for synthesis of the fiber Bragg grating (FBG) is an important progress [1,2], which allows synthesizing a FBG structure from a given spectrum, and is useful for reconstructing or designing FBGs. The LPA is efficient and accurate. However, for most FBGs the solutions from the LPA have typically non-symmetrical, sinc-like apodization profiles with many π -phase shifts and long tap, which are difficult to fabricate, especially with the conventional phase mask side-writing technique. Moreover, a large number of trials by human experts are required for tuning parameters in the synthesis for achieving the best FBG performance and taking into account trade-offs among variety of practical constraints. In this paper, we present an efficient FBG design method using the iterative LPAs. This scheme is recently used by Kolossovski et al in the last step optimization for multi-channel FBGs [3]. We propose the new iterative LPA as a generic scheme for designing FBGs. A variety of adequate constraints to both grating profile and its spectrum can be applied in this scheme, such that the designed FBG are easy to fabricate and satisfy the required spectral performance. We demonstrate a design of the well-known square passband dispersion-free FBG filter as an example of the new design method application. 2. Iterative LPA Exhaustive search by scanning all possible values of the parameters, ad-hoc search by human expert and the genetic algorithm are currently used in the FBG design in order to determine the optimal values of the FBG parameters. These approaches need to use only the analysis or the synthesis code. The LPA synthesis and the analysis using the transfer matrix method based on the coupled-mode theory form a loop, which can iterate. Iterative LPA is a more efficient optimization scheme, because it is close to an iterative gradient steepest descent optimization. The iterative Fourier transform algorithm is widely used in the design of computer generated holograms [4]. However, the Fourier transform (FT) design is applicable only to weak gratings. We replace the FT and inverse FT by the transfer-matrix method for analysis and the LPA for synthesis. Then, the proposed iterative LPA design method consists of the following steps: (1) From a given target spectrum, synthesize grating by the LPA; (2) Apply the fabrication constraint to the grating profile; (3) Compute spectrum of the modified grating by the transfer-matrix method ; (4) Apply the target spectrum constraint to the grating spectrum ; (5) Iterate steps from (1) to (4) until the grating satisfies the fabrication constraints and its spectrum satisfies the target specifications. When the input-output relation is linear, it is proven that the precedent iterative optimization corresponds to a steepest descent algorithm and the algorithm converges [5]. The errors can only decrease during the iterations. The Riccati equation for the FBGs is nonlinear, so that we do not ensure the convergence of the iterative LPA for strong gratings. But the iterative LPA did converge in our most designs. The key for success of the new iterative design method is to provide a high number of degree of freedom and to apply adequate constraints to both grating profile and its spectrum.
3. Design Example The bandpass filter is the most commonly useful WDM filter, which is extensively studied. Optimized of this filter with the Fourier analysis [5], the LPA [6] and the digital filter theory [7] have been proposed. We show here a numerical optimization of the bandpass filter with the iterative LPA. Our design purpose is to improve the manufacturability of the FBG, which is synthesized by the LPA. The ideal square bandpass filter is noncausal and is an IIR filter. Synthesized FBG by the LPA is then an approximation. The LPA is based on the causality. In the LPA one truncates the filter and shift it spatially, such that its impulse response h(t)=0 for t
