Design of binary long-period fiber grating filters by the inverse-scattering method with genetic algorithm optimization.

An approach is presented to the design of binary long-period fiber grating (LPFG) filters based on the Gel'fand-Levitan-Marchenko (GLM) inverse-scattering method and genetic algorithm optimization. The nonuniform coupling strength of the binary grating can be realized by varying the local duty ratio. A coupled-mode theory combined with the Poisson sum formula for treating the binary index perturbation is developed for the application of the GLM synthesis method. Since the coupled-mode theory, which smears out the discrete coupling nature, can be regarded only as an approximation to the modeling of a binary LPFG, we use instead the transfer-matrix model to analyze the coupling behavior of a nonuniform binary LPFG. Based on the synthesized grating patterns from the GLM method, a real-coded genetic algorithm with the transfer-matrix model is used to compensate for the discrepancies resulting from use of the coupled-mode theory and to optimize the design. We exemplify the above procedure by designing a flatband LPFG filter and a high-visibility all-fiber Mach-Zehnder filter.