Lagrange-multiplier-constrained optimization for designing narrowband dispersionless fiber Bragg gratings

Abstract

This paper presents a new synthesis method for designing complex fiber Bragg gratings (FBGs). The method is based on a multiobjective Lagrange-multiplier-constrained optimization (LMCO), to which various constraints on the designed filters can be added in consideration of practical application demands and fabrication requirements. The maximum amplitude of the index modulation profiles of the designed FBGs can be substantially reduced under constrained conditions. In contrast with the layer-peeling (LP) algorithm, the LMCO method can easily incorporate different types of requirements in terms of a user-defined cost function. Compared to stochastic approaches such as genetic algorithms, the proposed method is likewise a direct optimization method, but without using random numbers, and therefore has a smoother coupling coefficient profile as well as faster convergence. A theoretical model and investigation have been made in this study. A narrowband dispersionless FBG filter for optical fiber communication was designed, and its simulation results were compared with those of the LP algorithm. The study results demonstrate that the LMCO algorithm can provide an alternative for practical and complex fiber grating filters.