Synthesis of fiber Bragg gratings for use in transmission

A method for designing fiber Bragg gratings with desired complex transmission coefficients is proposed. The transmission coefficient of a fiber grating satisfies the minimum-phase condition when the linear phase from the pure propagation is ignored. Therefore only a finite bandwidth is considered for the synthesis. The algorithm is based on a result of Krein and Nudel'man [Prob. Peredachi Inf. 11, 37 (1975)]. A numerical algorithm is developed, and by numerical examples it is demonstrated that it is possible to realize gratings with specified complex transmission responses inside the considered bandwidth. The method is also applicable for thin-film filters. (C) 2001 Optical Society of America.