Synthesis of fiber Bragg gratings for use in transmission

A method for designing fiber Bragg gratings with desired complex transmissi on coefficients is proposed. The transmission coefficient of a fiber gratin g satisfies the minimum-phase condition when the linear phase from the pure propagation is ignored. Therefore only a finite bandwidth is considered fo r 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, a nd by numerical examples it is demonstrated that it is possible to realize gratings with specified complex transmission responses inside the considere d bandwidth. The method is also applicable for thin-film filters. (C) 2001 Optical Society of America.