Condition of gap soliton in fiber bragg grating

The condition of the gap soliton production in fiber Bragg grating and the parameters conditionality are advanced. The propagation equation of the solitons in fiber Bragg grating is described by the nonlinear coupled-mode equation, then the differential equations of parameters are obtained by applying the perturbation method, and the approximate results for parameters are calculated. Based on the conditions of the gap soliton in periodical nonlinear optical medium, two inequalities for relation of parameters are obtained. These parameters conditionality and physical significance are proved by numerical calculation. It is theoretically showed that proper parameters choice is needed for gap solitons production in fiber Bragg grating. The study lays the theoretical foundation for solitons production experiments and further engineering application in fiber Bragg grating.