Generation of Bragg solitons through modulation instability in a Bragg grating structure

Abstract

In this article, we consider the continuous wave cw propagation through the nonlinear periodicstructure that consists of alternating layers of both positive and negative Kerr coefficients along thepropagation direction. We investigate the modulational instability MI conditions required for thegeneration of ultrashort pulses for the nonlinearity management system. We study the occurrence ofMI at the top and bottom edges of the photonic band gap PBG where the forward and backwardpropagating waves are strongly coupled because of the presence of the grating structure. We alsostudy the MI when cw is detuned from the edges of the PBG into the anomalous and normaldispersion regimes. In addition, we discuss the existence of gap solitons for the nonlinearity managementsystem in the upper and lower branches of the dispersion curve through the MI gainspectra. We observe the generation of higher order solitons in the nonlinear periodic structure whenthe input power is increased beyond a certain critical level. Finally, we discuss the generation ofhigher order Bragg grating solitons through the intensity evolution of the forward and backwardpropagating fields.