Dynamic characteristics of nonlinear Bragg gratings in photonic crystal fibres

We study numerically the temporal and spatial dynamics of light in Bragg gratings in highly nonlinear photonic crystal fibre for a CW input signal. Our numerical model is based on the plane wave mode solver and a set of nonlinear coupled-mode equations which we solve using a variation of implicit fourth order Runge-Kutta method. We observe not only bistability of the intensity versus transmitted and reflected light but also complex dynamics. We demonstrate that for values of input intensity above the bistable region the steady state may undergo a supercritical Hopf bifurcation. For some ranges of the input intensity we also observe a coexistence of two periodic attractors. The dynamics found, in particular the features in the bifurcation diagram, strongly depend on the parameters of the fibre. Consequently, we suggest that by proper design of the photonic crystal in the cladding we can adjust such nonlinear features of the Bragg gratings as the width of the bistable region, the intensity at which the bifurcation occurs and also the characteristics of the dynamics at high values of input intensity.