Stability of nonlinear Bragg gratings with a finite material response time

Abstract

A linear stability analysis to investigate the instabilities in nonlinear distributed-feedback gratings with a finite material response time is presented. The amplification (or attenuation) rate and the frequency of sinusoidal perturbations generated in the grating are calculated for different values of the material response time, detuning, and coupling strength. To give the full picture of the stability boundaries, stability maps are plotted in the two cases of a weak grating and a strong grating. The stable region can be enlarged by increasing a response time of the nonlinearity. The required response time increases with the grating strength. A comparison with numerical simulations of the coupled-mode equations is done to confirm the validity of the stability analysis.