Effect of material response time on optical bistability in nonlinear distributed feedback gratings

The dynamic behaviors of nonlinear periodic waveguides with a finite material response time have been investigated by numerically solving both the coupled-mode equations and Debye relaxation equation, When the response time of the nonlinearity is more than the transit time through the grating, a modulational instability is sufficiently suppressed and one can obtain optical bistability. Unlike a nonlinear Fabry-Perot resonator or ring resonators, overshoot in the transmission never takes place in the case of zero detuning. However, a relaxation (or damped) oscillation always takes place in the presence of detuning. It is also found that the switch-on time depends on the material response time and the switch-off time is almost independent of it.