Dynamic behavior of reflection optical bistability in a nonlinear fiber ring resonator

We present an analysis of the dynamic behavior of a nonlinear fiber ring resonator when an optical pulse with an arbitrary shape envelope is incident into it through a fiber directional coupler. The transient analysis is based on the extension of a well-known multiple-beam interference method to nonlinear transmission problems. The steady-state analyses reported so far predict that the ring resonator exhibits reflection optical bistability in the input-output characteristics under appropriate conditions. But, our transient analysis shows that a nearly periodical oscillation of the transmitted power always takes place at a suitable initial detuning when the resonator has no loss or a small loss. It seems that the present instability is caused by the repetition of accumulation and release of the power in the ring resonator. We can obtain a bistable hysteresis loop by introducing a loss to the directional coupler. The dynamic behavior of bistability in a nonlinear fiber ring resonator with coupler loss is then investigated. It is found that a remarkable undershoot and overshoot occur in the switch-off curve and switch-on curve, respectively.