Self-pulsing in nonlinear Kerr-type coupled ring resonators with effect of loss

Abstract

We focus on dynamical analysis of nonlinear structures consisting of coupled ring resonators. We formulate a system of difference-differential equations that take into account non-instantaneous Kerr response and the effect of loss. The system is applied to investigation of a double-ring structure in the all-pass filter configuration. We observe rich dynamics, transitions from steady state to Hopf bifurcations and chaos. The system is highly sensitive for the values of detuning from resonance and input power. The influence of loss on oscillatory states is also presented.