Self-pulsing and chaos in Kerr-nonlinear coupled ring resonators

We investigate the dynamics of nonlinear resonant structures consisting of two coupled ring resonators. The time evolution of the system is modeled by difference-differential equations that take into account non-instantaneous Kerr response and the effect of loss. We demonstrate transitions from stable states to periodic (self-pulsing) and chaotic states. We identify parameters that can significantly affect onset and period of self-pulsing solutions.