Dynamics and instabilities in series of coupled nonlinear resonators

We explore the wide range of dynamical behaviour that is possible in networks of coupled nonlinear resonators. Our basis system consists of strongly localized photonic crystal cavities with a Kerr nonlinearity. The employed coupled mode equations are more general [1], so that ring resonators and Bragg cavities are also described. Already the simplest circuits, with two or three resonators, exhibit phenomena such as self-pulsing and chaos. The use of semi-analytical theory allows us to distinguish the interesting regions for experiments. We check the theory with rigorous FDTD simulations.