On the nonlinear dynamics of coupled micro-resonators

We present the study of the dynamics of a two-ring waveguide structure with space-dependent coupling, linear gain and nonlinear absorption; the system that can be implemented in polariton condensates, optical waveguides and nanocavities. We find that due to the modulation instability, it is possible to observe several complex nonlinear phenomena, including spontaneous symmetry breaking, stable inhomogeneous states, oscillating states (limit cycle) and even chaotic dynamics. We compare two systems of coupled rings, with one and two symmetrically located coupling centres.