Self-pulsing and chaos in short chains of coupled nonlinear microcavities

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Abstract
We examine time-domain instabilities in short chains of coupled Kerr-nonlinear resonators. We show that a large parameter region of self-pulsing or chaotic behavior can be realized. We give a detailed description of the possible states in systems with two and three cavities, using phenomenological coupled-mode equations and rigorous simulations. A particular geometry can exhibit a rich range of dynamics, dependent on input conditions. A clear link with the linear transmission properties is shown. This system complements the studies of the nonlinear Bragg reflector and electrons in a nonlinear lattice. Unlike the Bragg grating case, we observe wide detuning ranges that exhibit self-pulsing without first going through a bistable transition.