Periodic Oscillations and Chaos in a Fabry-Pérot Cavity Containing a Nonlinearity of Finite Response Time

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Abstract
We present a detailed analysis showing that positive-branch instabilities occur in nonlinear resonators in the Fabry-Pérot (folded) configuration. Responses in the unstable region can be unstable or chaotic, depending on parameter values. Values of the response/round-trip time ratio in excess of unity can still yield instabilities, albeit on progressively higher branches as the ratio increases. The analysis proceeds from the basic optical bistability equations through the Maxwell-Debye equations to an explicit expression for the nonlinear phase shift. Linearization leads to thresholds in good agreement with direct computation. A simple expression for the accessible domain of phase-space is derived. The fundamental oscillation is interpreted as a cavity-resonant sideband instability.