New Class of Instabilities in Passive Optical Cavities

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Abstract
In this Letter we show that the fixed points of the Ikeda map are more unstable to perturbations with a short-scale transverse structure than to plane-wave perturbations. We correctly predict the most unstable wavelength, the critical intensity, and the growth ratés of these disturbances. Our result establishes that, for a large class of nonlinear waves, spatial structure is inevitable and drastically alters the route to chaos. In an optical cavity the consequence is that the period-doubling cascade is an unlikely scenario for transition to optical chaos.