Abstract

The first analytic verification of the stability of topological solitons corresponding to wave-front solutions of the optical parametric oscillator is given. A translational invariance allows perturbations to the system to shift the front position without affecting the underlying exponential stability of the fronts themselves. For the two-dimensional problem with a positive O(1) signal detuning, the front curvature is shown to be governed by a heat equation, so that the only stable topological solitons supported must be stripes.

© 1999 Optical Society of America

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