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
[Optical Society of America ]
(190.2620) Nonlinear optics : Harmonic generation and mixing
(190.2640) Nonlinear optics : Stimulated scattering, modulation, etc.
(190.4970) Nonlinear optics : Parametric oscillators and amplifiers
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons
J. Nathan Kutz, Thomas Erneux, Stefano Trillo, and Marc Haelterman, "Curvature dynamics and stability of topological solitons in the optical parametric oscillator," J. Opt. Soc. Am. B 16, 1936-1941 (1999)