Order parameter description of walk-off effect on pattern selection in degenerate optical parametric oscillators

Degenerate optical parametric oscillators can exhibit both uniformly transl ating fronts and nonuniformly translating envelope fronts under the walk-of f effect. The nonlinear dynamics near threshold is shown to be described by a real convective Swift-Hohenberg equation, which provides the main charac teristics of the walk-off effect on pattern selection. The predictions of t he selected wave vector and the absolute instability threshold are in very good quantitative agreement with numerical solutions found from the equatio ns describing the optical parametric oscillator.