Nonlinear front competition and secondary absolute instabilities in optical parametric oscillators

Summary form only given. We study the convective/absolute nature of spatial-temporal instabilities in optical parametric oscillators (OPO´s) with negative detuning in presence of diffraction and walk-off effects. The asymptotic response of the signal and idler fields to a localized 2D perturbation of the transversal plane is evaluated. Presence of walk-off breaks the rotational symmetry: the system, at the absolute instability threshold, selects travelling waves propagating in the walk-off direction among an infinity of unstable spatial-temporal modes. We also show that in OPO´s with negative detuning, unlike the case of positive detuning, walk-off selects one mode, shrinks the region of convective instability, and may even suppress the convective/absolute transition. In the framework of coupled complex Ginzburg-Landau amplitude equations, the stability of nonlinear states is investigated, and the convective/absolute nature of secondary instabilities is determined.