Transverse dynamics of optical parametric oscillators in presence of walk-off

Abstract

We present a model for non degenerate optical parametric oscillators (OPO) including diffraction and walk-off effects, and report how the transverse beam profile is changed by the walk-off. A complex order-parameter description for the OPO near threshold leads to a two dimensional evolution equation with symmetry breaking stemming from the presence of walk-off. We find that the onset of instability is hastened and that the emerging transverse beam profile propagates in the walk-off direction. This prediction agrees qualitatively with recent experimental results. The convective nature of the instability at the first bifurcation predicts that only the noise-sustained structures may play an important role. The absolute instability observed at larger values of the pump parameter, gives rise to dynamically self-sustained patterns. Numerical simulations are reported to illustrate a possible sequence of convective and absolute instabilities together with the subsequent nonlinear transverse spatio-temporal dynamics.