TRANSVERSE DYNAMICS OF OPTICAL PARAMETRIC OSCILLATORS IN PRESENCE OF WALK-OFF

We present a model for non degenerate optical parametric oscillators ( OPO) including diffraction and walk-off effects, and report how the tr ansverse beam profile is changed by the walk-off. A complex order-para meter description for the OPO near threshold leads to a two dimensiona l cl evolution equation with symmetry breaking stemming from the prese nce 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 experiment al results. The convective nature of the instability at the first bifu rcation 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.