Eur. Phys. J. D 3, 275-288 (1998)
https://doi.org/10.1007/s100530050175

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

¹ Laboratoire de Physique des Lasers, Atomes et Molécules (Laboratoire associé au CNRS.) , Centre d'Études et de Recherches Lasers et Applications, Université des Sciences et Technologies de Lille, 59655 Villeneuve d'Ascq Cedex, France
² Laboratoire de Mécanique de Lilleb, Université des Sciences et Technologies de Lille, 59655 Villeneuve d'Ascq Cedex, France

Corresponding author: ^a majid.taki@univ-lille1.fr

Received: 4 March 1998
Revised: 15 June 1998
Accepted: 23 June 1998
Published online: 15 September 1998

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.