Moving localized structures in quadratic media with a saturable absorber

Spatial moving pulses are found in an optical resonator with a quadratic medium coupled to an intra-cavity saturable absorber. In the context of frequency degenerate optical parametric oscillators, the saturable absorber is shown to be able to generate large amplitude asymmetric pulses in the transverse section of the signal beam. They arise in a regime where the lasing solution undergoes both Hopf and Turing instabilities. These dynamical pulses have a constant velocity and are stable in a wide domain of parameters. The origin of their transverse velocity stems from the pulse asymmetry. For large enough values of the incident pump beam the moving pulses are destabilized giving rise to a complex spatio-temporal behavior.