SPATIOTEMPORAL PATTERNS AND LOCALIZED STRUCTURES IN NONLINEAR OPTICS

We show that in a degenerate optical parametric oscillator with satura ble losses for the frequency down-converted field, the steady state ca n be destabilized via either a Hopf or a Turing instability. The relat ive order between the two bifurcations is controlled by the linear los s of the saturable absorber. If the Turing bifurcation is subcritical and the Hopf bifurcation occurs in the hysteresis domain involving the homogeneous and inhomogeneous states, steady localized structures are generated below the Hopf bifurcation and time-periodic localized stru ctures are generated above the Hopf bifurcation.