Kinetics of Localized Pattern Formation in Optical Systems

We consider the nonlinear optics models describing nascent optical bistability and the optical parametric oscillator and study a pattern formation mechanism which relies on the existence of an unstable band of modes which includes the homogeneous or zero mode and originates from the interaction of a Turing (modulational) instability with a saddle-node bifurcation. We identify three regimes in the evolution from an initial unstable field distribution to a final localized stationary pattern which is a unique stripe in the transverse profile of the field inside the cavity. This kinetics has analogies with that of the spinodal decomposition in immiscible mixtures.