From domain walls to localized structures in degenerate optical parametricoscillators

Degenerate optical parametric oscillators (DOPO) possess one-dimensional st able domain wall solutions in the presence of diffraction. Such domain wall s connect two homogeneous stable states and display damped spatial oscillat ions. In two dimensions, domains of one homogeneous phase inside the other tend to shrink for zero and positive detunings. For pump values above an ap propriate threshold, the shrinking of the domains is stopped by the short-r ange interaction of the oscillatory tails of pump and signal domain walls l eading to local back conversion and radially symmetric localized states. Th is mechanism corresponds to the stabilization of a homoclinic orbit and is generic in that it requires neither peculiar bistability conditions nor the existence of a patterned state. Neither domain walls nor domain-wall-induc ed localized states survive in the non-degenerate case with a large frequen cy difference between signal and idler fields.