Abstract
Degenerate optical parametric oscillators (DOPO) possess one-dimensional stable domain wall solutions in the presence of diffraction. Such domain walls connect two homogeneous stable states and display damped spatial oscillations. In two dimensions, domains of one homogeneous phase inside the other tend to shrink for zero and positive detunings. For pump values above an appropriate threshold, the shrinking of the domains is stopped by the short-range interaction of the oscillatory tails of pump and signal domain walls leading to local back conversion and radially symmetric localized states. This 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-induced localized states survive in the non-degenerate case with a large frequency difference between signal and idler fields.