Turing Patterns in Nonlinear Optics

The phenomenon of pattern formation in nonlinear optical resonators is commonly related to an off-resonance excitation mechanism, where patterns occur due to mismatch between the excitation and resonance frequency. In this paper we show that the patterns in nonlinear optics can also occur due to the interplay between diffractions of coupled field components. The reported mechanism is analogous to that of local activation and lateral inhibition found in reaction-diffusion systems by Turing. We study concretely the degenerate optical parametric oscillators. A local activator-lateral inhibitor mechanism is responsible for generation of Turing patterns in form of hexagons.