Nonlinear dynamics in an optical system with controlled two-dimensional feedback: Black-eye patterns and related phenomena

We present experimental and theoretical results of spontaneous optical pattern formation in a nonlinear optical system. The nonlinear optical system we considered had a controllable phase-only spatial Fourier filter placed in the system's diffractive feedback loop. A change in feedback field spatial spectral component phase resulted in a transition between dynamic regimes, as observed in both experiments and numerics. Patterns originating from interactions between spatial modes belonging to different instability bands (black-eye patterns, decagons, etc.) were observed, as well as localized states and shock traveling waves.