Spontaneous hexagon formation in a nonlinear optical medium with feedback mirror

We present two-dimensional numerical simulations of a nonlinear optical system made of a thin slice of Kerr material and a feedback mirror. The phase modulation induced on the light by the nonlinear material is transformed into amplitude modulation by propagation to the mirror and back, thus forming a feedback loop. Our simulations show that the uniform plane-wave solution deforms for sufficient pump intensity into a nonuniform pattern of hexagonal symmetry, independently of the sign of the nonlinearity, a feature which may be generic for third-order nonlinear optical systems.