Two-Dimensional Transverse Solitary Waves as Asymptotic States of the Field in a Bistable Optical Resonator

The dynamical evolution of a two transverse dimensional laser beam profile is monitored as it switches from a low to a high transmission state in a bistable optical resonator. Sharp gradients appearing at the edge of the switched-on central portion of the beam initiate a train of solitary waves which grow inwards towards the beam center. In a high finesse resonator, strong saturation of the beam in the on state tends to stabilize the solitary waves as concentric rings. Unlike earlier one transverse dimensional studies, the central part of the beam under-goes a slow periodic oscillation, but the shapes of the outer rings are consistent with earlier one transverse dimensional predictions. Numerical evidence is provided for filamentation or lower amplitude rings.