Spatial pattern formation and instabilities in resonators with nonlinear dispersive media

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Abstract
We discuss instabilities of the fundamental single-transverse-mode solution and the formation of new transverse spatial patterns in optical systems, containing nonlinearly absorbing two-level media using two transverse cavity geometries (rectangular and cylindrical). Under the appropriate approximations, these two models can be described by the same set of dynamical equations. Though the equations for the two models differ in their coefficients, their dynamical solutions are comparable. We find hysteresis phenomena associated with transitions in the transverse structure of the intensity which are completely different from the steady-state bistability and hysteresis found in theories of single-mode operation.