Nonlinear Optical Ring-Cavity Model Driven by a Gas Laser

Abstract

The development of spontaneous stationary equilibrium patterns induced by the injection of a laser pump field into a purely absorptive two-level atomic sodium vapor ring cavity is investigated by means of a hexagonal planform nonlinear stability analysis applied to the appropriate governing evolution equation for this optical phenomenon. In the quasi-equilibrium limit for its atomic variables, the mathematical system modelling that phenomenon can be reduced to a single modified Swift-Hohenberg nonlinear partial differential time-evolution equation describing the intracavity field on an unbounded two-dimensional spatial domain. Diffraction of radiation can induce transverse patterns consisting of stripes and hexagonal arrays of bright spots or honeycombs in an initially uniform plane-wave configuration. Then, these theoretical predictions are compared with both relevant experimental evidence and existing numerical simulations from some recent nonlinear optical pattern formation studies. There are four problems: The first two fill in some details of this analysis while the last two examine bistability for a related nonlinear optical phenomenon and hexagonal pattern formation for the relevant amplitude-phase equations with a hypothetical growth rate and set of Landau constants.