Nonlinear stability analysis of hexagonal optical pattern formation in an atomic sodium vapor ring cavity

Francisco Alvarado

David J. Wollkind

David J. Wollkind, Francisco Alvarado, Dean Emmanuel Edmeade

The development of spontaneous stationary equilibrium patterns induced by the injection of a laser pump field into a purely absorptive two-level atomic sodium vapour ring cavity is investigated by means of various weakly non-linear stability analyses 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 non-linear partial differential time-evolution equation describing the intracavity field on an unbounded 2D spatial domain. Diffraction of radiation can induce transverse patterns consisting of stripes, squares 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 non-linear optical pattern formation studies.

T. Ackemann, Wulfhard K. Lange

W. J. Firth, Andrew J. Scroggie, Graham S. McDonald +1 more

The mean-field model of optical bistability in a ring cavity is extended to include diffraction in two transverse dimensions. Nonlinear analysis in the neighborhood of the instability of the homogeneous solution indicates the formation of stable hexagonal patterns, and this is confirmed by numerical simulation, with reasonable quantitative agreement. Simulations with higher excitation show defect structures and complex dynamical patterns.

Bonnie L. Schmittberger, Daniel J. Gauthier