Nonlinear Optical Ring-Cavity Model Driven by a Gas Laser

David J. Wollkind () and Bonni J. Dichone
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David J. Wollkind: Washington State University, Department of Mathematics
Bonni J. Dichone: Gonzaga University, Department of Mathematics

Chapter Chapter 17 in Comprehensive Applied Mathematical Modeling in the Natural and Engineering Sciences, 2017, pp 423-455 from Springer

Abstract: 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.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-73518-4_17

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DOI: 10.1007/978-3-319-73518-4_17

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