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Nonlinear Optical Ring-Cavity Model Driven by a Gas Laser

In: Comprehensive Applied Mathematical Modeling in the Natural and Engineering Sciences

Author

Listed:
  • David J. Wollkind

    (Washington State University, Department of Mathematics)

  • Bonni J. Dichone

    (Gonzaga University, Department of Mathematics)

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.

Suggested Citation

  • David J. Wollkind & Bonni J. Dichone, 2017. "Nonlinear Optical Ring-Cavity Model Driven by a Gas Laser," Springer Books, in: Comprehensive Applied Mathematical Modeling in the Natural and Engineering Sciences, chapter 0, pages 423-455, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-73518-4_17
    DOI: 10.1007/978-3-319-73518-4_17
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