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Symmetry induced heteroclinic cycles in a \(\text{CO}_2\) laser. (English) Zbl 1086.37528

Summary: The conditions for the existence of heteroclinic connections between the transverse modes of a CO\(_2\) laser whose setup has a perfect cylindrical symmetry are discussed by symmetry arguments for the cases of three, four and five interacting modes. Explicit conditions for the parameters are derived, which can guide observation of such phenomena.

MSC:

37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
78A60 Lasers, masers, optical bistability, nonlinear optics
34C37 Homoclinic and heteroclinic solutions to ordinary differential equations
37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics
34C14 Symmetries, invariants of ordinary differential equations
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References:

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