Theory of Circle Maps and the Problem of One-Dimensional Optical Resonator with a Periodically Moving Wall

Details Theory of Circle Maps and the Problem of One-Dimensional Optical Resonator with a Periodically Moving Wall Theory of Circle Maps and the Problem of One-Dimensional Optical Resonator with a Periodically Moving Wall

1998-10-09

arxiv.org/abs/physics/9810016v1

Phys. Rev. E 59:6 (1999) 6637-6651

Physics

Optics

34 pages LaTeX (revtex) with eps figures, PACS: 02.30.Jr, 42.15.-i, 42.60.Da, 42.65.Yj

Scientific paper

10.1103/PhysRevE.59.6637

We consider the electromagnetic field in a cavity with a periodically oscillating perfectly reflecting boundary and show that the mathematical theory of circle maps leads to several physical predictions. Notably, well-known results in the theory of circle maps (which we review briefly) imply that there are intervals of parameters where the waves in the cavity get concentrated in wave packets whose energy grows exponentially. Even if these intervals are dense for typical motions of the reflecting boundary, in the complement there is a positive measure set of parameters where the energy remains bounded.

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