Billiards with rational caustics as asymmetric resonant cavities

Pascal Heider

Lucent Labs / Columbia

Billiards with rational caustics have the special property that one can inscribe into the billiard boundary a one-parametric family of p-periodic orbits of the associated billiard- (aka Poincare-) map. Slight perturbations of the boundary destroy the curve of periodic points in SOS and a region analogous to the whispering gallery near boundary - existing in any strictly convex billiard domain - appears. This time however, the region is deep inside the domain.

In this talk the construction and algorithms for generation of billiard domains with rational caustics are presented. They leave enough degrees of freedom to allow one to influence the position of the invariant curve in SOS. The application of these billiard domains as asymmetric resonant cavities will be discussed and justified by numerical simulations.

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