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Abstract: Optical microcavities are open billiards for light in which electromagneticwaves can, however, be confined by total internal reflection at dielectricboundaries. These resonators enrich the class of model systems in the field ofquantum chaos and are an ideal testing ground for the correspondence of ray andwave dynamics that, typically, is taken for granted. Using phase-space methodswe show that this assumption has to be corrected towards the long-wavelengthlimit. Generalizing the concept of Husimi functions to dielectric interfaces,we find that curved interfaces require a semiclassical correction of Fresnel-slaw due to an interference effect called Goos-Haenchen shift. It is accompaniedby the so-called Fresnel filtering which, in turn, corrects Snell-s law. Thesetwo contributions are especially important near the critical angle. They are ofsimilar magnitude and correspond to ray displacements in independentphase-space directions that can be incorporated in an adjusted reflection law.We show that deviations from ray-wave correspondence can be straightforwardlyunderstood with the resulting adjusted reflection law and discuss itsconsequences for the phase-space dynamics in optical billiards.



Author: Martina Hentschel

Source: https://arxiv.org/







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