Optical microcavities are open billiards for light in which electromagnetic
waves can, however, be confined by total internal reflection at dielectric
boundaries. These resonators enrich the class of model systems in the field of
quantum chaos and are an ideal testing ground for the correspondence of ray and
wave dynamics that, typically, is taken for granted. Using phase-space methods
we show that this assumption has to be corrected towards the long-wavelength
limit. Generalizing the concept of Husimi functions to dielectric interfaces,
we find that curved interfaces require a semiclassical correction of Fresnel's
law due to an interference effect called Goos-Haenchen shift. It is accompanied
by the so-called Fresnel filtering which, in turn, corrects Snell's law. These
two contributions are especially important near the critical angle. They are of
similar magnitude and correspond to ray displacements in independent
phase-space directions that can be incorporated in an adjusted reflection law.
We show that deviations from ray-wave correspondence can be straightforwardly
understood with the resulting adjusted reflection law and discuss its
consequences for the phase-space dynamics in optical billiards.Comment: 12 pages, 5 figures, to appear in Adv. Sol. St. Phys. 4
