Berlin 2008 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 23: Quantum chaos I

DY 23.1: Invited Talk

Thursday, February 28, 2008, 09:30–10:00, MA 001

From the phase-space representation of optical microcavities to an improved ray dynamics — •Martina Hentschel — Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, D-01187 Dresden

Optical microcavities are open billiards for light in which electro-magnetic 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. We first generalize the concept of Husimi functions to dielectric interfaces where both the wave function and its derivative are non-zero. We then show that curved interfaces require a semiclassical correction of Fresnel’s law due to an interference effect called Goos-Hänchen 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. Implementing both effects into the ray model improves the agreement with wave optics by about one order of magnitude. We discuss the phase-space dynamics of light in this amended ray-optics picture and show that the Poincaré surface of section can be significantly modified.

Further reading: M. Hentschel et al., Europhys. Lett. 62, 636 (2003); H. Schomerus and M. Hentschel, Phys. Rev. Lett. 96, 243903 (2006).