Optical Microcavities as Quantum-Chaotic Model Systems: Openness Makes the Difference!

Abstract

Abstract.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-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 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.

Experimental test of a trace formula for two-dimensional dielectric resonators

“…First, the strict semiclassical approximation derived in the limit k → ∞, when applied for large but finite k, requires modifications which are especially important close to the critical angle. From the soluble case of the disk it follows that the reflection coefficient for such scattering is noticeably smaller than that predicted by the usual Fresnel formulas [19,33]. Second, it appears that long-lived resonances that can be observed experimentally mainly correspond to orbits which are not only confined by TIR, but also have an angle of incidence much larger than the critical angle.…”

“…The corresponding classical system is the billiard with the same shape. Rays travel freely inside the billiard domain S and are partially reflected back inside and partially transmitted outside of the billiard according to the Fresnel formulas [19] when they hit the boundary ∂S. The wave equations used for such 2D dielectric resonators are [20]…”

Behavior of three modes of decay channels and their self-energies of elliptic dielectric microcavity

“…Even though we do not exhibit all of the Husimi probability distributions, we can conclude that without loss of generality, unchanging groups are corresponding to the whispering-gallery modes group, the increasing groups are corresponding to the stablebouncing-ball modes group, and the decreasing groups are corresponding to the unstable-bouncing-ball modes group. The tilted Husimi probability distributions of bouncing-ball-type modes are attributed to breaking of time-reversal symmetry, but the origin is not still fully understood [4,31,32].…”

Application of a trace formula to the spectra of flat three-dimensional dielectric resonators

“…Open dielectric resonators have received great attention due to numerous applications [1], e.g., as microlasers [2][3][4][5] or as sensors [6][7][8], and as paradigms of open wave-chaotic systems [9]. The size of dielectric microcavities typically ranges from a few to several hundreds of wavelengths.…”