What Determines the Direction of Far-Field Emission in Chaotic Microcavities?

Abstract

It is crucial to know how to determine the direction of far-field emission in deformed microcavities. We review the recent advances on this issue focusing on our works. To realize a microlaser with extremely large Q value, the so-called whispering gallery mode (WGM) in the dielectric cavity with spherical or cylindrical boundary has been extensively investigated. The WGM is a mode generated from the ray trapped in the cavity by total internal reflection. Even though extremely high Q value e.g. 107 to 109 has been easily achieved, the fact that the direction of far-field emission is isotropic due to the spherical or cylindrical symmetry of the cavity limits its practical application. Obvious solution is to break such symmetries, which was the original motivation to study a deformed microcavity. When a cavity becomes deformed, one immediately encounters the complicated ray dynamics described by dynamical chaos. The corresponding mode can be obtained by solving Maxwell's equations with appropriate boundary conditions. In the viewpoint of a wave equation, the mode can also be regarded as a quasi-eigenstate of a time-independent Schrodinger equation describing a particle generating the dynamics of the ray. It then invokes the quantum mechanical manifestation of classical chaos, i.e. the so-called quantum chaos. Obvious from the motivation mentioned above it is crucial to know what determines the direction of far-field emission in the deformed microcavity [Nockel, J.U. and Stone, A.D.; 1997]. The existence of the emission itself also makes this problem highly non-trivial in the context of quantum chaos because the system is now open. It is necessary to develop the theory of quantum chaos for open systems. In this presentation we would like to review our recent advances to explain the direction of the far-field emission.