Angular momentum localization in oval billiards

Angular momentum ceases to be the preferred basis for identifying dynamical localization in an oval billiard at large excentricity. We give reasons for this, and comment on the classical phase-space structure that is encoded in the wave functions of “leaky” dielectric resonators with oval cross section. Geometric optics is an important engineering tool because of its explanatory and predictive power, even when wave effects are present, as is the case in resonant cavities. Nevertheless, quantum chaos has not been widely recognized as an issue in optical resonators until recently [1], because the engineer often has the freedom to choose geometries for which either the ray picture is simple or the wave equation is separable (up to small perturbations). This is a luxury that we do not usually have in naturally occuring, “self-assembled” optical resonators such as, e.g., aerosol droplets [2, 3] or microcrystallites [4].; these examples typically have mixed phase spaces. What we learn from such systems in turn allows us to accept chaotic ray dynamics as a way to introduce added freedom into the design of optical devices in a wide range of material systems, such as semiconductor microdisks [5, 6], polymers and glasses [7, 8, 9]. One of the essential phenomena that makes chaotic resonators useful in this respect is dynamical localization, because it allows cavity resonances with decay rates that exceed the values expected from classical ray considerations. Mixed dynamics does not necessarily make it impossible to identify localization [10], provided the classical phase space stucture is properly taken into account. In this paper, we discuss how localization can be characterized in oval dielectric cavities. From the quantum-chaos perspective, dielectric microcavities allow us to study the ray-wave duality in a class of open billiard systems bounded by “penetrable” walls which introduce an escape condition in phase space [11]. This openness arises because the internal and external region are coupled across the dielectric-air interface. In many cases this interface can be considred as abrupt