Emission from dielectric cavities in terms of invariant sets of the chaotic ray dynamics

The chaotic ray dynamics inside dielectric cavities is described by the properties of an invariant chaotic saddle. The localization of the far-field emission in specific directions, recently observed in different experiments and wave simulations, is found to be a consequence of the filamentary pattern of the saddle's unstable manifold. For cavities with mixed phase space, the chaotic saddle is divided in hyperbolic and nonhyperbolic components, related, respectively, to the intermediate exponential (t < t(c)) and the asymptotic power-law (t>t(c)) decay of the energy inside the cavity. The alignment of the manifolds of the two components of the saddle explains why even if the energy concentration inside the cavity dramatically changes from t < t(c) to t>t(c), the far-field emission changes only slightly. Simulations in the annular billiard confirm and illustrate the main results.