Resonance--Assisted Tunneling in Deformed Optical Microdisks with a Mixed Phase Space

The life times of optical modes in whispering-gallery cavities crucially depend on the underlying classical ray dynamics and may be spoiled by the presence of classical nonlinear resonances due to resonance–assisted tunneling. Here we present an intuitive semiclassical picture which allows for an accurate prediction of decay rates of optical modes in systems with a mixed phase space. We also extend the perturbative description from near-integrable systems to systems with a mixed phase space and find equally good agreement. Both approaches are based on the approximation of the actual ray dynamics by an integrable Hamiltonian, which enables us to perform a semiclassical quantization of the system and to introduce a ray-based description of the decay of optical modes. The coupling between them is determined either perturbatively or semiclassically in terms of complex paths.