Semiclassical description of regular-to-chaotic tunneling in cavities

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Designing optical cavities which exhibit directional lasing emission is anactive area of experimental and theoretical research.Typical cavities have a mixed phase space in which regions of regular andchaotic motion coexist.In such systems, regular-to-chaotic tunneling determines the experimentallyrelevant quality factors and the far-field emission pattern.While an excellent theoretical understanding of regular-to-chaotic tunneling inquantum maps is available, this is not yet the case for cavities.In this project we want to derive quantum-mechanical predictionsfor regular-to-chaotic tunneling rates in cavitiesbased on integrable approximations of the regular region.In particular we want to quantitatively describethe enhancement of tunneling rates due to the influenceof resonance-assisted tunneling.A central goal will be the semiclassical description using complex paths.From this we expect to obtain an intuitive picture ofboth regular-to-chaotic tunneling and resonance-assisted tunneling in cavities.This will allow for designing cavity shapeswith strongly directional emission and large quality factorsand for comparing with experimental results.