Emission from dielectric cavities in terms of invariant sets of the chaotic ray dynamics
arXiv:0805.2190 · doi:10.1103/PhysRevA.79.013830
Abstract
In this paper, the chaotic ray dynamics inside dielectric cavities is described by the properties of an invariant chaotic saddle. I show that the localization of the far field emission in specific directions is related to the filamentary pattern of the saddle's unstable manifold, along which the energy inside the cavity is distributed. For cavities with mixed phase space, the chaotic saddle is divided in hyperbolic and non-hyperbolic 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 predictions.
Corrected version, as published. 9 pages, 6 figures
References in corpus (14)
- Combining directional light output and ultralow loss in deformed microdisks
- Fractal Weyl laws for chaotic open systems
- Semiclassical structure of chaotic resonance eigenfunctions
- Fractal Weyl law for chaotic microcavities: Fresnel's laws imply multifractal scattering
- Poincare recurrences and transient chaos in systems with leaks
- Fractal Weyl law for quantum fractal eigenstates
- Directional emission of stadium-shaped micro-lasers
- Classical Phase Space Revealed by Coherent Light
- Poincare recurrences from the perspective of transient chaos
- Light emission patterns from stadium-shaped semiconductor microcavity lasers
- Prevalence of marginally unstable periodic orbits in chaotic billiards
- Ray-wave correspondence in the nonlinear description of stadium-cavity lasers
- A model for chaotic dielectric microresonators
- Regular Spectra and Universal Directionality of Emitted Radiation from a Quadrupolar Deformed Microcavity