Trace formula for dielectric cavities II: Regular, pseudo-integrable, and chaotic examples

Abstract

Dielectric resonators are open systems particularly interesting due to their wide range of applications in optics and photonics. In a recent paper [PRE, vol. 78, 056202 (2008)] the trace formula for both the smooth and the oscillating parts of the resonance density was proposed and checked for the circular cavity. The present paper deals with numerous shapes which would be integrable (square, rectangle, and ellipse), pseudo-integrable (pentagon) and chaotic (stadium), if the cavities were closed (billiard case). A good agreement is found between the theoretical predictions, the numerical simulations, and experiments based on organic micro-lasers.

18 pages, 32 figures

References in corpus (4)

• Inferring periodic orbits from spectra of simple shaped micro-lasers
• Directional emission of stadium-shaped micro-lasers
• Experimental Test of a Two-dimensional Approximation for Dielectric Microcavities
• Experimental test of a trace formula for two-dimensional dielectric resonators

Cited by in corpus (20)

• Spectral problems in open quantum chaos
• Möbius Strip Microlasers: a Testbed for Non-Euclidean Photonics
• Gain properties of dye-doped polymer thin films
• An insight into polarization states of solid-state organic lasers
• Three-Dimensional Organic Microlasers with Low Lasing Thresholds Fabricated by Multiphoton Lithography
• Nearest level spacing statistics in open chaotic systems: a generalization of the Wigner Surmise
• Localized lasing modes of triangular organic microlasers
• Application of a trace formula to the spectra of flat three-dimensional dielectric resonators
• Origin of emission from square-shaped organic microlasers
• Trace formula for chaotic dielectric resonators tested with microwave experiments
• Trace formula for a dielectric microdisk with a point scatterer
• Chaotic resonance modes in dielectric cavities: Product of conditionally invariant measure and universal fluctuations
• Three-dimensional micro-billiard lasers: the square pyramid
• Three-dimensional emission from organic Fabry-Perot microlasers
• Dielectric Square Resonator Investigated with Microwave Experiments
• Spectral Properties and Dynamical Tunneling in Constant-Width Billiards
• Waves and rays in plano-concave laser cavities, Part~II: a semiclassical approach
• Trace formula for dielectric cavities III: TE modes
• Resonance states of the three-disk scattering system
• Decay Rates of Optical Modes Unveil the Island Structures in Mixed Phase Space