Fractal Weyl law for chaotic microcavities: Fresnel's laws imply multifractal scattering

Abstract

We demonstrate that the harmonic inversion technique is a powerful tool to analyze the spectral properties of optical microcavities. As an interesting example we study the statistical properties of complex frequencies of the fully chaotic microstadium. We show that the conjectured fractal Weyl law for open chaotic systems [W. T. Lu, S. Sridhar, and M. Zworski, Phys. Rev. Lett. 91, 154101 (2003)] is valid for dielectric microcavities only if the concept of the chaotic repeller is extended to a multifractal by incorporating Fresnel's laws.

8 pages, 12 figures

References in corpus (5)

• Combining directional light output and ultralow loss in deformed microdisks
• Fractal Weyl laws for chaotic open systems
• Quantum-to-classical crossover of quasi-bound states in open quantum systems
• Directional emission of stadium-shaped micro-lasers
• Ray-wave correspondence in the nonlinear description of stadium-cavity lasers

Cited by in corpus (24)

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• Resonances in open quantum maps
• Weyl asymptotics: From closed to open systems
• Emission from dielectric cavities in terms of invariant sets of the chaotic ray dynamics
• Transmission zeros and ultrasensitive detection in complex systems
• Fractal Weyl law for three-dimensional chaotic hard-sphere scattering systems
• Lifetime statistics in chaotic dielectric microresonators
• Resonance distribution in open quantum chaotic systems
• Use of Transmission and Reflection Complex Time Delays to Reveal Scattering Matrix Poles and Zeros: Example of the Ring Graph
• Quantum signatures of classical multifractal measures
• Chaotic Scattering with Localized Losses: S-Matrix Zeros and Reflection Time Difference for Systems with Broken Time Reversal Invariance
• Universal intensity statistics of multifractal resonance states
• Lagrangian descriptors for open maps
• Transient features of quantum open maps
• Weyl law for open systems with sharply divided mixed phase space
• Lagrangian descriptors for the Bunimovich stadium billiard
• Local random vector model for semiclassical fractal structure of chaotic resonance states
• Resonance chains in open systems, generalized zeta functions and clustering of the length spectrum
• Resonance states of the three-disk scattering system
• Cavity-induced backscattering in a two-dimensional photonic topological system
• Transport properties of diffusive particles conditioned to survive in trapping environments
• Dynamics of transmission in disordered topological insulators
• Self-Similarity Among Energy Eigenstates
• Left-Right Husimi Representation of Chaotic Resonance States: Invariance and Factorization