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.

arXiv comment8 pages, 12 figures

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Cited by in corpus (43)

• Leaking Chaotic Systems
• Bound states in the continuum in open acoustic resonators
• Resonance widths in open microwave cavities studied by harmonic inversion
• Experimental Tuning of Transport Regimes in Hyperuniform Disordered Photonic Materials
• Spectral problems in open quantum chaos
• 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
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• Trace formula for dieletric cavities : I. General properties
• Fractal Weyl law for three-dimensional chaotic hard-sphere scattering systems
• Lifetime statistics in chaotic dielectric microresonators
• Statistics of Chaotic Resonances in an Optical Microcavity
• Hierarchical Fractal Weyl Laws for Chaotic Resonance States in Open Mixed Systems
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• Recent advances in open billiards with some open problems
• Chaotic Systems with Absorption
• Use of Transmission and Reflection Complex Time Delays to Reveal Scattering Matrix Poles and Zeros: Example of the Ring Graph
• Formation and interaction of resonance chains in the open 3-disk system
• Harmonic inversion analysis of exceptional points in resonance spectra
• Structure of resonance eigenfunctions for chaotic systems with partial escape
• Quantum signatures of classical multifractal measures
• Localization of Chaotic Resonance States due to a Partial Transport Barrier
• 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
• The role of short periodic orbits in quantum maps with continuous openings
• Lagrangian descriptors for the Bunimovich stadium billiard
• Weyl law for open systems with sharply divided mixed phase space
• Escape dynamics of Bose-Hubbard dimer out of a trap
• Local random vector model for semiclassical fractal structure of chaotic resonance states
• Ray model and ray-wave correspondence in coupled optical microdisks
• 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
• Dynamics of transmission in disordered topological insulators
• Transport properties of diffusive particles conditioned to survive in trapping environments
• Time delay in a disordered topological system
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• Counting statistics of chaotic resonances at optical frequencies: theory and experiments
• Self-Similarity Among Energy Eigenstates
• Left-Right Husimi Representation of Chaotic Resonance States: Invariance and Factorization