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Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials
Published on: September 26, 2014
Trace formula for dielectric cavities. II. Regular, pseudointegrable, and chaotic examples
E Bogomolny1, N Djellali, R Dubertrand
1Univ. Paris-Sud, Laboratoire de Physique Théorique et Modèles Statistiques, F-91405 Orsay, France.
Summary
This study validates a trace formula for dielectric resonator density across various shapes, including integrable and chaotic systems. Results show good agreement between theory, simulations, and microlaser experiments.
Area of Science:
- Optics and Photonics
- Theoretical Physics
- Cavity Quantum Electrodynamics
Background:
- Dielectric resonators are open systems with significant applications in optics and photonics.
- A prior study established a trace formula for resonance density in circular cavities.
- Understanding resonance properties in diverse cavity shapes is crucial for device optimization.
Purpose of the Study:
- To extend and validate the trace formula for resonance density to various integrable, pseudointegrable, and chaotic cavity shapes.
- To compare theoretical predictions with numerical simulations and experimental data.
- To assess the applicability of the trace formula beyond circular cavities.
Main Methods:
- Theoretical derivation of the trace formula for non-circular cavities.
- Numerical simulations of resonance properties for different cavity geometries (square, rectangle, ellipse, pentagon, stadium).
- Experimental validation using organic microlasers with varying resonator designs.
Main Results:
- The trace formula accurately predicts both smooth and oscillating parts of the resonance density for diverse cavity shapes.
- Excellent agreement was observed between theoretical predictions, numerical simulations, and experimental results.
- The study confirms the formula's validity for integrable, pseudointegrable, and chaotic systems.
Conclusions:
- The validated trace formula provides a powerful tool for analyzing dielectric resonators of various geometries.
- This work advances the understanding of resonance phenomena in open systems relevant to photonics.
- The findings support the design and optimization of advanced optical and photonic devices.
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