dorsal/arxiv
View SchemaModes of wave-chaotic dielectric resonators
| Authors | Hakan E. Tureci, Harald G. L. Schwefel, Philippe Jacquod, A. Douglas Stone |
|---|---|
| Categories | |
| ArXiv ID | physics/0308016 |
| URL | https://arxiv.org/abs/physics/0308016 |
| Journal | Progress in Optics, Vol 47: 75-137 (2005) |
Abstract
Dielectric optical micro-resonators and micro-lasers represent a realization of a wave-chaotic system, where the lack of symmetry in the resonator shape leads to non-integrable ray dynamics. Modes of such resonators display a rich spatial structure, and cannot be classified through mode indices which would require additional constants of motion in the ray dynamics. Understanding and controlling the emission properties of such resonators requires the investigation of the correspondence between classical phase space structures of the ray motion inside the resonator and resonant solutions of the wave equations. We first discuss the breakdown of the conventional eikonal approximation in the short wavelength limit, and motivate the use of phase-space ray tracing and phase space distributions. Next, we introduce an efficient numerical method to calculate the quasi-bound modes of dielectric resonators, which requires only two diagonalizations per N states, where N is approximately equal to the number of half-wavelengths along the perimeter. The relationship between classical phase space structures and modes is displayed via the Husimi projection technique. Observables related to the emission pattern of the resonator are calculated with high efficiency.
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"abstract": "Dielectric optical micro-resonators and micro-lasers represent a realization\nof a wave-chaotic system, where the lack of symmetry in the resonator shape\nleads to non-integrable ray dynamics. Modes of such resonators display a rich\nspatial structure, and cannot be classified through mode indices which would\nrequire additional constants of motion in the ray dynamics. Understanding and\ncontrolling the emission properties of such resonators requires the\ninvestigation of the correspondence between classical phase space structures of\nthe ray motion inside the resonator and resonant solutions of the wave\nequations. We first discuss the breakdown of the conventional eikonal\napproximation in the short wavelength limit, and motivate the use of\nphase-space ray tracing and phase space distributions. Next, we introduce an\nefficient numerical method to calculate the quasi-bound modes of dielectric\nresonators, which requires only two diagonalizations per N states, where N is\napproximately equal to the number of half-wavelengths along the perimeter. The\nrelationship between classical phase space structures and modes is displayed\nvia the Husimi projection technique. Observables related to the emission\npattern of the resonator are calculated with high efficiency.",
"arxiv_id": "physics/0308016",
"authors": [
"Hakan E. Tureci",
"Harald G. L. Schwefel",
"Philippe Jacquod",
"A. Douglas Stone"
],
"categories": [
"physics.optics",
"cond-mat.mes-hall",
"nlin.CD",
"quant-ph"
],
"journal_ref": "Progress in Optics, Vol 47: 75-137 (2005)",
"title": "Modes of wave-chaotic dielectric resonators",
"url": "https://arxiv.org/abs/physics/0308016"
},
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