dorsal/arxiv
View SchemaTraceable 2D finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators
| Authors | Mark Oxborrow |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0611099 |
| URL | https://arxiv.org/abs/quant-ph/0611099 |
| DOI | 10.1109/TMTT.2007.897850 |
Abstract
This paper explains how a popular, commercially-available software package for solving partial-differential-equations (PDEs), as based on the finite-element method (FEM), can be configured to calculate, efficiently, the frequencies and fields of the whispering-gallery (WG) modes of axisymmetric dielectric resonators. The approach is traceable; it exploits the PDE-solver's ability to accept the definition of solutions to Maxwell's equations in so-called `weak form'. Associated expressions and methods for estimating a WG mode's volume, filling factor(s) and, in the case of closed(open) resonators, its wall(radiation) loss, are provided. As no transverse approximation is imposed, the approach remains accurate even for quasi-transverse magnetic/electric modes of low, finite azimuthal mode order. The approach's generality and utility are demonstrated by modeling several non-trivial structures: (i) two different optical microcavities [one toroidal made of silica, the other an AlGaAs microdisk]; (ii) a 3rd-order sapphire:air Bragg cavity; (iii) two different cryogenic sapphire WG-mode resonators; both (ii) and (iii) operate in the microwave X-band. By fitting one of (iii) to a set of measured resonance frequencies, the dielectric constants of sapphire at liquid-helium temperature have been estimated.
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"abstract": "This paper explains how a popular, commercially-available software package\nfor solving partial-differential-equations (PDEs), as based on the\nfinite-element method (FEM), can be configured to calculate, efficiently, the\nfrequencies and fields of the whispering-gallery (WG) modes of axisymmetric\ndielectric resonators. The approach is traceable; it exploits the PDE-solver\u0027s\nability to accept the definition of solutions to Maxwell\u0027s equations in\nso-called `weak form\u0027. Associated expressions and methods for estimating a WG\nmode\u0027s volume, filling factor(s) and, in the case of closed(open) resonators,\nits wall(radiation) loss, are provided. As no transverse approximation is\nimposed, the approach remains accurate even for quasi-transverse\nmagnetic/electric modes of low, finite azimuthal mode order. The approach\u0027s\ngenerality and utility are demonstrated by modeling several non-trivial\nstructures: (i) two different optical microcavities [one toroidal made of\nsilica, the other an AlGaAs microdisk]; (ii) a 3rd-order sapphire:air Bragg\ncavity; (iii) two different cryogenic sapphire WG-mode resonators; both (ii)\nand (iii) operate in the microwave X-band. By fitting one of (iii) to a set of\nmeasured resonance frequencies, the dielectric constants of sapphire at\nliquid-helium temperature have been estimated.",
"arxiv_id": "quant-ph/0611099",
"authors": [
"Mark Oxborrow"
],
"categories": [
"quant-ph"
],
"doi": "10.1109/TMTT.2007.897850",
"title": "Traceable 2D finite-element simulation of the whispering-gallery modes of axisymmetric electromagnetic resonators",
"url": "https://arxiv.org/abs/quant-ph/0611099"
},
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