dorsal/arxiv
View SchemaEx-house 2D finite-element simulation of the whispering-gallery modes of arbitrarily shaped axisymmetric electromagnetic resonators
| Authors | Mark Oxborrow |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0607156 |
| URL | https://arxiv.org/abs/quant-ph/0607156 |
Abstract
It is described, explicitly, 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 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 approxi-mation is imposed, the approach remains accurate even for so-called quasi-TM and -TE 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 microwave Bragg cavity containing alumina layers (iii) two different cryogenic sapphire X-band microwave resonators. By fitting one of the latter to a set of measured resonance frequencies, the dielectric constants of sapphire at liquid-helium temperature have been estimated.
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"date_modified": "2026-03-02T18:02:27.552000Z",
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"abstract": "It is described, explicitly, how a popular, commercially-available software\npackage for solving partial-differential-equations (PDEs), as based on the\nfinite-element method (FEM), can be configured to calculate the frequencies and\nfields of the whispering-gallery (WG) modes of axisymmetric dielectric\nresonators. The approach is traceable; it exploits the PDE-solver\u0027s ability to\naccept the definition of solutions to Maxwell\u0027s equations in so-called `weak\nform\u0027. Associated expressions and methods for estimating a WG mode\u0027s volume,\nfilling factor(s) and, in the case of closed(open) resonators, its wall\n(radiation) loss, are provided. As no transverse approxi-mation is imposed, the\napproach remains accurate even for so-called quasi-TM and -TE modes of low,\nfinite azimuthal mode order. The approach\u0027s generality and utility are\ndemonstrated by modeling several non-trivial structures: (i)two different\noptical microcavities [one toroidal made of silica, the other an AlGaAs\nmicrodisk]; (ii) a 3rd-order microwave Bragg cavity containing alumina layers\n(iii) two different cryogenic sapphire X-band microwave resonators. By fitting\none of the latter to a set of measured resonance frequencies, the dielectric\nconstants of sapphire at liquid-helium temperature have been estimated.",
"arxiv_id": "quant-ph/0607156",
"authors": [
"Mark Oxborrow"
],
"categories": [
"quant-ph"
],
"title": "Ex-house 2D finite-element simulation of the whispering-gallery modes of arbitrarily shaped axisymmetric electromagnetic resonators",
"url": "https://arxiv.org/abs/quant-ph/0607156"
},
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