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Ex-house 2D finite-element simulation of the whispering-gallery modes of
arbitrarily shaped axisymmetric electromagnetic resonators
Mark Oxborrow
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.
- oai_identifier:
- oai:arXiv.org:quant-ph/0607156
- categories:
- quant-ph
- comments:
- 21 pages, 8 figures, 4 tables; submitted to IEEE Transactions on
Microwave Theory and Techniques. Corrected 20th March 2007
- arxiv_id:
- quant-ph/0607156
- created:
- 2006-07-23
- updated:
- 2007-03-20
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