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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Grover Swartzlander
  • Vol. 30, Iss. 11 — Nov. 1, 2013
  • pp: 3056–3063

Analytical estimates of eigenfrequencies, dispersion, and field distribution in whispering gallery resonators

Yury A. Demchenko and Michael L. Gorodetsky  »View Author Affiliations

JOSA B, Vol. 30, Issue 11, pp. 3056-3063 (2013)

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The problem of accurate calculation of eigenfrequencies in resonators of complex geometry is not only fundamental but also has many practical applications. In particular, a possibility for calculating the eigenfrequencies and geometry dependent dispersion of whispering gallery modes is important for optimization of dielectric microresonator-based Kerr frequency combs. In this case, the required anomalous second-order dispersion may be controlled by means of small shape variations of the resonator. Unfortunately, all uniform approximations for the eigenfrequencies do not reach the required precision for this purpose. We propose new approximations for spheroids, quartics, and toroids with better precision, which also allow for the estimation of the second-order dispersion. We also obtain analytical expressions for field distribution in microresonators and investigate the possibility of achieving better approximations by combining analytical and numerical methods.

© 2013 Optical Society of America

OCIS Codes
(140.4780) Lasers and laser optics : Optical resonators
(230.5750) Optical devices : Resonators
(050.1755) Diffraction and gratings : Computational electromagnetic methods
(140.3945) Lasers and laser optics : Microcavities
(140.3948) Lasers and laser optics : Microcavity devices

ToC Category:
Lasers and Laser Optics

Original Manuscript: July 10, 2013
Revised Manuscript: September 2, 2013
Manuscript Accepted: October 8, 2013
Published: October 31, 2013

Yury A. Demchenko and Michael L. Gorodetsky, "Analytical estimates of eigenfrequencies, dispersion, and field distribution in whispering gallery resonators," J. Opt. Soc. Am. B 30, 3056-3063 (2013)

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