Variational principle in whispering gallery mode sensor responses

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Abstract

We present a variational method for whispering gallery modes (WGMs) and apply it to sensor responses of WGMs in a spherical resonator to two types of perturbation for which we know the exact answers. The perturbations are adsorption of a thin dielectric layer and a uniform change in the surroundings' refractive index. The variational method gives the perturbed wave function and, if a suitable trial function is chosen, the resonance wavelength shift up to the second order in the perturbation. The linear part is identical to the result of the first-order perturbation theory.

Original languageEnglish (US)
Pages (from-to)1038-1045
Number of pages8
JournalJournal of the Optical Society of America B: Optical Physics
Volume25
Issue number6
DOIs
StatePublished - 2008

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whispering gallery modes
variational principles
perturbation
sensors
perturbation theory
resonators
wave functions
refractivity
adsorption
shift
wavelengths

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

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abstract = "We present a variational method for whispering gallery modes (WGMs) and apply it to sensor responses of WGMs in a spherical resonator to two types of perturbation for which we know the exact answers. The perturbations are adsorption of a thin dielectric layer and a uniform change in the surroundings' refractive index. The variational method gives the perturbed wave function and, if a suitable trial function is chosen, the resonance wavelength shift up to the second order in the perturbation. The linear part is identical to the result of the first-order perturbation theory.",
author = "Iwao Teraoka and Stephen Arnold",
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