Perturbation approach to resonance shifts of whispering-gallery modes in a dielectric microsphere as a probe of a surrounding medium

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Abstract

A first-order perturbation theory similar to the one widely used in quantum mechanics is developed for transverse-electric and transverse-magnetic photonic resonance modes in a dielectric microsphere. General formulas for the resonance frequency shifts in response to a small change in the exterior refractive index and its radial profile are derived. The formulas are applied to three sensor applications of the microsphere to probe the medium in which the sphere is immersed: a refractive-index detector, an adsorption sensor, and a refractive-index profile sensor. When they are applied to a uniform change in the refractive index in the surrounding medium, the formulas give the same results that one would obtain from the exact resonance equations for the two modes. In the application to adsorption of a thin layer onto the sphere surface, the results are identical to the first-order terms in the exact formulas obtained for the adsorption layer. In the last-named example, a scheme is proposed for instantaneous measurement of the refractive-index profile near the sphere's surface.

Original languageEnglish (US)
Pages (from-to)1937-1946
Number of pages10
JournalJournal of the Optical Society of America B: Optical Physics
Volume20
Issue number9
StatePublished - 2003

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whispering gallery modes
refractivity
perturbation
probes
shift
adsorption
sensors
profiles
frequency shift
quantum mechanics
perturbation theory
photonics
detectors

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

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title = "Perturbation approach to resonance shifts of whispering-gallery modes in a dielectric microsphere as a probe of a surrounding medium",
abstract = "A first-order perturbation theory similar to the one widely used in quantum mechanics is developed for transverse-electric and transverse-magnetic photonic resonance modes in a dielectric microsphere. General formulas for the resonance frequency shifts in response to a small change in the exterior refractive index and its radial profile are derived. The formulas are applied to three sensor applications of the microsphere to probe the medium in which the sphere is immersed: a refractive-index detector, an adsorption sensor, and a refractive-index profile sensor. When they are applied to a uniform change in the refractive index in the surrounding medium, the formulas give the same results that one would obtain from the exact resonance equations for the two modes. In the application to adsorption of a thin layer onto the sphere surface, the results are identical to the first-order terms in the exact formulas obtained for the adsorption layer. In the last-named example, a scheme is proposed for instantaneous measurement of the refractive-index profile near the sphere's surface.",
author = "Iwao Teraoka and Stephen Arnold and Frank Vollmer",
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journal = "Journal of the Optical Society of America B: Optical Physics",
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AU - Vollmer, Frank

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N2 - A first-order perturbation theory similar to the one widely used in quantum mechanics is developed for transverse-electric and transverse-magnetic photonic resonance modes in a dielectric microsphere. General formulas for the resonance frequency shifts in response to a small change in the exterior refractive index and its radial profile are derived. The formulas are applied to three sensor applications of the microsphere to probe the medium in which the sphere is immersed: a refractive-index detector, an adsorption sensor, and a refractive-index profile sensor. When they are applied to a uniform change in the refractive index in the surrounding medium, the formulas give the same results that one would obtain from the exact resonance equations for the two modes. In the application to adsorption of a thin layer onto the sphere surface, the results are identical to the first-order terms in the exact formulas obtained for the adsorption layer. In the last-named example, a scheme is proposed for instantaneous measurement of the refractive-index profile near the sphere's surface.

AB - A first-order perturbation theory similar to the one widely used in quantum mechanics is developed for transverse-electric and transverse-magnetic photonic resonance modes in a dielectric microsphere. General formulas for the resonance frequency shifts in response to a small change in the exterior refractive index and its radial profile are derived. The formulas are applied to three sensor applications of the microsphere to probe the medium in which the sphere is immersed: a refractive-index detector, an adsorption sensor, and a refractive-index profile sensor. When they are applied to a uniform change in the refractive index in the surrounding medium, the formulas give the same results that one would obtain from the exact resonance equations for the two modes. In the application to adsorption of a thin layer onto the sphere surface, the results are identical to the first-order terms in the exact formulas obtained for the adsorption layer. In the last-named example, a scheme is proposed for instantaneous measurement of the refractive-index profile near the sphere's surface.

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