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Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry M. Van Driel
  • Vol. 25, Iss. 6 — Jun. 1, 2008
  • pp: 1038–1045

Variational principle in whispering gallery mode sensor responses

Iwao Teraoka and Stephen Arnold  »View Author Affiliations


JOSA B, Vol. 25, Issue 6, pp. 1038-1045 (2008)
http://dx.doi.org/10.1364/JOSAB.25.001038


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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.

© 2008 Optical Society of America

OCIS Codes
(170.4520) Medical optics and biotechnology : Optical confinement and manipulation
(260.2110) Physical optics : Electromagnetic optics
(300.6490) Spectroscopy : Spectroscopy, surface

ToC Category:
Physical Optics

History
Original Manuscript: January 10, 2008
Manuscript Accepted: March 12, 2008
Published: May 27, 2008

Virtual Issues
Vol. 3, Iss. 7 Virtual Journal for Biomedical Optics

Citation
Iwao Teraoka and Stephen Arnold, "Variational principle in whispering gallery mode sensor responses," J. Opt. Soc. Am. B 25, 1038-1045 (2008)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-25-6-1038


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References

  1. F. Vollmer, D. Braun, A. Libchaber, M. Khoshsima, I. Teraoka, and S. Arnold, “Protein detection by optical shift of a resonant microcavity,” Appl. Phys. Lett. 80, 4057-4049 (2002). [CrossRef]
  2. S. Arnold, M. Khoshsima, I. Teraoka, S. Holler, and F. Vollmer, “Shift of whispering-gallery modes in microspheres by protein adsorption,” Opt. Lett. 28, 272-274 (2003). [CrossRef] [PubMed]
  3. A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Review of applications of whispering-gallery mode resonators in photonics and nonlinear optics,” in The Interplanetary Network Progress Report, Vol. 42-162 (NASA, 2005), pp. 1-51.
  4. F. Baldini and A. Giannetti, “Optical chemical and biochemical sensors: new trends,” Proc. SPIE 5826, 485-496 (2005). [CrossRef]
  5. I. Teraoka, S. Arnold, and F. Vollmer, “Perturbation approach to resonance shifts of whispering-gallery modes in a dielectric microsphere as a probe of a surrounding medium,” J. Opt. Soc. Am. B 20, 1937-1946 (2003). [CrossRef]
  6. I. Teraoka and S. Arnold, “Theory on resonance shifts in TE and TM whispering gallery modes by non-radial perturbations for sensing applications,” J. Opt. Soc. Am. B 23, 1381-1389 (2006). [CrossRef]
  7. N. M. Hanumegowda, C. J. Stica, B. C. Patel, I. White, and X. Fan, “Refractometric sensors based on microsphere resonators,” Appl. Phys. Lett. 87, 201107 (2005). [CrossRef]
  8. M. Noto, D. Keng, I. Teraoka, and S. Arnold, “Detection of protein orientation on silica microsphere surface using TE/TM whispering gallery modes,” Biophys. J. 92, 4466-4472 (2007). [CrossRef] [PubMed]
  9. C. Boozer, G. Kim, S. Cong, H. W. Guan, and T. Londergan, “Looking towards label-free biomolecular interaction analysis in a high-throughput format: a review of new surface plasmon resonance technologies,” Curr. Opin. Biotechnol. 17, 400-405 (2006). [CrossRef] [PubMed]
  10. A. Janshoff and C. Steinem, “Label-free detection of protein-ligand interactions by the quartz crystal microbalance,” Methods Mol. Biol. 305, 47-64 (2005). [PubMed]
  11. A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, “Label-free, single-molecule detection with optical microcavities,” Science 317, 783-787 (2007). [CrossRef] [PubMed]
  12. S. Arnold and S. Holler, “Microparticle photophysics: fluorescence microscopy and spectroscopy of a photonic atom,” in Cavity-Enhanced Spectroscopies, R.D.van Zee and J.P.Looney, eds., Vol. 40 of Experimental Methods in the Physical Sciences (Academic, 2002).
  13. I. Teraoka and S. Arnold, “Enhancing sensitivity of a whispering gallery mode microsphere sensor by a high-refractive index surface layer,” J. Opt. Soc. Am. B 23, 1434-1441 (2006). [CrossRef]
  14. I. M. White, H. Oveys, and X. Fan, “Liquid-core optical ring-resonator sensors,” Opt. Lett. 31, 1319-1321 (2006). [CrossRef] [PubMed]
  15. I. S. Grudinin, A. B. Matsko, A. A. Savchenkov, D. Strekalov, V. S. Ilchenko, and L. Maleki, “Ultra high Q crystalline microcavities,” Opt. Commun. 265, 33-38 (2006). [CrossRef]
  16. B. R. Johnson, “Theory of morphology-dependent resonances: shape resonances and width formulas,” J. Opt. Soc. Am. A 10, 343-352 (1993). [CrossRef]

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