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Applied Optics

Applied Optics


  • Vol. 41, Iss. 15 — May. 20, 2002
  • pp: 2955–2961

Semiclassical theory to optical resonant modes of a transparent dielectric spheroidal cavity

Pedro C. G. de Moraes and Luiz G. Guimarães  »View Author Affiliations

Applied Optics, Vol. 41, Issue 15, pp. 2955-2961 (2002)

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We study the resonant scattering of light by a transparent dielectric spheroid. We try to understand the features of the resonant modes of a spheroidal optical cavity. In this way, we use an analogy between optics and quantum mechanics. Through this analogy it is possible to interpret resonances as quasi-bound states of light. Using semiclassical methods such as the WKB method and a uniform asymptotic expansion for spheroidal radial functions, we developed algorithms that permit us to calculate the resonance position as well as the resonance width.

© 2002 Optical Society of America

OCIS Codes
(260.5740) Physical optics : Resonance
(290.4020) Scattering : Mie theory
(290.5850) Scattering : Scattering, particles

Original Manuscript: July 13, 2001
Revised Manuscript: October 22, 2001
Published: May 20, 2002

Pedro C. G. de Moraes and Luiz G. Guimarães, "Semiclassical theory to optical resonant modes of a transparent dielectric spheroidal cavity," Appl. Opt. 41, 2955-2961 (2002)

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  1. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  2. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  3. J. A. Lock, “Ray scattering by an arbitrarily oriented spheroid. 1. Diffraction and specular reflection,” Appl. Opt 35, 500–514 (1996). [CrossRef] [PubMed]
  4. J. A. Lock, “Ray scattering by an arbitrarily oriented spheroid. 2. Transmission and cross-polarization effects,” Appl. Opt 35, 515–531 (1996). [CrossRef] [PubMed]
  5. S. Asano, G. Yamamoto, “Light-scattering by a spheroidal particle,” Appl. Opt. 14, 29–49 (1975). [CrossRef] [PubMed]
  6. C. Flammer, Spheroidal Wave Functions (Stanford U. Press, Stanford, Calif., 1957).
  7. J. A. Stratton, P. M. Morse, L. J. Chu, D. C. Little, F. J. Corbato, Elliptic and Spheroidal Wave Functions (Wiley, New York, 1956).
  8. N. V. Voshchinnikov, V. G. Farafonov, “Optical-properties of spheroidal particles,” Astrophys. Space Sci. 204, 19–86 (1993). [CrossRef]
  9. S. Asano, “Light-scattering properties of spheroidal particles,” Appl. Opt. 18, 712–723 (1979). [CrossRef] [PubMed]
  10. B. P. Sinha, R. H. MacPhie, “On the computation of the prolate spheroidal radial functions of the second kind,” J. Math. Phys. 16, 2378–2381 (1975). [CrossRef]
  11. D. B. Hodge, “Eigenvalues and eigenfunctions of spheroidal wave equation,” J. Math. Phys. 11, 2308–2312 (1970). [CrossRef]
  12. H. A. Eide, J. J. Stamnes, K. Stamnes, F. M. Schulz, “New method for computing expansion coefficients for spheroidal functions,” J. Quant. Spectrosc. Radiat. Transfer 63, 191–203 (1999). [CrossRef]
  13. L. G. Guimarães, “Explicit asymptotic formulas for the spheroidal angular eigenvalues,” J. Phys. A 28, L233–L237 (1995). [CrossRef]
  14. P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D 3, 825–839 (1971). [CrossRef]
  15. F. M. Schulz, K. Stamnes, J. J. Stamnes, “Scattering of electromagnetic waves by spheroidal particles: a novel approach exploiting the T matrix computed in spheroidal coordinates,” Appl. Opt. 37, 7875–7896 (1998). [CrossRef]
  16. M. I. Mishchenko, “Extinction of light by randomly-oriented nonspherical grains,” Astrophys. Space Sci. 164, 1–13 (1990). [CrossRef]
  17. M. I. Mishchenko, “Light-scattering by randomly oriented axially symmetrical particles,” J. Opt. Soc. Am. A 8, 871–882 (1991). [CrossRef]
  18. M. I. Mishchenko, “Light-scattering by randomly oriented axially symmetrical particles,” J. Opt. Soc. Am. A 9, 497–497 (1992). [CrossRef]
  19. J. J. Goodman, B. T. Draine, P. J. Flatau, “Application of fast-Fourier-transform techniques to the discrete-dipole approximation,” Opt. Lett. 16, 1198–1200 (1991). [CrossRef] [PubMed]
  20. J. I. Hage, J. M. Greenberg, R. T. Wang, “Scattering from arbitrarily shaped particles—theory and experiment,” Opt. Lett. 30, 1141–1152 (1991).
  21. K. A. Fuller, D. W. Mackowski, “Electromagnetic scattering by compounded spherical particles,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, New York, 2000). [CrossRef]
  22. H. M. Nussenzveig, Diffraction Effects in Semiclassical Scattering (Cambridge U. Press, Cambridge, England, 1992). [CrossRef]
  23. P. C. G. de Moraes, “Análise semiclássica do espalhamento da luz por um esferóide,” Master’s thesis (Universidade Federal do Rio de Janeiro, Brazil, 1999).
  24. H. M. Lai, P. T. Leung, K. Young, P. W. Barber, S. C. Hill, “Time-independent perturbation for leaking electromagnetic modes in open systems with application to resonances in microdroplets,” Phys. Rev. A 41, 5187–5198 (1990). [CrossRef] [PubMed]
  25. M. L. Gorodetsky, V. S. Ilchenko, “High-Q optical whispering gallery microresonators: precession approach for spherical mode analysis and emission patterns with prism couplers,” Opt. Commun 113, 133–143 (1994). [CrossRef]
  26. F. W. J. Olver, Asymptotic and Special Functions (Academic, New York, 1974).
  27. M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).
  28. L. G. Guimarães, H. M. Nussenzveig, “Uniform approximation to Mie resonances,” J. Mod. Opt. 41, 625–647 (1994). [CrossRef]

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