OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 16, Iss. 4 — Apr. 1, 1999
  • pp: 882–895

Eigenmodes of spherical dielectric cavities: coupling of internal and external rays

G. Roll, T. Kaiser, and G. Schweiger  »View Author Affiliations


JOSA A, Vol. 16, Issue 4, pp. 882-895 (1999)
http://dx.doi.org/10.1364/JOSAA.16.000882


View Full Text Article

Acrobat PDF (432 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Eigenmodes of spherical dielectric cavities are investigated within the framework of geometrical optics. A model for the coupling of internal and external rays is presented. Approximate expressions for the expansion coefficients of Mie theory are derived. Formulas for the modulus and the phase are given. The systematic behavior of the phase angle is investigated. All expressions are explicit equations and may be used to calculate the expansion coefficients as a function of order l or size parameter x. All features of the presented results are understandable in terms of light rays. A plane interface analog is presented. The so-called resonance regime (Λ/n<x<Λ), where n is the relative refractive index and Λ=l+1/2, is considered especially. An implicit equation for these resonance positions is rederived, and explicit relations for their strengths and widths are given. All findings are in agreement with results derived from Mie theory.

© 1999 Optical Society of America

OCIS Codes
(080.0080) Geometric optics : Geometric optics
(080.1510) Geometric optics : Propagation methods
(140.4780) Lasers and laser optics : Optical resonators
(260.5740) Physical optics : Resonance
(290.0290) Scattering : Scattering
(290.4020) Scattering : Mie theory

Citation
G. Roll, T. Kaiser, and G. Schweiger, "Eigenmodes of spherical dielectric cavities: coupling of internal and external rays," J. Opt. Soc. Am. A 16, 882-895 (1999)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-4-882


Sort:  Author  |  Year  |  Journal  |  Reset

References

  1. F. R. Faxvog and D. M. Roessler, “Optical absorption in thin slabs and spherical particles,” Appl. Opt. 20, 729–731 (1981).
  2. C. F. Bohren, “Scattering by a sphere and reflection by a slab: some notable similarities,” Appl. Opt. 27, 205–206 (1988).
  3. P. Chýlek and J. Zhan, “Interference structure of the Mie extinction cross section,” J. Opt. Soc. Am. A 6, 1846–1851 (1989).
  4. P. W. Barber and S. C. Hill, Light Scattering by Particles: Computational Methods (World Scientific, Singapore, 1990). Chap. 1.
  5. J. A. Lock, “Interference enhancement of the internal fields at structural resonances of a coated sphere,” Appl. Opt. 29, 3180–3187 (1990).
  6. J. A. Lock and L. Yang, “Interference between diffraction and transmission in the Mie extinction efficiency,” J. Opt. Soc. Am. A 8, 1132–1134 (1991).
  7. E. Hecht, Optik (Addison-Wesley, Bonn, 1989), Chap. 9.
  8. G. Roll, T. Kaiser, S. Lange, and G. Schweiger, “Ray interpretation of multipole fields in spherical dielectric cavities,” J. Opt. Soc. Am. A 15, 2879–2891 (1998).
  9. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1993).
  10. P. J. Moser, J. D. Murphy, A. Nagl, and H. Überall, “Creeping-wave excitation of the eigenvibrations of dielectric resonators,” Wave Motion 3, 283–295 (1981).
  11. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  12. Note that, in contrast to this discussion, in the book of Bohren and Huffman11 an outgoing wave is represented by a Hankel function of the second kind, which is a consequence of the exp(+ωt) time dependence assumed by Bohren and Huffman in contrast to the exp(−ωt) time dependence assumed here. In the literature a discussion of the consequences of a reversed time dependence can be found.13
  13. K. S. Shifrin and I. G. Zolotov, “Remark about the notation used for calculating the electromagnetic field scattered by a spherical particle,” Appl. Opt. 32, 5397–5398 (1993).
  14. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1957).
  15. I. K. Ludlow and J. Everitt, “Systematic behavior of the Mie scattering coefficients of spheres as a function of order,” Phys. Rev. E 53, 2909–2924 (1996).
  16. P. Chýlek, “Large-sphere limits of the Mie-scattering functions,” J. Opt. Soc. Am. A 63, 699–706 (1973).
  17. J. B. Keller and S. I. Rubinow, “Asymptotic solution of eigenvalue problems,” Ann. Phys. (N.Y.) 9, 24–75 (1960).
  18. S. J. Maurer and L. B. Felsen, “Ray-optical techniques for guided waves,” Proc. IEEE 55, 1718–1729 (1967).
  19. J. D. Love and A. W. Snyder, “Optical fiber eigenvalue equation: plane wave derivation,” Appl. Opt. 15, 2121–2125 (1976).
  20. G. Roll, T. Kaiser, and G. Schweiger, “Controlled modification of the expansion order as a tool in Mie computations,” Appl. Opt. 37, 2483–2492 (1998).
  21. C. C. Lam, P. T. Leung, and K. Young, “Explicit asymptotic formulas for the positions, widths, and strength of resonances in Mie scattering,” J. Opt. Soc. Am. B 9, 1585–1592 (1992).
  22. B. R. Johnson, “Theory of morphology-dependent resonances: shape resonances and width formulas,” J. Opt. Soc. Am. A 10, 343–352 (1993).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited