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

JOSA A, Vol. 16, Issue 4, pp. 882-895 (1999)

http://dx.doi.org/10.1364/JOSAA.16.000882

Enhanced HTML Acrobat PDF (432 KB)

### 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 *n* is the relative refractive index and

© 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

**History**

Original Manuscript: August 12, 1998

Manuscript Accepted: November 6, 1998

Published: April 1, 1999

**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: Year | Journal | Reset

### References

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

## 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.