## Ray interpretation of multipole fields in spherical dielectric cavities

JOSA A, Vol. 15, Issue 11, pp. 2879-2891 (1998)

http://dx.doi.org/10.1364/JOSAA.15.002879

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### Abstract

We present a caustic model of morphology-dependent resonances based on geometrical optics, which describes the electromagnetic field in cylinders or spheres by families of ray congruences. A ray congruence in this model is basically a family of rays that osculate in phase on a common circle, the caustic. The circumference of this circle is in the plane case an integer multiple of the wavelength. This integer number corresponds to the mode number in the multipole expansion. In the spherical case two families of caustics exist. The mode numbers *l*, *m* of the multipole expansion for spherical particles define the corresponding radii of the caustics of the two ray families. The localization principle follows in this model simply by conservation of angular momentum. The condition for narrow modes caused by total internal reflection and the leaking of these modes is explained. The excitation of narrow resonances can also be explained in a straightforward manner by requiring that rays propagating from the caustic to the surface couple in phase to the caustic after reflection. Comparison with the exact solution shows excellent agreement.

© 1998 Optical Society of America

**OCIS Codes**

(060.2310) Fiber optics and optical communications : Fiber optics

(080.1510) Geometric optics : Propagation methods

(130.2790) Integrated optics : Guided waves

(140.4780) Lasers and laser optics : Optical resonators

(240.7040) Optics at surfaces : Tunneling

(260.5740) Physical optics : Resonance

**Citation**

Günther Roll, Thomas Kaiser, Stefan Lange, and Gustav Schweiger, "Ray interpretation of multipole fields in spherical dielectric cavities," J. Opt. Soc. Am. A **15**, 2879-2891 (1998)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-15-11-2879

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### References

- C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
- S. C. Hill and R. K. Chang, “Nonlinear optics in droplets,” in Studies in Classical and Quantum Nonlinear Optics, O. Keller, ed. (Nova Science, New York, 1995).
- S. C. Hill and R. E. Benner, “Morphology-dependent resonances,” in Optical Effects Associated with Small Particles, P. W. Barber and R. K. Chang, eds. (World Scientific, Singapore, 1988).
- J. B. Keller and S. I. Rubinow, “Asymptotic solution of eigenvalue problems,” Ann. Phys. (N.Y.) 9, 24–75 (1960).
- L. A. Vainshtein, Open Resonators and Open Waveguides (Golem, Boulder, Colo., 1969).
- S. J. Maurer and L. B. Felsen, “Ray-optical techniques for guided waves,” Proc. IEEE 55, 1718–1729 (1967).
- H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1957).
- A. Ungut, G. Gréhan, and G. Gouesbet, “Comparisons between geometrical optics and Lorenz–Mie theory,” Appl. Opt. 20, 2911–2918 (1981).
- J. A. Lock, “Ray scattering by an arbitrarily oriented spheroid. I. Diffraction and specular reflection,” Appl. Opt. 35, 500–513 (1996).
- J. A. Lock, “Ray scattering by an arbitrarily oriented spheroid. II. Transmission and cross-polarization effects,” Appl. Opt. 35, 515–531 (1996).
- K. Muinonen, T. Nousiainen, P. Fast, K. Lumme, and J. I. Peltoniemi, “Light scattering by gaussian particles: ray optics approximation,” J. Quant. Spectrosc. Radiat. Transf. 55, 577–601 (1996).
- H. M. Lai, P. T. Leung, K. L. Poon, and K. Young, “Characterization of the internal energy density in Mie scattering,” J. Opt. Soc. Am. A 8, 1553–1558 (1991).
- D. Q. Chowdhury, P. W. Barber, and S. C. Hill, “Energy-density distribution inside large nonabsorbing spheres by using Mie theory and geometrical optics,” Appl. Opt. 31, 3518–3523 (1992).
- M. A. Jarzembski and V. Srivastava, “Electromagnetic field enhancement in small liquid droplets using geometric optics,” Appl. Opt. 28, 4962–4965 (1989).
- N. Velesco, T. Kaiser, and G. Schweiger, “Computation of the internal field of a large sphere by using the geometrical optics approximation,” Appl. Opt. 36, 8724–8728 (1997).
- J. A. Lock and E. A. Hovenac, “Internal caustic structure of illuminated liquid droplets,” J. Opt. Soc. Am. A 8, 1541–1552 (1991).
- D. Q. Chowdhury, D. H. Leach, and R. K. Chang, “Effect of the Goos–Hänchen shift on the geometrical-optics model for spherical-cavity mode spacing,” J. Opt. Soc. Am. A 11, 1110–1116 (1994).
- J. U. Nöckel, A. D. Stone, and R. K. Chang, “Q spoiling and directionality in deformed ring cavities,” Opt. Lett. 19, 1693–1695 (1994).
- A. Mekis, J. U. Nöckel, G. Chen, A. D. Stone, and R. K. Chang, “Ray chaos and Q spoiling in lasing droplets,” Phys. Rev. Lett. 75, 2682–2685 (1995).
- M. Robnik, “Quantising a generic family of billiards with analytic boundaries,” J. Phys. A 17, 1049–1074 (1984).
- E. S. C. Ching, P. T. Leung, and K. Young, “Optical processes in microcavities—the role of quasinormal modes,” in Optical Processes in Microcavities, R. K. Chang and A. J. Campillo, eds. (World Scientific, Singapore, 1996), p. 13.
- H. Inada and M. A. Plonus, “The geometric optics contribution to the scattering from a large dense dielectric sphere,” IEEE Trans. Antennas Propag. 18, 89–99 (1970).
- J. D. Murphy, P. J. Moser, A. Nagl, and H. Überall, “A surface wave interpretation for the resonances of a dielectric sphere,” IEEE Trans. Antennas Propag. 28, 924–927 (1980).
- V. Khare and H. M. Nussenzveig, “Theory of the glory,” Phys. Rev. Lett. 38, 1279–1282 (1977).
- H. M. Nussenzveig, “Complex angular momentum theory of the rainbow and the glory,” J. Opt. Soc. Am. 69, 1068–1079 (1979).
- M. Born and E. Wolf, Principles of Optics, (Pergamon, Oxford, UK, 1993).
- J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).
- J. P. Barton, D. R. Alexander, and S. A. Schaub, “Internal fields of a spherical particle illuminated by a tightly focused laser beam: focal point positioning effects at resonance,” J. Appl. Phys. 65, 2900–2906 (1989).
- G. Gouesbet and J. A. Lock, “Rigorous justification of the localized approximation to the beam-shape coefficients in generalized Lorenz–Mie theory. II. Off-axis beams,” J. Opt. Soc. Am. A 11, 2516–2525 (1994).
- E. Esam, M. Khaled, S. C. Hill, P. W. Barber, and D. Q. Chodhury, “Near resonance excitation of dielectric spheres with plane waves and off-axis Gaussian beams,” Appl. Opt. 31, 1166–1169 (1992).
- P. M. Aker, P. A. Moortgat, and J. X. Zhang, “Morphology-dependent stimulated Raman scattering imaging. I. Theoretical aspects,” J. Chem. Phys. 105, 7268–7282 (1996).
- G. C. Chen, W. P. Aker, R. K. Chang, and S. C. Hill, “Fine structures in the angular distribution of stimulated Raman scattering from single droplets,” Opt. Lett. 16, 117–119 (1991).
- D. S. Jones, “Electromagnetic tunnelling,” Q. J. Mech. Appl. Math. 31, 409–434 (1977).
- A. W. Snyder and J. D. Love, “Reflection at a curved dielectric interface: electromagnetic tunneling,” IEEE Trans. Microwave Theory Tech. 23, 134–141 (1975).
- R. Y. Chiao, P. G. Kwiat, and A. M. Steinberg, “Analogies between electron and photon tunneling,” Phys. Rev. B 175, 257–262 (1991).
- B. R. Johnson, “Theory of morphology-dependent resonances: shape resonances and width formulas,” J. Opt. Soc. Am. A 10, 343–352 (1993).
- H. M. Nussenzveig, “Tunneling effects in diffractive scattering and resonance,” Comments At. Mol. Phys. 23, 175–187 (1989).
- J. B. Keller, “A geometrical theory of diffraction,” in Calculus of Variations and Its Applications, Proceedings of Symposia in Applied Mathematics, L. M. Graves, ed. (McGraw-Hill, New York, 1958), Vol. 8.
- W. D. Wang and G. A. Deschamps, “Application of complex ray tracing to scattering problems,” Proc. IEEE 62, 1541–1551 (1974).
- M. Abramowitz and I. E. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965).
- R. Landauer, “Associated Legendre polynomial approximations,” J. Appl. Phys. 22, 87–89 (1951).

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