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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 17, Iss. 7 — Jul. 1, 2000
  • pp: 1301–1311

Geometrical optics model of Mie resonances

Günter Roll and Gustav Schweiger  »View Author Affiliations

JOSA A, Vol. 17, Issue 7, pp. 1301-1311 (2000)

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The geometrical optics model of Mie resonances is presented. The ray path geometry is given and the resonance condition is discussed with special emphasis on the phase shift that the rays undergo at the surface of the dielectric sphere. On the basis of this model, approximate expressions for the positions of first-order resonances are given. Formulas for the cavity mode spacing are rederived in a simple manner. It is shown that the resonance linewidth can be calculated regarding the cavity losses. Formulas for the mode density of Mie resonances are given that account for the different width of resonances and thus may be adapted to specific experimental situations.

© 2000 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

Original Manuscript: March 4, 1999
Revised Manuscript: February 15, 2000
Manuscript Accepted: February 15, 2000
Published: July 1, 2000

Günter Roll and Gustav Schweiger, "Geometrical optics model of Mie resonances," J. Opt. Soc. Am. A 17, 1301-1311 (2000)

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  16. Throughout this paper we mean the trigonometric expansions of Bessel functions [compare expressions (18) and (19)] when we use the term Debye expansion. This must not be confused with the Debye series expansion of the scattering coefficients of Mie theory. Both the Debye expansion of Bessel functions and the Debye series expansion of the Mie coefficients play an important role in the ray description of the interaction of light with dielectric spheres. The former expansions are approximations to the exact functions, which break down in regions where the argument approaches the order. These expansions are found when the field within an illuminated sphere is investigated by means of geometrical optics.11 The Debye series expansion, on the other hand, denotes a mathematically exact technique to formulate the scattering process in terms of surface interactions of multipole waves. The Debye series expansion is equivalent to Mie theory but shows many similarities to the multiple-interference description of geometrical optics.17
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  24. At first glance this may be surprising, since we always assumed the rays to be confined by total internal reflection, which should mean T=0. However, owing to the curved surface, the energy confinement is not perfect, but there is a so-called evanescent leakage. Consequently the energy loss—although small—is not zero.
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  26. The fact that the transmission coefficient t is complex in the case of total reflection indicates the fact that the evanescent field is phase shifted with respect to the incident wave. The phase shift is half as large as that of the reflected wave.
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