## Geometrical optics model of Mie resonances

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

http://dx.doi.org/10.1364/JOSAA.17.001301

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### Abstract

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

**History**

Original Manuscript: March 4, 1999

Revised Manuscript: February 15, 2000

Manuscript Accepted: February 15, 2000

Published: July 1, 2000

**Citation**

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

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-17-7-1301

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### References

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- 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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- 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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