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using the Debye series

Resonant scattering of spherical particles is often referred to as "morphology-dependent resonances" (MDRs) or whispering-gallery modes. This topic has been studied by many authors (see the brief bibilography at the end of this page).

This page uses results of calculations using the Debye series to investigate the contributions made to these resonances by propagation paths of order

*p*= 0 corresponds to external reflection plus diffraction*p*= 1 corresponds to direct transmission through the sphere*p*= 2 corresponds to 1 internal reflection*p*= 3 corresponds to 2 internal reflections- and so on ......

where

Refractive index of the sphere = 1.33. Refractive index of the medium = 1. Scattering angle θ = 150°.

Fig. 2 below reproduces the Mie results from Fig. 1 (shown in red/brown) and compares them with the Debye series contributions (shown in blue) made by propagation paths for

The broader maxima (e.g. A and C in Fig. 1) can be explained by propagation paths of order

Figs. 7 and 8 below (which show

- Petr Chılek, "Partial-wave resonances and the ripple structure in the Mie normalized extinction cross section," J. Opt. Soc. Am.
**66**, 285-287 (1976). - B. R. Johnson, "Theory of morphology-dependent resonances: shape resonances and width formulas," J. Opt. Soc. Am. A
**10**, 343–352 (1993). - 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). - G. Roll and G. Schweiger, "Geometrical optics model of Mie resonances," J. Opt. Soc. Am. A
**17**, 1301-1311 (2000).

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