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The Extension of Mie Theory to Multiple Spheres

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The Mie Theory

Part of the book series: Springer Series in Optical Sciences ((SSOS,volume 169))

Abstract

A generalized mathematical formulation is presented for the scattering and absorption of electromagnetic time harmonic waves by multiple spherical particles. A central element of this formulation is the addition theorem for vector wave functions, which allows a scattered field from one sphere to be represented as an exciting field about another sphere. A simplified derivation of the addition theorem, and important characteristics of where it can and can not be used, are developed. The Mie solution, coupled with the addition theorem, results in a system of linear interaction equations for the multipole coefficients that describe the scattered field from each sphere in the system. In this regard, the multiple sphere formulation results in an implicit, rather than explicit, solution for the scattered field; numerical methods (i.e., linear equation solvers) must be applied to obtain numerical results. The calculation of the \(T\) matrix of the multiple sphere system, from which orientation averaged scattering and absorption properties can be obtained, is described. The presentation ends with a discussion on the application of the multiple sphere formulation to describing the propagation of electromagnetic waves in discretely inhomogeneous media.

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Notes

  1. 1.

    The \({\overline{a}}_{np}\) coefficients defined by Eq. (8.9) are the negative of those formulated in previous works, e.g., Bohren and Huffman.

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Authors and Affiliations

  1. Mechanical Engineering Department, Auburn University, Auburn, AL, 36849, USA

    Daniel Mackowski

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  1. Daniel Mackowski
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Correspondence to Daniel Mackowski .

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Editors and Affiliations

  1. Halle-Wittenberg, Fakultät für Naturwissenschaften II, Martin-Luther-Universität, Von-Seckendorff-Platz 1, Halle/Saale, 06120, Germany

    Wolfram Hergert

  2. Stiftung Institut für Werkstofftechnik, Badgasteiner Str. 3, Bremen, 28359, Germany

    Thomas Wriedt

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Mackowski, D. (2012). The Extension of Mie Theory to Multiple Spheres. In: Hergert, W., Wriedt, T. (eds) The Mie Theory. Springer Series in Optical Sciences, vol 169. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28738-1_8

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  • DOI: https://doi.org/10.1007/978-3-642-28738-1_8

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