Mie-Type Calculation of the Generalized Electromagnetic Nonlocal Conductivity Tensor for a Sphere and Its Equivalence to the T-Matrix Operator

The purpose of this article is to calculate the generalized nonlocal conductivity tensor of a spherical particle made of isotropic and linear materials. The generalized conductivity tensor is a crucial element in the formulation of the mean-field theories of the electromagnetic response of random pa...

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Bibliographic Details
Published in:Mathematical problems in engineering 2019-01, Vol.2019 (2019), p.1-20
Main Authors: Gutiérrez-Reyes, E., García-Valenzuela, A., Barrera, Rubén G.
Format: Article
Language:English
Subjects:
Conductivity
Electric fields
Electromagnetism
Engineering
Equivalence
Fourier transforms
Integral equations
Mathematical analysis
Mathematical functions
Optics
Permeability
Scattering
Spheres
Tensors
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Summary:The purpose of this article is to calculate the generalized nonlocal conductivity tensor of a spherical particle made of isotropic and linear materials. The generalized conductivity tensor is a crucial element in the formulation of the mean-field theories of the electromagnetic response of random particulate systems. This is equivalent to what is called the T-Matrix in multiple scattering theories. Here, a new method is proposed for finding explicit expressions for this tensor directly from its definition including the magnetic response of the spheres. Its relation with the S-Matrix in the theory of single scattering is stated as a generalization. Several approximations and limit cases of possible interest in specific systems are analyzed and the results of some calculations are presented as a numerical example.
ISSN:1024-123X
1563-5147
DOI:10.1155/2019/1530821