Abstract
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.
Highlights
In a previous paper [1], a reference was made to the generalized nonlocal conductivity tensor, as the main physical concept in the development of a formalism for the calculation of the effective bulk electromagnetic response of randomly located discrete scatterers such as turbid colloids
The surface term given by (62) associated to the surface current and by the application of the integration formulas (82)-(83) we find that its Fourier transform, when we consider that the external electric field has a unitary amplitude, gives the part of the nonlocal conductivity tensor associated to these surface currents; consider the following
0.635μm, and electric permittivity ε/ε0 = 18.0958 + 0.484224i corresponding to the silver properties at that wavelength
Summary
In a previous paper [1], a reference was made to the generalized nonlocal conductivity tensor, as the main physical concept in the development of a formalism for the calculation of the effective bulk electromagnetic response of randomly located discrete scatterers such as turbid colloids. This approach was later extended to the calculation of the reflection and transmission amplitudes of the average electric field of colloidal suspensions confined in a half-space [2]. The total electromagnetic field conformed in this way can be split into two components, an average component with a smooth spatial variation and traveling in a definite direction, called the coherent beam, and a fluctuating component with abrupt spatial variations and traveling in all different directions, called the diffuse field
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