Electromagnetic scattering by an arbitrary configuration of dielectric spheres

Abstract

An analytic solution is obtained for the problem of plane electromagnetic-wave scattering by an arbitrary configuration of N dielectric spheres. The multipole expansion method is employed, and the boundary condition is imposed using the translational addition theorem for vector spherical wave functions. A system of simultaneous linear equations is given in matrix form for the scattering coefficients. An approximate solution, which has been developed and employed by the authors for the scattering by N conducting spheres, is extended to the dielectric spheres case. Plots for the normalized backscattering, bistatic, and forward-scattering cross sections are presented over wide ranges of permittivity, size, and electrical separations between the neighbouring spheres. The results show a reduction in the normalized backscattering and bistatic cross sections for certain choices of permittivity relative to conducting arrays of spheres of the same dimensions and separations.

Local field intensity in aggregates illuminated by diffuse light: T matrix approach

“…[20]), Others use different sets of basis functions [21] and one must convert to the VSWFs before employing Eqs. (15) and (16), and this can apparently can only be done if the smallest circumscribing spheres around each scatterer do not overlap. Lastly we point out that, contrary to Cruz et al [22,23], who used the global T-matrix approach and consequently were limited to evaluating the local field intensity outside the smallest circumscribing spheres of the entire system, the use of the centered T-matrix formalism allows one to readily calculate the field at any point of space outside of the smallest circumscribing sphere of each scatterer [24].…”

“…It directly relates the expansion coefficients of the incident field on the entire N particle system to the expansion coefficients, f Once the N-body T matrices are evaluated by solving Eq. (3) [ 16,17], analytic expressions can be derived for the total cross sections of the entire system [10]. Although in theory the analytical expressions of the electric fields involve infinite expansions on the VSWFs, in practice it is now well known that an accurate representation of the fields can be achieved when truncating the series to an order n max that depends on the product of the incident wave number and the size of the particles.…”

Observations and Calculations of Light Scattering from Clusters of Spheres

“…This last relation defines a group of ./Vcoupled linear equations whose unknown variables are the expansion coefficients of the scattered field of each individual sphere. The solution can be found with different techniques, such as the order of scattering [4], the direct inversion matrix [22], or the iteration method [23]. Nevertheless, it is convenient to introduce f'W, the N-scatterer T-matrix of the z'th scattered This formulation includes all the information about multiple scattering effects due to the presence of the N scatterers.…”

Effect of Temperature and Multiple Scattering on Rain Attenuation of Electromagnetic Waves by a Simple Spherical Model

“…In spite of all these works dealing with multiple scattering, it is still an important task to quantitatively evaluate the interaction among realistic raindrops distribution in a numerically exact manner. With regard to this, we can make use of an effective tool based on the multipole expansion [10][11][12], and thereby it is expected that even the spherical model yields quantitative information to some extent. This is why we choose this simple model as a starting point.…”

“…This procedure is the same as that of Ref. [11], except that we make an adaptive choice of the truncation numbers according to the sphere size to reduce the CPU time. The specific rain attenuation can be evaluated directly from the extinction cross section of a set of raindrops, which are randomly allocated inside a big fictitious sphere.…”