Local cross-sections and energy efficiencies in the multiple optical scattering by two conducting particles

TL;DR

This paper derives exact mathematical formulas for electromagnetic cross-sections of two conducting cylinders, analyzing how their energy efficiencies vary with distance, angle, and size, aiding in the characterization of multiple scattering systems.

Contribution

It introduces a rigorous multipole modal expansion method to compute intrinsic cross-sections for two conducting cylinders at any frequency range, including re-scattering effects.

Findings

Cross-section formulas derived for arbitrary incident angles.

Numerical analysis of energy efficiencies based on size and distance.

Results facilitate better understanding of multiple particle scattering.

Abstract

In this work, exact mathematical expansions for the intrinsic electromagnetic (EM) or optical cross-sections (i.e., extinction, scattering and absorption) for a pair of perfectly conducting circular cylinders in a homogeneous medium are derived. The incident illuminating field is an axially-polarized electric field composed of plane travelling waves with an arbitrary angle of incidence in the polar plane. The formalism is based on the multipole modal expansion method in cylindrical coordinates and the translational addition theorem applicable to any range of frequencies. An effective EM field, incident on the probed cylinder, is defined first, which includes the initial and re-scattered field from the second cylinder. Subsequently, it is used jointly with the scattered field to derive the mathematical expressions for the intrinsic/local cross-sections based on integrating their corresponding time-averaged intensities over the surface of the probed object by applying the Poynting theorem. Numerical computations for the intrinsic extinction (or scattering) energy efficiencies for a pair of conducting circular cylinders with different radii in a homogeneous medium are considered. Emphasis is given on varying the interparticle distance, the angle of incidence, and the dimensionless sizes of the cylinders. The results computed a priori can be useful in the full characterization of a multiple scattering system of many particles, in conjunction with experimental data for the extrinsic cross-sections.