Analysis of Interaction Scattering Cross Sections and Their Physical Bounds for Multiple-Dipole Stimulation of a Three-Dimensional Layered Medium

Andreas Kalogeropoulos,Nikolaos L Tsitsas

doi:10.1109/ojap.2021.3070199

Andreas Kalogeropoulos, Nikolaos L Tsitsas

Open Access

https://doi.org/10.1109/ojap.2021.3070199

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Abstract

A three-dimensional layered and isotropic medium is excited by primary spherical waves due to $N$ magnetic dipoles radiating inside or outside the medium. Interaction scattering cross sections (ISCS) are defined as the differences between the overall scattering cross section and the sum of the individual cross sections generated by all dipoles within a layer or by all $N$ dipoles. Optical theorems and physical bounds for the ISCS are established. Extensive numerical investigations are performed for the variations of the ISCS and their physical bounds with respect to the geometrical and physical characteristics of the layered medium. Conditions for which ISCS contribute significantly in the overall cross section are analyzed. It is also demonstrated that the number of excitation layers and the total number $N$ of dipoles can be determined by means of the individual scattering cross sections.

Highlights

E XCITATION of a three-dimensional layered medium by N electric or magnetic dipoles, located in different internal layers or in the medium’s exterior, constitutes a realistic model for applications spreading from low frequencies to the visible range
Optical theorems and physical bounds on the interaction scattering cross sections (ISCS) together with numerical results with respect to changes in the layered medium and the excitation dipoles are presented in Sections III and IV, for the single-layer and mixed excitation cases, respectively
We present optical theorems for all cross sections involved as well as physical bounds for the ratios of the ISCS over the corresponding scattering cross sections. These theorems and physical bounds are important in determining the additivity of the cross sections, and, elaborate that the energy flux quantified by the ISCS contributes significantly to the overall flux–especially when strong near-field interaction occurs between fields generated by the N dipoles

Summary

INTRODUCTION

E XCITATION of a three-dimensional layered (piecewise homogeneous) medium by N electric or magnetic dipoles, located in different internal layers or in the medium’s exterior, constitutes a realistic model for applications spreading from low frequencies to the visible range. We, first, formulate the boundary-value problems for the generated electric fields corresponding to the excitation of a piecewise homogeneous medium composed of annuli-like layers by N internal and external magnetic dipoles. For each of the two cases, we derive optical theorems determining the individual and overall scattering cross sections by means of the secondary fields at the dipoles’ positions. It is shown that the number of excitation layers and the total number N of dipoles can be determined by the derived physical bounds involving the individual scattering cross sections. Optical theorems and physical bounds on the ISCS together with numerical results with respect to changes in the layered medium and the excitation dipoles are presented in Sections III and IV, for the single-layer and mixed excitation cases, respectively.

MATHEMATICAL FORMULATION

SINGLE-LAYER EXCITATION

OPTICAL THEOREMS AND PHYSICAL BOUNDS

MIXED EXCITATION

Findings

CONCLUSION