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

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.

Electromagnetic interactions of dipole distributions with a stratified medium: Power fluxes and scattering cross sections

“…This reduces the pace of the energy flow towards the scatterer's exterior, which in turn reduces the energy flux rate and is manifested by the negative 𝑞-ISCS. 15 Additionally, we stress that the power fluxes of (76) include only those induced by the interactions between individual fields and not the individual power fluxes.…”

“…When 𝑁 > 2, there is a chance to have both types of induced IPF, which might significantly affect the overall scattering cross section. 15 Furthermore, for 𝑁 = 2, the partial fields and the partial IPF coincide with the individual fields; for 𝑁 > 2, this never holds, which adds to the complexity of separating each individual fields' contribution to the overall power flux.…”

“…A parametric analysis for the physical bounds and the behavior of the ISCS for a layered sphere was F I G U R E 1 The considered layered scatterer 𝑉 excited by multiple external and internal magnetic dipoles performed in Ref. 15. Physical bounds for bistatic-radar cross sections with respect to the number of closely spaced radiators excited by a plane wave were presented in Ref.…”

Analysis of the energy transfer process for multiple scattering problems involving lossy media

“…The results presented here aim to provide (i) the theoretical framework for the analysis of the energy transfer process in multiple scattering, based on a rigorous mathematical formulation, (ii) a ‘benchmark’ for evaluation of numerical techniques and a tool for parametrical analysis, as is performed, e.g. in [34] and (iii) a tool for analytic calculations; e.g. optical theorems have been extensively used to estimate far-field radiation by means of near-field measurements [8].…”

Analytical algorithms for direct and inverse problems pertaining to the electromagnetic excitation of a layered medium by N dipoles

“…Volume-integral formulations for layered particles were developed in [20], while generalizations of the optical theorem for multipoles were investigated in [21]. Physical bounds for the electromagnetic bistatic-radar scattering cross-section and the interaction scattering cross-sections were established in [22] and [23,24], respectively. Importantly, the direct scattering problem in the spherical geometry has been treated by different analytical and numerical methods over the years, depending on the specifics of each problem [25][26][27][28].…”