On Huygens' Principle, Extinction Theorem, and Equivalence Principle (Metal-Material Combined System in Inhomogeneous Anisotropic Environment)

TL;DR

This paper extends fundamental electromagnetic principles like Huygens' principle and the extinction theorem to complex, inhomogeneous, anisotropic, and multiply connected systems, including metal-material combined environments, with a focus on topological additivity and equivalence.

Contribution

It generalizes existing electromagnetic principles to more complex environments and systems, including metal-material combinations, and introduces a line-surface equivalence principle.

Findings

Generalization of HP, ET, and FHF to complex environments

Proof of topological additivity in generalized principles

Introduction of line-surface equivalence principle

Abstract

In this paper, we generalize Huygens' principle (HP), extinction theorem (ET), and Franz-Harrington formulation (FHF). In our previous works, the traditional HP, ET, and FHF in homogeneous isotropic environment are generalized to inhomogeneous anisotropic lossy environment; the traditional FHF of homogeneous isotropic material system is generalized to inhomogeneous anisotropic lossy material system and then to piecewise inhomogeneous anisotropic lossy material system; the traditional HP, ET, and FHF of simply connected material system are generalized to multiply connected system and then to non-connected system; the traditional FHF of external scattering field and internal total field are generalized to internal scattering field and internal incident field. In previous work, it is proved that the generalized HP (GHP) and generalized ET (GET) are equivalent to each other; the GHP, GET, and generalized FHF (GFHF) satisfy so-called topological additivity, i.e., the GHP/GET/GFHF of whole electromagnetic (EM) system equals to the superposition of the GHP/GET/GFHF corresponding to all sub-systems. In this paper, the above results obtained in our previous works, which focuses on the EM system constructed by material bodies, are further generalized to the metal-material combined EM system in inhomogeneous anisotropic lossy environment, and traditional surface equivalence principle is generalized to line-surface equivalence principle.