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

TL;DR

This paper generalizes Huygens' principle, extinction theorem, and Franz's formulation to complex inhomogeneous anisotropic environments, providing new mathematical frameworks for electromagnetic theory and establishing their equivalence.

Contribution

It extends traditional EM principles to inhomogeneous anisotropic lossy media and introduces multiple closed surfaces for Huygens' surfaces, with future plans for open boundaries.

Findings

Huygens' principle and extinction theorem are proven equivalent.

Generalized formulations for inhomogeneous anisotropic media.

Extended FHF to internal scattering and incident fields.

Abstract

Huygens' principle (HP), extinction theorem (ET), and Franz's / Franz-Harrington formulation (FHF, which is a mathematical expression of surface equivalence principle) are the important components of electromagnetic (EM) theory, and they are generalized from the following aspects. 1) Traditional HP, ET, and FHF in homogeneous isotropic environment are generalized to inhomogeneous anisotropic lossy environment. 2) Traditional FHF for homogeneous isotropic material system is generalized to inhomogeneous anisotropic lossy material system in this paper, and will be further generalized to metal-material combined system in future works. 3) The Huygens' surface in traditional HP and ET is a single closed surface. In this paper, it is generalized to the "Huygens' surface" which is constructed by multiple closed surfaces. In future works, it will be further generalized to the "Huygens' boundary" which includes some lines and open surfaces. 4) For a material body, traditional FHF has only ability to express the external scattering field and the internal total field (the summation of scattering and incident fields) in terms of the equivalent sources on material boundary, and it is generalized to formulating the internal scattering and incident fields in this paper. In addition, the relationships among HP, ET, and FHF are studied, and it is proved that HP and ET are equivalent to each other.