3D Diagonalization and Supplementation of Maxwell’s Equations in Fully Bi-anisotropic and Inhomogeneous Media Part Ⅰ: Proof of Existence by Construction

摘要

Consider the Maxwell's curl equations in fully bi-anisotropic and inhomogeneous media in three dimensional (x, y, z) spatial Cartesian coordinates. Let the media be characterized by 3 x 3 permittivity, electro-magnetic coupling, magneto-electric coupling, and permeability matrices epsilon(3x3)(x, y, z), xi(3x3) (x, y, z), zeta(3x3) (x, y, z), and mu(3x3)(x, y, z), respectively. Assume a harmonic time-dependence according to exp(-j omega t). The prime objective in this paper is to establish that the Maxwell's electrodynamic equations jointly with the constitutive equations can be diagonalized, leading to the D-, and the associated supplementary S-forms. A finitary algorithm involving "structural,'' "differential,'' and "material'' matrices has been proposed, and the existence of the D- and S-forms proved by construction. In the accompanying paper (Part II) the internal consistency of the D- and S-forms has been shown, by proving their sharp equivalence with Maxwell's and constitutive equations.