3D Diagonalization and Supplementation of Maxwell’s Equations in Fully Bi-anisotropic and Inhomogeneous Media - Part I: Proof of Existence by Construction
Keywords:
Bi-anisotropic and inhomogeneous media, diagonalization, Maxwell’s equations, supplementaionAbstract
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 × 3 permittivity, electro-magnetic coupling, magneto-electric coupling, and permeability matrices epsilon3x3(x, y, z), xi 3x3(x, y, z), zeta3×3(x, y, z), and mu3×3(x, y, z), respectively. Assume a harmonic time-dependence according to exp(–jwt). 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.
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References
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