Electromagnetic theorems for complex anisotropic media

Abstract

Complex anisotropic media can generally be described by a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6 \times 6</tex> macroscopic constitutive tensor <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\hat{C}</tex> . Using <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\hat{C}</tex> properties, a reaction integral formula is derived from which an anisotropic reaction theorem (modified reciprocity theorem) is developed. Reduction of the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\hat{C}</tex> medium into a reciprocal medium is discussed including tensor symmetry attributes and limiting cases. The anisotropic reaction theorem is utilized to derive a zero reaction theorem, and then treated in relation to the moment method. Mutual and self-impedance elements of a network are also derived in terms of reaction integrals, symmetry covered using the anisotropic reaction theorem, and impedance elements related to moment calculations. Use of spectral domain analysis is also covered.