Electromagnetic scattering from anisotropic materials, part I: General theory

Abstract

Integro-differential equations are obtained for the electric and magnetic fields inside a linear, lossy, and anisotropic scatterer, in the frequency domain. The material of the scatterer is characterized by arbitrary values of the elements of the relative permittivity tensor <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\bar{\epsilon}</tex> , the relative permeability tensor <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\bar{\mu}</tex> , and the conductivity tensor <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\bar{\sigma}</tex> . The results are specialized to the case of oblique scattering in two dimensions, for which a numerically efficient computer code has been developed and tested, as described in a companion paper (Part II). The method developed herein is based on a comparison between macroscopic and microscopic descriptions of electromagnetic fields in material media, and is of general applicability.