A New Theory of the Generalized Optical Theorem in Anisotropic Media

A new general approach for the generalized optical cross-section theorem and its particular manifestation, the ordinary optical theorem, is developed for electromagnetic scattering in anisotropic media (corresponding to the scatterer and the background medium where the scatterer is embedded). The derived results are based on cross-flux concepts, and interaction and reciprocity relations, and apply under arbitrary incident fields, hence they apply in arbitrary representational domains for the data or scattering matrix. This generalization is demonstrated for arbitrary anisotropic scatterers embedded in lossless anisotropic background media by means of the so-called modified reciprocity theorem plus duality. A new reactive optical theorem is also derived which clarifies the possibilities and limitations of the extraction of reactive energy storage information of an scatterer from scattering field data. Fundamental and practical imaging implications of the derived optical theorems are discussed. The developed theory is elaborated for general anisotropic scatterers embedded in free space via the multipole expansion of the electromagnetic field.