Dispersion relations, stored energy and group velocity for anisotropic electromagnetic media

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Abstract
The Hermitian and skew-Hermitian components of the susceptibility matrix of a general linear electromagnetic medium are represented as Hilbert transforms of each other. These so-called dispersion relations lead to a priori inequalities which must be satisfied by the susceptibility of a passive medium in a frequency interval in which the medium is lossless. One such inequality states that the stored energy density for a given E ( ω ) E\left ( \omega \right ) and H ( ω ) H\left ( \omega \right ) is always greater than in free space. This is also verified directly from the usual gyrotropic susceptibilities of ferrites and plasmas.