## Abstract

Dispersion relations and sum rules for the dichroic reflectivity and phase shifts of circularly polarized modes are developed for the magneto-optical case. The reduction in crossing-relation symmetry arising from the presence of a magnetic field and the consequent non-Kramers-Kronig form of the dichroism dispersion relations are discussed in terms of the analyticity of the amplitude reflectivity. Sum rules are derived from the low- and high-frequency limits of the dichroism dispersion relations. These rules include the general results that
${\int}_{0}^{\infty}{\omega}^{-1}\hspace{0.17em}\text{ln}[{r}_{+}(\omega )/{r}_{-}(\omega )]\text{d}\omega =0$ and
${\int}_{0}^{\infty}[{\theta}_{+}(\omega )-{\theta}_{-}(\omega )]\hspace{0.17em}d\omega =\pi {\omega}_{c}$, where *r*_{±}(*ω*) and *θ*_{±}(*ω*) are the amplitude and phase of the amplitude reflectivity for the circular modes and *ω** _{c}* is the cyclotron frequency. Approximate finite-energy dispersion relations and sum rules are developed and their range of validity examined.

© 1976 Optical Society of America

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