Dispersion relations and sum rules for magnetoreflectivity

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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 ∫∞0 ω-1 ln[r+(ω)/r-(ω)]dω = 0 and ∫∞0[θ+(ω)-θ-(ω)]dω = πωc, where r±(ω) and θ±(ω) are the amplitude and phase of the amplitude reflectivity for the circular modes and ωc is the cyclotron frequency. Approximate finite-energy dispersion relations and sum rules are developed and their range of validity examined.

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