Superconvergence and sum rules for the optical constants: Natural and magneto-optical activity

Superconvergence techniques are systematically applied to dispersion relations for the index of refraction in optically active systems to find sum rules applicable to the optical constants for circularly polarized electromagnetic waves. New results include the theorems that (i) the zeroth moment of the circular dichroism and (ii) the first moment of the circular birefringence are zero. The latter theorem yields the simple rule that the rotation of the plane of polarization of linear light caused by an optically active medium averages to zero when integrated over all energies. Generalizations of the $f$ and inertial sum rules to circularly polarized modes are given, as well as a new rule relating the second moment of the circular dichroism to the cyclotron frequency in magneto-optics or to the rotatory strengths in natural optical activity.