Abstract
A generalized Cauchy dispersion formula applicable to both normal andanomalous dispersion in the refractive index of transparent materials isderived from the Kramers-Kronig relations. Several commonly used dispersionformulae are closely related to this result. The expansion coefficients,heretofore considered empirical, are simply the odd moments of the absorptionspectrum. These ideas are illustrated for natural diamond, and high-puritysilicon and germanium. Analysis of published data for these materialsdiscloses extrinsic dispersive effects in the far infrared, even for`high-purity' samples. We attribute this dispersion to free-carrier ordefect-induced absorptions at energies below the range of measurements.
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