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A general expression for the complex Faraday rotation is obtained by generalizing the Kramers-Heisenberg dispersion formula. It shows that the pure rotation is proportional to the sum of circular dichroism in in all resonance transitions weighted by the appropriate resonance-dispersion factors. The cases of free ions and rare-earth ions in solids are discussed. It is shown how Gd^3+ and Eu^2+, having the same electronic structure, may possess very different rotatory powers in a given frequency range through the difference in their optical spectra. The formula for the anomalous rotatory dispersion about sharp lines is also given.
Y. R. Shen (Mon,) studied this question.
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