The generalization to circularly polarized modes of the Kramers-Kronig relations for the complex refractive index is discussed in terms of the analyticity of the index to clarify the physical basis of the generalized dispersion relations. A compact form for the circular-mode dispersion relations is obtained that is particularly useful in treating dichroic effects and for deriving optical sum rules. The procedure is generalized to elliptically polarized modes. It is shown that the generalized dispersion relations must be used for the optical constants of elliptic modes that retain their ellipticity to arbitrarily small frequencies, while dispersion relations of the Kramers-Kronig form apply to elliptic modes that are linearly polarized in the limit of small frequencies.
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