Influence of Interband Transitions on the Optics of Anisotropic Crystals

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Abstract
The contribution of the interband transitions, single exciton→single exciton, to the susceptibility Cr(12) of an anisotropic crystal is evaluated. It is shown that this contribution is not of the form which may be inferred from the Maxwell equations using the usual constitutive relations. A general discussion of the optics of anisotropic crystals based on a previously derived equation of motion for the vector potential ensues. The modifications of classical optics necessitated by the interband transitions are found. The optics of uniaxial crystals is discussed in detail. It is shown that in regions of negligible absorption the presence of interband transitions modifies the angular dependence of the index of refraction of the extraordinary wave. The possible existence of a cone of optic axes is predicted for suitable values of the interband contributions. In regions of absorption it is shown that the interband transitions give rise to a characteristic dependence of the imaginary part of the index of refraction on propagation directions. This differs from that of classical optics and allows for a simple experimental determination of the contribution of interband transitions to Cr(12). A discussion of the relation between the directions of the optic axes and optical parameters in orthorhombic crystals is given. It is shown that crystals of this class have at least one pair of optic axes, and possibly three pairs of optic axes, depending on the strength of the interband transitions.