Algebraic determination of the principal refractive indices and axes in the electro-optic effect.

A systematic algebraic approach is presented as a preferred alternative to an iterative numerical method for deriving expressions for the principal refractive indices and dielectric axes of a nonmagnetic crystal in a uniform electric field. This approach is applicable for an arbitrary field and for any symmetry point group. The results, to the chosen order in the field, are expressed algebraically in terms of measurable crystal tensors. Illustrations are given of the linear electro-optic effect for the point groups 4?3m, 3m, 4?2m, and 1 and of the quadratic effect in 4?2m. The latter serves to highlight a shortcoming in the numerical approach. Comparisons are drawn with numerical results published previously.