Interactions of bound electrons with an electromagnetic wave mix the electronic states and contribute terms to the wave functions linear in the propagation constant k of the light. These terms contribute O(k2) to the dielectric tensor ∊ij, with a resulting birefringence in an Oh crystal when k is not parallel to a three-or fourfold axis. By substitution of the dielectric tensor with its k dependence into Maxwell’s equations, the three possible polarization E directions for each k and the corresponding propagation velocities can be predicted. Retardation of approximately transverse waves in a crystal with small anisotropy is a maximum along 〈110〉 and zero along 〈100〉 and 〈111〉. Retardation is also small for k directions lying on the shorter segment of a great circle of the unit sphere connecting a given pair of three- and fourfold axes. An investigation is also made of directions of maximum and minimum retardation in an Oh cube when anisotropy is not small. All of these results serve to correct analyses of earlier authors who assumed polarization directions appropriate only to a uniaxial crystal.
R. E. NETTLETON, "Quadrupole Exciton Transitions and Optical Anisotropy in Cubic Crystals," J. Opt. Soc. Am. 61, 1060-1064 (1971)