Interactions of bound electrons with an electromagnetic wave mix the electronic states and contribute terms to the wave functions linear in the propagation constant <i>k</i> of the light. These terms contribute <i>O</i>(<i>k</i><sup>2</sup>) to the dielectric tensor ∊<i><sub>ij</sub></i>, with a resulting birefringence in an <i>O<sub>h</sub></i> crystal when <b>k</b> is not parallel to a three-or fourfold axis. By substitution of the dielectric tensor with its <b>k</b> dependence into Maxwell’s equations, the three possible polarization <b>E</b> directions for each <b>k</b> 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 <b>k</b> 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 <i>O<sub>h</sub></i> 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)