Linear electro-optic effects due to high order spatial dispersion

Two new types of electro-optic effect that are linear in the applied electric field strength are theoretically predicted to exist in transparent dielectric crystals due to high order spatial dispersion. The first effect, which is quadratic in the wave vector of light, is possible in materials belonging to all noncentrosymmetric crystal classes. The second, which is cubic in the wave vector, is possible in all crystals. In the ${\bm O}(432)$ and $\bm{O_h}(m\bar 3m)$ crystal classes, for which the primary and secondary linear electro-optic effects and linear electrogyration are simultaneously absent, these effects lead, respectively, to qualitatively new behavior and constitute the dominant bulk electro-optic effect in the limit of small fields. Thus, bulk linear electro-optic effects are predicted to exist in a wide range of materials---including many of considerable technological importance, such as silicon---where they were previously considered impossible.