Crystal optics
Crystal optics is the branch of optics that describes the behaviour of light in anisotropic media, that is, media (such as crystals) in which light behaves differently depending on which direction the light is propagating. The index of refraction depends on both composition and crystal structure and can be calculated using the Gladstone–Dale relation. Crystals are often naturally anisotropic, and in some media (such as liquid crystals) it is possible to induce anisotropy by applying an external electric field.
Typical transparent media such as glasses are isotropic, which means that light behaves the same way no matter which direction it is travelling in the medium. In terms of Maxwell's equations in a dielectric, this gives a relationship between the electric displacement field D and the electric field E:
where ε0 is the permittivity of free space and P is the electric polarization (the vector field corresponding to electric dipole moments present in the medium). Physically, the polarization field can be regarded as the response of the medium to the electric field of the light.
In an isotropic and linear medium, this polarization field P is proportional to and parallel to the electric field E:
where χ is the electric susceptibility of the medium. The relation between D and E is thus:
...
Wikipedia