Birefringence, or double refraction, is the decomposition of a ray of light into two rays (the ordinary ray and the extraordinary ray) when it passes through certain types of material, such as calcite crystals or boron nitride, depending on the polarization of the light. This effect can occur only if the structure of the material is anisotropic (directionally dependent). If the material has a single axis of anisotropy or optical axis, (i.e. it is uniaxial) birefringence can be formalized by assigning two different refractive indices to the material for different polarizations. The birefringence magnitude is then defined by
where no and ne are the refractive indices for polarizations perpendicular (ordinary) and parallel (extraordinary) to the axis of anisotropy respectively.
The reason for birefringence is the fact that in anisotropic media the electric field vector and the dielectric displacement can be nonparallel (namely for the extraordinary polarisation), although being linearly related.
Birefringence can also arise in magnetic, not dielectric, materials, but substantial variations in magnetic permeability of materials are rare at optical frequencies.
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