More generally, an anisotropic dielectric material has a dielectric constant that is a rank-2 tensor (3 by 3 matrix). A birefringent material corresponds to the special cases of a real-symmetric dielectric tensor ε with eigenvalues of , , and along the three orthogonal principle axes of polarization. (Or, sometimes, only two axes are considered, corresponding to a single propagation direction.)
(In principle, birefringence could also arise in magnetic, not dielectric, materials, but substantial variations in magnetic permeability are rare at optical frequencies.)
See also crystal optics.
The cellophane paper is a cheap birefringent material.