More generally, an anisotropic dielectric material has a dielectric constant that is a rank2 tensor (3 by 3 matrix). A birefringent material corresponds to the special cases of a realsymmetric dielectric tensor ε with eigenvalues of <math>n_o^2</math>, <math>n_o^2</math>, and <math>n_e^2</math> 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.
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