Optical isotropy

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An optically isotropic material is one that has the same optical properties in every direction.

In the literature, optical isotropy is usually seen as equivalent to the fact that the dielectric tensor function is a scalar function or is reduced to a scalar function in case of polydomain materials. The latter is not correct, however, if the domains can not be considered as small compared to the wavelength. Then, the individual reflectance or transmittance of the domains has to be averaged if the macroscopic reflectance or transmittance is to be calculated. This can be verified simply by investigating, e.g., a polycrystalline material under a polarizing microscope having the polarizers crossed: If the crystallites are larger than the resolution limit, they will be visible in general. The magnitude of the local cross-polarization reflectance or transmittance depends on the orientation of the crystallite. The local cross-polarization terms add up incoherently to a non-zero macroscopic cross-polarization of the sample despite being macroscopically isotropic. A non-zero cross-polarization, however, proves that it is not possible to characterize a material with a scalar dielectric tensor function.