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I need a same help with it. Some books where i can find a real math explanation of this effect will be good help!! simple exp of this effect will be good too)

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Typically, in professional optics, dichroism refers to differential absorption between two (or more) different polarization states.

Since the complex index of refraction $n+i\kappa$ contains both the speed of light transformation and the absorption transformation of a particular material, this can be generalized to a tensor valued index of refraction for any material: $$ {\bf{n}}_{\text{tensor}}=\begin{pmatrix}n_{00}+i\kappa_{00}&n_{01}+i\kappa_{01}&n_{02}+i\kappa_{02}\\ n_{10}+i\kappa_{10}&n_{11}+i\kappa_{11}&n_{12}+i\kappa_{12}\\ n_{20}+i\kappa_{20}&n_{21}+i\kappa_{21}&n_{22}+i\kappa_{22} \end{pmatrix} $$ so that different directions in a volumetric material have different indices of refraction. This matrix can then be diagonalized to obtain three principal indices of refraction corresponding to three (not necessarily orthogonal) principal axes (i.e. the directions along which light propagating will "see" the respective principal index of refraction).

In an isotropic medium, all indices of refraction are equal. In a uniaxial crystal, two indices of refraction are equal and one axis is different. In a biaxial crystal, all three indices of refraction are different.

The dichroism can then be thought of as the difference between the absorptions of different indices of refraction. In a biaxial crystal there will be three dichroisms, in a uniaxial crystal there will be a single dichroism, and in an isotropic medium there will be no dichroism.

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How can i explain a different absorption of the different polarization parts of wave? And what is the real nature of dichroism? What is the center of absorption? Dipoles or electron-vacancy pairs?? –  user_user Jan 18 '13 at 17:50
    
since the absorption (captured in the complex index of refraction) is dependent upon direction, then the polarized wave can be deposed into the principal axis basis, then propagated in that basis according to each index of refraction, then summed back together or changed back to the laboratory frame after propagation. –  daaxix Jan 18 '13 at 19:27
    
The real nature of dichroism can be quite complicated, it ultimately depends on crystal structure, quantum probability of absorption of the electrons in the crystal lattice (which is dependent on their state and the polarization of light), and light energy and wavelength. –  daaxix Jan 18 '13 at 20:04

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