Dielectric tensor of organic anisotropic crystals

As an example of an anisotropic crystal, let us consider a molecular crystal with a 1 molecules per unit cell. Let us investigate the optical properties of the crystal in the frequency range u io where io is the transition frequency to that of a nondegenerate excited state of the isolated molecule. The polarizability of the molecule in the vicinity of the dipole-allowed transition can be presented by the relation 

When we substitute eqn (5.22) into eqn (5.3) and find the scalar product on the left with a we obtain the following system of equations for the quantities (Ea a) where a = 1, 2. a  

For a crystal with one molecule per unit cell eqn (5.23) directly yields (E1 1) = [1-M11(w,k)]-1(E 1), so that the polarization per unit volume is 

Taking this relationship and eqn (5.24) we find the following expression for the 

The tensor (5.25) has the symmetry of a uniaxial crystal. If one of the coordinate axes, for instance, the x-axis, is taken parallel to then the tensor (5.25) is reduced to diagonal form with the following nonzero components  

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