Eigenvector approach to the evaluation of the Jones N matrices of nonabsorbing crystalline media

An eigenvector equation within the electric octopole–magnetic quadrupole approximation is derived, from which it is possible in principle to establish the eigenvectors and the refractive indices of polarized light forms sustained by an anisotropic crystal for any chosen direction of phase propagation. It is shown that, for propagation along the crystal axes when the rays do not separate, a decomposition technique based on eigenvectors and the Jones resolution of a medium into independent differential plates substantially simplifies solution of the general problem. Precise expressions are obtained for the Jones parameters n, (ny − nx), (n−45 − n45), and (nR − nL) in terms of multipole-property tensors of the crystal. The effects of crystal symmetry on these expressions are summarized.