EIGENVECTOR APPROACH TO THE EVALUATION OF THE JONES N-MATRICES OF NONABSORBING CRYSTALLINE MEDIA

An eigenvector equation within the electric octopole-magnetic quadrupo le approximation is derived, from which it is possible in principle to establish the eigenvectors and the refractive indices of polarized li ght forms sustained by an anisotropic crystal for any chosen direction of phase propagation. It is shown that, for propagation along the cry stal axes when the rays do not separate, a decomposition technique bas ed on eigenvectors and the Jones resolution of a medium into independe nt differential plates substantially simplifies solution of the genera l problem. Precise expressions are obtained for the Jones parameters n , (n(y) - n(x)), (n-45 - n45), and (n(R) - n(L)) in terms of multipole -property tensors of the crystal. The effects of crystal symmetry on t hese expressions are summarized.