Vectorial nonparaxial propagation equation in the presence of a tensorial refractive-index perturbation

The standard scalar paraxial parabolic (Fock–Leontovich) propagation equation is generalized to include allorder nonparaxial corrections in the significant case of a tensorial refractive-index perturbation on a homogeneous isotropic background. In the resultant equation, each higher-order nonparaxial term (associated with diffraction in homogeneous space and scaling as the ratio between beam waist and diffraction length) possesses a counterpart (associated with the refractive-index perturbation) that allows one to preserve the vectorial nature of the problem (11 • E Þ 0). The tensorial character of the refractive-index variation is shown to play a particularly relevant role whenever the tensor elements dnxz and dnyz (z is the propagation direction) are not negligible. For this case, an application to elasto-optically induced optical activity and to nonlinear propagation in the presence of the optical Kerr effect is presented. © 2000 Optical Society of America [S0740-3224(00)00405-7] OCIS codes: 260.0260, 350.5500.