General vector auxiliary differential equation finite-difference time-domain method for nonlinear optics

The auxiliary differential equation finite-difference time-domain method for modeling electromagnetic wave propagation in dispersive nonlinear materials is applied to problems where the electric field is not constrained to a single vector component. A full-vector Maxwell's equations solution incorporating multiple-pole linear Lorentz, nonlinear Kerr, and nonlinear Raman polarizations is presented. The application is illustrated by modeling a spatial soliton having two orthogonal electric field components. To the best of our knowledge, the numerical technique presented here is the first to model electromagnetic wave propagation with two or three orthogonal vector components in dispersive nonlinear materials. This technique offers the possibility of modeling sub-wavelength interactions of vector spatial solitons.