General vector auxiliary differential equation finite-difference time-domain method for rotationally symmetric vector wave propagation in nonlinear optics

In this paper, the theory and simulation results are presented for 3D vector cylindrical rotationally symmetric electromagnetic wave propagation in an isotropic nonlinear medium using a modified finite-difference time-domain general vector auxiliary differential equation method for nonlinear polarization vectors, the nonlinear dipole moment per unit volume, including both an isotropic part and an anisotropic part. The theory is presented for both the transverse magnetic and transverse electric cases, along with the combined equations. The simulation results for transverse electric spatial soliton propagation in BK7, and the simulation results for transverse electric and transverse magnetic spatial soliton propagation in fused silica, assuming a purely isotropic polarization vector, are shown. The simulation results for both transverse magnetic and transverse electric spatial soliton propagation in carbon disulfide, including the anisotropic part of the polarization vector, are also shown.