A modeling of dispersive tensorial second-order nonlinear effects for the finite-difference time-domain method

A generalized formalism is developed to model second-order nonlinear processes in finite-difference time-domain (FDTD) simulations. The method is capable of modeling frequency-conversion from all 18 elements of the second-order nonlinear tensor, where dispersion of the tensor elements is included at both the pump and generated frequencies. The model is validated by considering frequency-conversion in a LiNbO₃ crystal, which has highly dispersive second-order nonlinear susceptibilities near the phonon resonances. The developed nonlinear formalism is able to model any arbitrary excitation polarization state and can be applied to investigate second-order nonlinear processes in type I or type II phase-matching. This generalized second-order nonlinear formalism represents an advancement for the FDTD computational technique and can provide more realistic modeling of second-order nonlinear interactions in nanoscale devices and waveguiding structures.