The split-field finite-difference time-domain (SF-FDTD) method for one-dimensionally periodic structures is extended to include the coefficient-tensor description of second- and third-order nonlinear-optical media. A set of nonlinear equations related to the split-field values of the electric field is established. An iterative fixed-point approach for solving the coupled nonlinear system of equations needed to update the electric field components in the SF-FDTD is then developed. The third-order nonlinear susceptibility dispersion is also considered by means of the Raman effect and its implementation in the SF-FDTD scheme. Different scenarios are considered in order to verify the reliability of the method for simulating second- and third-order nonlinear-optical media. First, second-harmonic generation and its efficiency are investigated in a homogeneous layer with and without the quasi-phase-matching technique. Second, the nonlinear dispersion is analyzed by means of the generation of solitons in Kerr media due to the Raman effect. Last, a set of binary phase gratings with nonlinear pillars is considered under oblique incidence. Here the nonlinear refractive index is generated by different physical mechanisms modeled with the nonscalar third-order susceptibility.
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