Abstract
Application of the pseudospectral method in numerical calculations is well established. The method is used in several disciplines, from geology to applied mathematics. The pseudospectral method also appears in computational electromagnetism. Its implementation already has been carried out for the finite element method and finite difference time domain method. In this study, we implement the pseudospectral method for the finite difference frequency domain (FDFD) method, and hence the resulting method is called the pseudospectral frequency domain (PSFD) method. The PSFD method is compared to the FDFD method in terms of the numerical phase velocity and anisotropy. The method is extended for the nonlinear process PSFD (NL-PSFD) of second-harmonic generation. It is shown how a plane wave source at oblique incidence can be implemented, and its performance for tilted quasi-phase-matched grating is discussed. Finally, a specific method is deduced from NL-PSFD for large-volume simulation, where only second-order nonlinearity is spatially structured, and a two-dimensional nonlinear photonic crystal is simulated.
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