Frequency conversion in second-order nonlinear materials is sensitive to the phase velocities of interacting optical waves. Accurate modeling of such problems with the finite-difference time-domain method requires extremely fine grid resolutions to minimize numerical dispersion errors. We propose an alternative approach based on a pseudospectral time-domain (PSTD) method for solving the nonlinear Maxwell’s equations. Low-dispersion PSTD schemes with second- and fourth-order time stepping are developed and investigated. Benchmark simulations of second-harmonic generation (SHG) demonstrate that the PSTD schemes offer significant improvements in computational efficiency and accuracy. We demonstrate use of these schemes by modeling SHG in a nonlinear grating illuminated at an oblique angle, where phase matching is achieved in two dimensions.
© 2004 Optical Society of America
Tae-Woo Lee and Susan C. Hagness, "Pseudospectral time-domain methods for modeling optical wave propagation in second-order nonlinear materials," J. Opt. Soc. Am. B 21, 330-342 (2004)