Pseudospectral time-domain methods for modeling optical wave propagation in second-order nonlinear materials

Abstract

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. Lowdispersion 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.

3D pseudospectral time domain for modeling second-harmonic generation in periodically poled lithium niobate ridge-type waveguides

“…As a consequence, this numerical method can be used to study various problems on larger scales, more efficiently and with a better accuracy than Finite-Difference TimeDomain (FDTD) methods [11,[14][15][16][17][18]. In particular, because accurate modelling of nonlinear optical processes with the FDTD method requires extremely fine sampling to minimize numerical dispersion errors, PSTD schemes offer significant improvements in computational efficiency and accuracy [19,20]. In the present work, 3D-PSTD algorithm models the SHG in periodically poled and uniformly poled Lithium Niobate (LN) ridge-type waveguides.…”

Comparison of Finite Difference Schemes for the Wave Equation Based on Dispersion

“…Sometimes, due to truncation of higher order terms, frequency dependent numerical errors called dispersion is produced. A large amount of work has been developed for higher order accurate scheme with low dispersion; for instance, Krum [3] developed time-domain schemes based on multiresolution analysis, Lee [4] introduced a low-dispersive schemes based on Pseudo-spectral approach.…”

Reduction of Simulation Times for High-Q Structures Using the Resonance Equation

“…While the use of the finite-difference time-domain (FDTD) method for the analysis of radio-frequency components is well established [1][2][3][4], electrically large (more than a few wavelengths (λ) in one dimension) components require large simulation times that are computationally prohibitive. It is generally considered, based on the stability criteria of the finite difference formulas, that a minimum of 10 to 20 spatial grid points per the minimum simulated λ will be needed to ensure accurate results [1].…”

“…Such details are important in the analysis of any abnormalities that have been observed during real-world operation. Spectral methods, such as the pseudospectral time domain (PSTD) methodology, reduce the mesh through calculating the spatial derivatives in Maxwells Equations using a Fourier transform based methodology [1,4]. This reduces the mesh size to 2 grid points per λ based on the Nyquist sampling theorem.…”