Comparative analysis of Maxwell solvers for simulation of relativistic harmonic generation in particle-in-cell code.

With advances in laser technology reaching the multipetawatt era, the expanding experimental prospects for high-order harmonic generation from solid targets prompt more rigorous particle-in-cell (PIC) simulation campaigns for elucidating the generation mechanisms. However, accurately representing a broad range of high frequencies in multidimensional simulations remains challenging. The commonly employed finite difference time domain (FDTD) method, the Yee stencil, introduces artificial numerical dispersion, inducing unphysical angular deviation of higher-order harmonics. This paper uses EPOCH and WarpX PIC codes to present a comprehensive analysis of numerical dispersion mitigation for two-dimensional (2D) simulations of high-order harmonic generation. Results conclude that carefully orienting high-frequency elements within the 2D simulated grid for the standard FDTD scheme can provide significant accuracy improvements at moderate resolution and computational power for cases with a distinct propagation direction for the electromagnetic radiation of interest. This study also evaluates higher-order pseudospectral analytical time-domain (PSATD) solvers, which eliminate angular deviations across all tested angles of incidence and promise to enhance scalability in exascale computing environments.