Efficiency of the Perfectly Matched Layer with high-order finite difference and pseudo-spectral Maxwell solvers

The commonly used second order Finite-Difference Time-Domain (FDTD) scheme for electromagnetic solvers in Particle-In-Cell codes produces fast solvers that scale well in parallel, but suffers from anomalous numerical effects resulting from discretization, such as numerical dispersion. High order schemes are therefore seen as the remedy for reducing the discretization errors. In the modeling of various applications, an open boundary is necessary for simulating vacuum extending beyond the computational box, for which algorithms based on-or derived from-Bérenger's Perfectly Matched Layers (PML) have demonstrated high efficiency over a wide range of wavelength and angle of incidence. The amount of numerical reflection of PMLs has been studied numerically and analytically for low order stencils but not systematically at higher order, nor for the pseudo-spectral scheme. In this paper, we extend the theoretical and numerical analysis of the coefficient of reflection of PML layers to solvers of any order of accuracy. Results show that the PML efficiency is preserved at any order, including at the infinite order limit that is attained by the pseudo-spectral formulation.