Improving accuracy by subpixel smoothing in the finite-difference time domain

TLDR

Finite‑difference time‑domain (FDTD) methods lose accuracy when modeling discontinuous dielectric materials due to inherent pixelization. The authors aim to develop a subpixel smoothing scheme for FDTD based on a perturbation‑theory criterion and benchmark it against existing methods. The scheme is constructed using the perturbation‑theory criterion, and the authors also analyze challenges posed by sharp dielectric corners. The proposed smoothing method yields the lowest errors among compared techniques and uniquely achieves quadratic convergence with resolution for arbitrarily sloped interfaces.

Abstract

Finite-difference time-domain (FDTD) methods suffer from reduced accuracy when modeling discontinuous dielectric materials, due to the inhererent discretization (pixelization). We show that accuracy can be significantly improved by using a subpixel smoothing of the dielectric function, but only if the smoothing scheme is properly designed. We develop such a scheme based on a simple criterion taken from perturbation theory and compare it with other published FDTD smoothing methods. In addition to consistently achieving the smallest errors, our scheme is the only one that attains quadratic convergence with resolution for arbitrarily sloped interfaces. Finally, we discuss additional difficulties that arise for sharp dielectric corners.