A More Accurate, Stable, FDTD Algorithm for Electromagnetics in Anisotropic Dielectrics

TL;DR

This paper introduces a new FDTD algorithm for electromagnetics in anisotropic dielectrics that improves accuracy and stability, especially at high dielectric contrasts, by effectively handling boundary discontinuities and ensuring stable updates.

Contribution

The paper presents a novel, more accurate, and stable FDTD algorithm that addresses instability issues at high dielectric contrasts and improves boundary treatment for anisotropic materials.

Findings

Enhanced accuracy over previous FDTD methods.

Remedies for instability at high dielectric contrasts.

Supports first-order error convergence in field calculations.

Abstract

A more accurate, stable, finite-difference time-domain (FDTD) algorithm is developed for simulating Maxwell's equations with isotropic or anisotropic dielectric materials. This algorithm is in many cases more accurate than previous algorithms (G. R. Werner et. al., 2007; A. F. Oskooi et. al., 2009), and it remedies a defect that causes instability with high dielectric contrast (usually for \epsilon{} significantly greater than 10) with either isotropic or anisotropic dielectrics. Ultimately this algorithm has first-order error (in the grid cell size) when the dielectric boundaries are sharp, due to field discontinuities at the dielectric interface. Accurate treatment of the discontinuities, in the limit of infinite wavelength, leads to an asymmetric, unstable update (C. A. Bauer et. al., 2011), but the symmetrized version of the latter is stable and more accurate than other FDTD methods. The convergence of field values supports the hypothesis that global first-order error can be achieved by second-order error in bulk material with zero-order error on the surface. This latter point is extremely important for any applications measuring surface fields.