High order FDTD methods for transverse magnetic modes with dispersive interfaces

A new finite-difference time-domain (FDTD) algorithm is introduced to solve two dimensional (2D) transverse magnetic (TM) modes with a straight dispersive interface. Driven by the consideration of simplifying interface jump conditions, the auxiliary differential equation of the Debye constitution model is rewritten to form a new Debye–Maxwell TM system. Interface auxiliary differential equations are utilized to describe the transient changes in the regularities of electromagnetic fields across a dispersive interface. The resulting time dependent jump conditions are rigorously enforced in the FDTD discretization by means of a matched interface and boundary scheme. Higher order convergences are numerically achieved for the first time in the literature in 2D FDTD simulations of dispersive inhomogeneous media. 2013 Elsevier Inc. All rights reserved.