A new high order dispersive FDTD method for Drude material with complex interfaces

In this paper, motivated by the needs of tracking the transient change in the regularity of the electromagnetic fields across a Drude interface, we propose a new Maxwell-Drude formulation for transverse magnetic problems with inhomogeneous Drude dispersive materials. Based on the auxiliary differential equation approach, the proposed formulation couples the wave equation for the electric component with Maxwell's equations for the magnetic components. A new finite-difference time-domain (FDTD) algorithm is introduced for solving the proposed Maxwell-Drude system, in which the time dependent jump conditions across the Drude interface are enforced through the matched interface and boundary (MIB) method. The proposed FDTD method achieves a second order of accuracy in solving Drude interfaces with fluctuating curvatures and non-smooth corners based on a simple Yee lattice, while it can be generalized to up to sixth order in dealing with a straight Drude interface. Therefore, the proposed FDTD method is more accurate and cost-efficient than the classical FDTD methods for Drude material with complex interfaces.