Truly high-order FDTD method for inhomogeneous electromagnetic media

The paper introduces a series of novel hierarchical implicit derivative matching methods to restore the accuracy of high-order finite difference time-domain (FDTD) schemes of computational electromagnetics (CEM) with material interfaces in one and two spatial dimensions (1D and 2D). By making use of fictitious points, systematic approaches are proposed to enforce locally the physical jump conditions at material interfaces in a preprocessing stage, to arbitrarily high orders of accuracy in principle. While often limited by numerical instability, orders up to 16 and 10 are achieved, respectively, in 1D and 2D. Numerical experiments on both 1D and 2D problems indicate that the proposed approaches might lead to practical high order schemes for CEM.