Treatment of Grid-Conforming Dielectric Interfaces in FDTD Methods

A new solution to the problem of implementing extended-stencil finite-difference operators across material interfaces is presented in this paper for time-domain electromagnetic simulations. In essence, modified spatial approximations are applied within a transition layer that encloses the discontinuity, while preserving the stencil size of the scheme employed in the homogeneous areas. The necessary difference expressions are determined with the aid of a straightforward design procedure, which is based on the reliable modeling of exact solutions, following a one-dimensional formulation. The proposed approach, whose beneficial effects are exemplified via numerical simulations, is analyzed for the case of the (2,4) method. Yet, its concepts are global and easily adapted to any discretization algorithm.