Subpixel smoothing finite-difference time-domain method for material interface between dielectric and dispersive media
When modeling curved material interfaces, the standard Finite-Difference Time-Domain (FDTD) technique uses the staircasing approximation, in which any structure surface, no matter whether it is curved or flat, normal or oblique, is approximated by an array of cubic cells. This leads to reduced accuracy in the FDTD modeling of the electromagnetic wave’s interaction with the structure when the material surface is curved or oblique to the direction of incidence. Methods have been developed to decrease the errors caused by the staircasing approximation in FDTD simulations. For example, the subpixel smoothing technique consists of simple coordinate rotations and translations, followed by averaging or interpolation of the transformed electromagnetic field components within each FDTD cubic cell crossing the material interface, such that the electromagnetic boundary conditions at the material interface are satisfied (e.g. the tangential electric field and the normal electric displacement are continuous). Depending on the specific geometry of the subsurface of a medium interface, different treatments of the field components in each FDTD grid cell crossing the interface are needed to obtain more accurate results along the material surface and therefore to reduce errors in the whole FDTD computational domain.
In this paper, the subpixel smoothing method is extended to material interfaces between dielectric and dispersive media by local coordinate rotation. This extension has a much wider range of applications, such as the FDTD simulation of electromagnetic wave scattering by metallic targets. Although this method does not achieve second order accuracy, it has the potential of improving significantly the accuracy of FDTD simulations of electromagnetic wave scattering by a material surface. Its main advantage is its efficiency, as it does not require the storage and computation of split fields and additional equations since all of the treatments are performed locally in the cubic cells crossing the material surface, increasing only slightly the CPU time need for the FDTD calculations.