Generalized Sheet Transition Condition FDTD Simulation of Metasurface

We propose a finite-difference time-domain (FDTD) scheme based on generalized sheet transition conditions (GSTCs) for the simulation of polychromatic, nonlinear, and space-time varying metasurfaces. This scheme consists in placing the meta-surface at virtual nodal plane introduced between the regular nodes of the staggered Yee grid and inserting fields determined by GSTCs in this plane in the standard FDTD algorithm. The resulting update equations are an elegant generalization of the standard FDTD equations. Indeed, in the limiting case of a null surface susceptibility (chi(surf) = 0), they reduce to the latter, while in the next limiting case of a time-invariant metasurface [chi(surf) not equal chi(surf)(t)], they split in two terms, one corresponding to the standard equations for a one-cell (Delta x) thick slab with diluted volume susceptibility (chi = chi(surf)/(2 Delta x)), and the other one reducing that slab to a quasi-zero-thickness mesh-less sheet. The proposed scheme is fully numerical and very easy to implement. Although it is explicitly derived for a monoisotropic metasurface, it may be straightforwardly extended to the bianisotropic case. Except for some particular cases, it is not applicable to dispersive metasurfaces, for which an efficient auxiliary different equation extension of the scheme is currently being developed by the authors. The scheme is validated and illustrated by five representative examples.