Implicit and explicit FDTD methods for modelling EM metasurfaces

A numerical comparison between the explicit and implicit finite difference time-domain (FDTD) methods is presented for simulating broadband and dispersive metasurfaces. It has been found that, while the implicit method is rigorous in computing the scattered fields in both reflection and transmission region of the metasurface, care must be taken using the explicit method, which is applicable under paraxial wave propagation conditions only.