Stable and Efficient Time-Domain Simulation of Metamaterials with an Extended Equivalent Circuit (EEC) Graded Mesh FDTD

A stable and efficient extended equivalent circuit (EEC) graded mesh FDTD scheme for composite right/left-handed (CRLH) metamaterials (MTMs) is presented along with a novel stability criterion based on a Lyapunov-type energy function. This criterion is firstly derived for a purely right-handed (PRH) medium, where it has been found to be advantageous compared to the Courant condition for highly non-uniform meshes, which are quite common in practice. Moreover, this criterion was extended to the cases of epsilon-negative (ENG), mu-negative (MNG) and CRLH MTMs, for which no stability condition was available so far. As an illustration of the EEC FDTD scheme, a spatial-frequencies quasi-optical diplexer principle is proposed