Symmetric Energy-Conserved S-FDTD Scheme for Two-Dimensional Maxwell's Equations in Negative Index Metamaterials

A new time second-order symmetric energy-conserved splitting FDTD scheme is proposed for solving the two-dimensional Maxwell's equations in negative index metamaterials with Drude model. The scheme is proved to preserve the discrete electromagnetic energies in metamaterials and is of second order accuracy both in time and space. The proposed scheme also possesses the superconvergence and the second-order convergence for the discrete divergence. Numerical experiments confirm the theoretical results. Simulations of CW Gaussian beam interactions with double negative matematerials slabs and the electromagnetic waves propagating in metamaterials excited by sinusoidal point source are carried out to show supernormal phenomena in negative index metamaterials.