A symplectic FDTD algorithm for the simulations of lossy dispersive materials

A high-order symplectic finite-difference time-domain (SFDTD) algorithm, based on the matrix splitting, the symplectic integrator propagator and the auxiliary differential equation (ADE) technique, is presented. The algorithm is applied to the lossy Lorentz-Drude dispersive model. With the rigorous and artful formula derivation, the detailed formulations are provided. Moreover, the present algorithm can also be applicable to the lossy Drude and Lorentz dispersive model in a straightforward manner. An excellent agreement is achieved between the SFDTD-calculated and exact theoretical results when calculating the transmission coefficient in simulation of metal films. Focusing action of the matched left-handed materials (LHMs) slab is also achieved as the second example in the two-dimensional space. Numerical results for a more realistic structure, the simulation of periodic arrays of silver split-ring resonators (SRRs) using the Drude dispersion model, are also included, and the results agree well with those obtained by the finite element method (FEM).