  The accuracy of finite-difference time-domain (FDTD) modelling of left-handed
metamaterials (LHMs) is dramatically improved by using an averaging technique
along the boundaries of LHM slabs. The material frequency dispersion of LHMs is
taken into account using auxiliary differential equation (ADE) based dispersive
FDTD methods. The dispersive FDTD method with averaged permittivity along the
material boundaries is implemented for a two-dimensional (2-D) transverse
electric (TE) case. A mismatch between analytical and numerical material
parameters (e.g. permittivity and permeability) introduced by the time
discretisation in FDTD is demonstrated. The expression of numerical
permittivity is formulated and it is suggested to use corrected permittivity in
FDTD simulations in order to model LHM slabs with their desired parameters. The
influence of switching time of source on the oscillation of field intensity is
analysed. It is shown that there exists an optimum value which leads to fast
convergence in simulations.
