  The letter contains an important message regarding the numerical modeling of
left-handed media (LHM) using the finite-difference time-domain (FDTD) method
which remains at the moment one of the main techniques used in studies of these
exotic materials. It is shown that conventional implementation of the
dispersive FDTD method leads to inaccurate description of evanescent waves in
the LHM. This defect can be corrected using the spatial averaging at the
interfaces. However, a number of results obtained using conventional FDTD
method has to be reconsidered. For instance, the accurate simulation of
sub-wavelength imaging by the finite-sized slabs of left-handed media does not
reveal the cavity effect reported in [Phys. Rev. Lett. 92, 107404 (2004)].
Hence the finite transverse dimension of LHM slabs does not have significant
effects on the sub-wavelength image quality, in contrary to previous
assertions.
