  Pairing together material slabs with opposite signs for the real parts of
their constitutive parameters has been shown to lead to interesting and
unconventional properties that are not otherwise observable for single slabs.
One such case was demonstrated analytically for the conjugate (i.e.,
complementary) pairing of infinite planar slabs of epsilon-negative (ENG) and
mu-negative (MNG) media [A. Alu, and N. Engheta, IEEE Trans. Antennas Prop.,
51, 2558 (2003)]. There it was shown that when these two slabs are juxtaposed
and excited by an incident plane wave, resonance, complete tunneling, total
transparency and reconstruction of evanescent waves may occur in the
steady-state regime under a monochromatic excitation, even though each of the
two slabs by itself is essentially opaque to the incoming radiation. This may
lead to virtual imagers with sub-wavelength resolution and other anomalous
phenomena overcoming the physical limit of diffraction. Here we explore how a
transient sinusoidal signal that starts at t = 0 interacts with such an ENG-MNG
pair of finite size using an FDTD technique. Multiple reflections and
transmissions at each interface are shown to build up to the eventual steady
state response of the pair, and during this process one can observe how the
growing exponential phenomenon may actually occur inside this bilayer.
