FDTD analysis of the tunneling and growing exponential in a pair of   epsilon-negative and mu-negative slabs
  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. 
Andrea Alu, Nader Engheta, Richard W. Ziolkowski