Finite-difference time-domain analysis of the tunneling and growing exponential in a pair of ε-negative and µ-negative slabs

Pairing together planar material slabs with opposite signs for the real parts of their constitutive parameters has been shown to lead in the steady-state regime to interesting and unconventional properties that are not otherwise observable for single slabs, such as resonance, anomalous tunneling, transparency, and subwavelength imaging through the reconstruction of evanescent waves [A. Alù and N. Engheta, IEEE Trans. Antennas Prop. 51, 2558 (2003)]. The mechanics of the phenomenon, however, and in particular how the steady-state resonant response is reached, has not been explored. Here we analyze how a transient sinusoidal signal that starts at t = 0 interacts with such a complementary pair of finite size using a finite-difference time-domain (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. As with any resonant phenomena, the time response of this effect depends on the Q of the system, which is related to the geometrical and electrical parameters of the bilayer. Transparency to finite beams and reconstruction of the subwavelength details of an image are shown in the transient and steady-state response of the setup through one-dimensional and two-dimensional FDTD simulations.