Two-Dimensional Simulation of Left-Handed Metamaterial Flat Lens Using Remcon XFDTD

Summary Remcom’s XFDTD software was used to model the properties of a two-dimensional left-handed metamaterial (LHM) flat lens. The focusing capability and attenuation of the material were examined. The results showed strong agreement with both experimental results and theoretical predictions of focusing effects and focal length. Moreover, the inherent attenuation in the model corresponds well with the experimental results and implies that the code does a reasonably accurate job of modeling the actual metamaterial. Introduction Recently there has been considerable interest in left-handed metamaterials (LHM), which are also known as double negative metamaterials or negative index materials. These materials are engineered so that their effective electrical permittivity e and magnetic permeability μ values are negative over a specific frequency range. In 1968, Veselago (ref. 1) postulated that a flat piece of material with simultaneous negative values of e and μ would alter the phase and group velocities of electromagnetic radiation so that they would propagate in opposite directions and also invert Snell’s law of refraction, the Doppler effect, and Cherenkov radiation. Pendry et al. (refs. 2 and 3) first showed that a three-dimensional array of intersecting thin wires could be used to create negative values of e and that a periodic array of copper split-ring resonators could produce an effective negative μ. In 2000 Smith et al. were the first to successfully combine the two arrays and produce a LHM which had negative values of e and μ for a band of frequencies in the GHz range (ref. 4). Wilson and Schwartz experimentally tested a flat lens constructed of LHM (ref. 5). They created a 20- by 20- by 3-unit cell array comprising copper split-ring resonators and thin copper wires etched onto a fiberglass substrate. The entire block measured 100 by 100 by 10 mm, and a partial view is shown in figure 1. The LHM block was placed in a parallel-plate waveguide as shown in the photograph of its experimental setup (fig. 2). On one side of the LHM, a coaxial cable was attached to the top plate of the waveguide and the center conductor of the cable was fed through to the bottom plate. Cylindrical waves with a vertically directed electric field radiated from this source point and passed through the LHM. In order to detect the microwave power distribution after the waves had passed through the LHM, a detecting probe was attached to a computer-controlled x-y positioning stage and was scanned over a distance of 100 mm in the x-direction (toward and away from the LHM) and over a distance of 60 mm in the y-direction (from edge to edge in the waveguide). A top view of the experimental setup is shown schematically in figure 3. The LHM was placed at nine locations away from the source so that the front focal length (designated as ffl in fig. 3) ranged from 30 to 70 mm. The signal was swept from 9.50 to 12.50 GHz in 0.10-GHz intervals at each location. The back focal length (bfl), which for this experiment is defined as the distance from the back edge of the block to the power maximum along the x-axis (see fig. 3), was measured for each frequency. The results of the experiment at 10.30 GHz are shown in figure 4. A focusing effect can be seen around the