Experimental Observations of a Left-Handed Material That Obeys Snell’s Law

We measure two-dimensional profiles of collimated microwave beams transmitted through composite wire and split-ring resonator prisms. Prior experiments suggest these structures have a negative index of refraction, though these claims have been questioned. Our 2D measurements demonstrate that transmission obeys Snell’s law with a negative index, confirming the refractive nature of this signal and refuting alternatives posed in the criticisms. In addition, we present preliminary evidence that a flat rectangular slab of this material can focus power from a point source.

Figure 1

A composite material with a negative index. (a) A photograph of the composite material, showing arrays of split-ring resonators and vertical wires. The individual strips are cut from sheets of printed circuit board using a computer controlled laser cutter. This cutting process often leaves a thin carbon film on the surface of the board; we have found that care is needed in removing this film in order to see LHM behavior. (b) Transmission spectra for a material with only wires (blue) and a material with only resonators (red). The low transmission regions correspond to negative $ϵ$ (shaded blue) or negative $\mu$ (shaded tan). Transmission is measured through a flat slab of material as a spatial average of the emerging beam. The high transmission at low frequency for the wires is not in agreement with the model proposed by Ref. 13; however, it is clear that we have $ϵ<0$ in a broad frequency range. Microwaves are sourced at $-10\mathrm{d}\mathrm{B}\mathrm{m}$ in these experiments. (c) Transmission through composite material with plate touching top of material (blue) and raised 2 mm (red). Transmission is high for low and high frequencies, where both $ϵ$ and $\mu$ are positive. The LHM passband (shaded tan) emerges from the feature at 10.5 GHz (shaded blue and tan) as the height of the top waveguide plate is raised via stepper motors. We believe this is due to a change in capacitance from the vertical wires to ground. From 1.5 to 3 mm above the top of the material, we observe LHM behavior. Even in this passband, losses are still on the order of 20–25 dB. Above 3 mm, we begin to see leakage above the material, which appears as broadband noise that overwhelms the LHM signal.

Figure 2

Results of a microwave scattering experiment to measure the angle of refraction from a prism with a single angled surface. The input antenna is at the bottom of the scans, and the propagation is towards the top of the figure. Absorbing foam is used in the lower half of the figures to both collimate microwaves and prevent leakage out of the sides of the prism. The measured indices were (a) $n=1.5$ for Teflon with a $\phi =18°$ face. (b) $n=1.3\pm 0.15$ for our composite material with a $\phi =26°$ face and the top plate lowered. (c) $n=-0.36\pm 0.13$ for our composite material with a $\phi =18°$ face and the top plate raised. (d) $n=-0.35\pm 0.08$ for our composite material with a $\phi =26°$ face and the top plate raised.

Figure 3

Experimental observations of LHM focusing. (a) A flat rectangular slab of LHM is placed in front of an antenna that serves as a point source. The radiation from the input antenna with no LHM present is shown in the bottom halves of (b), (c), and (d), to show the power incident on the material. (b) With the plate raised 2 mm, we see an elongated focus, removed from the surface of the material. The dark blue region at the edge of the material was not scanned. (c) Transmission through the material with the plate lowered. The focusing effect disappears, confirming that it is due to the negative index of the material. (d) Theoretical electric field profile expected from a lossy material with index $n=1.3$, but $6\mathrm{d}\mathrm{B}/\mathrm{c}\mathrm{m}$ attenuation. Path length differences through the material result in a collimated image similar to transmission through our material with the plate lowered. This lossy medium is one of the most common failure modes of our LHM.