A LEFT-HANDED METAMATERIAL OPERATING AT 100 GHz

  The idea of a LH (left-handed) material, first described by Veselago [1], was recently investigated experimentally [2, 3]. Such materials have large   number of potential applications [4, 5]. First experimental realization of LH materials was achieved by separately constructing ε < 0 wire arrays [6], and   μ < 0 SRR (split ring resonator) arrays [7], and then by combining them together forming a composite metamaterial (CMM) [2, 3, 8]. The use of a _stack   of planar substrates has been common to all CMMs reported up to date. The periodicity in the two directions is achieved by printing 2D-arrays _of   metallic patterns on such planar substrates, whereas the periodicity in the third direction is achieved by stacking a large number of these patterned _planar   substrates. Our work concentrates on the design, fabrication, and characterization of the worlds smallest CMM reported to date, which has an _operating   frequency of 100 GHz. This is a first step towards infrared and optical frequencies and corresponds to a 10-fold improvement of the _previous highest   operating frequency LH metamaterial.

  Limitations in the practical realization of CMM eliminate the possibility of a mere geometrical scaling of previous designs. In particular, the thickness of   the substrate layer is a constraint. We used standard 22mm x 22mm x 150μm layers of Corning glass as the substrate. This thickness ensures structural   rigidity and the air gap between the layers present in the microwave structures is eliminated. The challenging task is to design the wire-only medium   subject to the predetermined periodicity by SRR geometry and substrate thickness, with a plasma frequency ωp, high above the magnetic resonance f   frequency of SRRs. We achieve this requirement by letting the unit cell to accommodate multiple parallel wires. This gives a -fold increase in the plasma   frequency, where n is the number of wires in each unit cell.

  Figure 1 shows one unit cell of the wire micropattern (Fig. 1(a)), and the SRR micropattern (Fig. 1(b)). In each unit cell there are two concentric split   rings, and six continuous wires (two layers of three wires each). The exact dimensions of the components are as follows: Inner ring inner radius: rii =    43μm, inner ring outer radius: rio = 67.2μm, outer ring inner radius: roi = 80.7μm, outer ring outer radius: roo = 107.5μm, split ring gap: d =    7.2μm, wire _width: w = 26.9μm, wire separation: dw = 53.7μm. In addition, the unit cell dimensions in x- and y-directions are                                  ax = ay = 262.7 μ _ m.

  The metamaterial pattern is printed on glass substrates by employing UV-photolithography followed by microfabrication.  The substrate is 22mm x   22mm x 150μm pieces of Corning glass, while the metal coating is 100Å Ti / 4500 Å Au. Split-ring resonators, closed-ring resonators (CRR, i.e. SRRs   with no gaps) and wire type samples were fabricated separately in this manner, and then stacked for measurements. For SRR-only, CRR-only and   wire-only stacks, plain glass substrates were used as spacers, to keep the unit cell size constant. The final CMM was composed of 100 layers, having a   15 mm (100x150μm) width (z-direction), 20 mm height (y-direction) and 2.6 mm length (x-direction), which is the propagation direction. Figure 1(c)   shows the schematic geometry of the CMM, while Fig. 2 is a photomicrograph of one SRR-layer and one wire-layer stacked on top of each other. The   patterns were aligned to the glass substrate edge during photolithography, hence the alignment within the resulting metamaterial structure is limited by the   edge uniformity of the glass substrates.

Fig. 1: (a) Wire geometry employed for the mm-wave CMM. (b) SRR geometry employed for the mm-wave (CMM). (c) Schematic geometry of the CMM, consisting of periodically stacked (along z-direction) two layers of wire-patterned substrates and one layer of SRR-patterned substrate.

Fig. 2: Photomicrograph showing the mm-wave CMM sample. No special alignment procedure using the microscope was performed for this picture. The two patterns were aligned by aligning the edges of the glass substrates.

  The samples are prepared for measurement by stacking the glass layers with the patterns (SRRs, CRRs, wires) inside a Plexiglas cube. SRR-only,   CRR-only and wire-only stacks were also prepared. In the construction of these samples, plain glass substrates were used as spacers, to keep the unit   cell size in the z-direction, to be the same as that of the CMM.

   Figure 3 shows the transmission spectra of CMM structures incorporating SRRs, and CRRs, respectively, measured by a network analyzer. The   CMM structure exhibits a pass band between 96 GHz to 107 GHz with a -25 dB maximum at 101 GHz. Note that this band matches the µ < 0 stop   band of SRRs. This is contrasted by the CMM incorporating CRR layers which remains opaque throughout the frequency range. The left-handed nature   of the peak was also proved by theoretical simulations. As a result, we conclude that the pass band of CMM indicates truly a left-handed behaviour.

 Fig. 3:  Transmission spectra of CMM (solid), Closed-CMM (CRR+wire) (dashed) and SRR-only structures (dotted). The SRR-only spectrum is shown to compare left-handed transmission band and negative permittivity gap.

  References

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  2.        D.R. Smith, W.J. Padilla, D.C. Vier, S.C. Nemat-Nasser, and S.Schultz, Phys. Rev. Lett. 84, 4184 (2000).

  3.        R.A. Shelby, D.R. Smith, S.C. Nemat-Nasser, and S.Schultz, Apl. Phys. Lett. 78, 480 (2001).

  4.        N. Engheta, R.W. Ziolkowski, IEEE Tran. Microw. Theory Tech. 53, 1535 (2005).

  5.        J.B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).

  6.        J.B. Pendry, A.J. Holden, W.J. Stewart, and I. Youngs, Phys. Rev. Lett. 76, 4773 (1996).

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  8.        K. Aydin, K. Guven, M. Kafesaki, L. Zhang, C. M. Soukoulis, and E. Ozbay, Opt. Lett. 29, 2623 (2004).

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