PLANAR

LOADED-TRANSMISSION-LINE

NEGATIVE-REFRACTIVE-INDEX

METAMATERIALS

Experimental Verification of Focusing

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Recently there has been a proliferation of emerging new man-made materials with superior properties that cannot be found in nature. For this reason, these materials are referred to as "metamaterials" (the prefix "meta" means "beyond" in Greek). In the late 1960s, V.G. Veselago proposed that materials with simultaneously negative permittivity and permeability are physically permissible and possess a negative index of refraction [1]. Veselago termed these Left-Handed Media (LHM), because the vectors E, H, and k would form a left-handed triplet instead of a right-handed triplet, as is the case in conventional, Right-Handed Media (RHM). His conceptual exploration of this phenomenon revealed that, through negative refraction, planar slabs of such media would cause light or electromagnetic radiation to focus in on itself, as depicted in Figure 1.

Figure 1: Internal and external focusing using a LHM slab of thickness d.

Materials with such exotic properties have the potential to radically change the world of wireless and optical communications, radars and surveillance. Their unique characteristics could enable unprecedented levels of RF/microwave device and antenna miniaturization, antenna beam steering, and RF/optical signal switching and routing. In addition, the technology may enable the creation of miniaturized RF lenses with a unique sub-wavelength resolution capability [3], as well as ultra-fast signalling between two points. At optical frequencies, metamaterial super-resolving lenses could enable printing microelectronic devices at the nanoscale with light.

Recently, novel electromagnetic metamaterials have successfully demonstrated negative refraction and suggest an approach whereby the permittivity and permeability functions are made to be simultaneously negative using an array of resonant cells consisting of thin wire strips and Split-Ring Resonators (SRRs), respectively [2], [4].

Our research has yielded a new class of LHM metamaterials that take a step further than the original wire/SSR concept. These new LHM metamaterials consist of connected unit cells that do not explicitly rely on resonances to synthesize the required negative material parameters. The unit cells are equipped with (possibly tunable) lumped elements (inductors and capacitors), which permit them to be compact and therefore scalable from the MHz to the tens of GHz range. Moreover, these new metamaterials offer large operating bandwidths, and are completely planar thus inherently supporting 2-D wave propagation making them well suited for RF/microwave device and circuit applications [7]-[12].

A 30mm X 55mm "left-handed" focusing metamaterial prototype has been implemented and tested around 2GHz [7]. This approach yielded the first experimental demonstration of focusing in a "left-handed" negative-refractive-index metamaterial: An incident cylindrical wave was confined over an electrically small area, a phenomenon suggestive of near-field focusing. [6], [7], [8]. More recently our L-C loaded transmission-line periodic metamaterials were shown to GROW evanescent waves which is essential for sub-diffraction focusing in a homogeneous medium [9].

Based on the same concept of devising left-handed metamaterials, a backward radiating planar antenna was implemented and tested at 15 GHz [10], [11]. This is perhaps the first experimental demonstration of backward wave radiation from a left-handed medium, an effect analogous to reversed Cherenkov radiation originally predicted by Veselago [1]. This antenna radiates the fundamental spatial harmonic.

In the figures to follow, we provide a sample of results reported in [7]

Figure 2: Microwave circuit simulations showing a plane wave illuminating a RHM/LHM interface at an incident angle of 29°

The refractive indices of the RHM and LHM are +1.2 and -2.4, respectively. Refraction is observed at -14°, in accordance with Snell?s Law. The axes are labeled according to cell number, and the right vertical scale designates radians.

Figure 3: Microwave circuit simulations showing a point source illuminating a RHM/LHM interface. The refractive indices of the RHM and LHM are +1.2 and -2.4, respectively. Focusing is observed in both phase and magnitude; the axes are labelled according to cell number.

Figure 4: Focusing device: LHM prototype interfaced with a parallel-plate waveguide (60mm X 95mm); the inset magnifies the surface of the LHM unit cell..

Figure 5: Correspondence of (a) full-wave field simulation results and (b) experimental results at 1.5GHz (normalized to the maximum respective focal amplitudes in each case).

Figure 6: Experimentally detected vertical E-field distribution over a 30mm´55mm LHM as the frequency is varied from 1 to 2GHz; focusing is apparent over a band extending from approximately 1.3 to 1.9GHz, over which the index of refraction is determined to vary from -5.5 to -1.2, with a well-confined focal spot near 1.5GHz.

REFERENCES
[1] V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of e and m," Sov. Phys. Usp, vol. 10, no. 4, pp. 509-514, Jan.-Feb.1968.

[2] J. B. Pendry, A. J. Holden, D. J. Robins, W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. on Microwave Theory and Tech., vol. 47, no. 11, pp. 2075-2084, Nov. 1999.

[3] J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett., 85, 3966-3969 (2000).

[4] D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett., vol. 84, no. 18, pp. 4184-4187, May 2000.

[5] R. A. Shelby, D. R. Smith, S. Schultz, "Experimental verification of a negative index of refraction," Science, vol. 292, 6 April 2001, pp. 77-79.

[6] A.K. Iyer and G.V. Eleftheriades, “Negative refractive index metamaterials supporting 2-D waves.” IEEE International Microwave Symposium Digest, pp. 1067-1070, June 2-7, 2002, Seattle, WA. (2nd place in MTT-S Best Student Paper Contest) (reprint).

[7] G.V. Eleftheriades, A.K. Iyer and P.C. Kremer, “Planar negative refractive index media using periodically L-C loaded transmission lines,” IEEE Trans. on Microwave Theory and Techniques, vol. 50, no. 12, pp. 2702-2712, Dec. 2002 (reprint, 3MB), (1MB version).

[8] A.K. Iyer, P.C. Kremer and G.V. Eleftheriades, “Experimental and theoretical verification of focusing in a large, periodically loaded transmission line negative refractive index metamaterial.” Optics Express 11, pp. 696-708, April 07, 2003. http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-7-696 (invited).

[9] A. Grbic and G.V. Eleftheriades, “Growing Evanescent Waves in Negative-Refractive-Index Transmission-Line Media,” Applied Physics Letters, vol. 82, no. 12, pp. 1815-1817, March 24, 2003.(reprint)

[10] A. Grbic and G.V. Eleftheriades, "A backward-wave antenna based on negative refractive index L-C networks." Proc. of the IEEE Intl. Symposium on Antennas and Propagation, Vol. IV, pp. 340-343, June 16-21, 2002, San Antonio, TX

[11] A. Grbic and G.V. Eleftheriades, “Experimental verificiation of backward-wave radiation from a negative refractive index metamaterial.” Journal of Applied Physics, vol. 92, no. 10, pp. 5930-5935, Nov. 2002. (reprint)

[12] G.V. Eleftheriades, "Planar Negative Refractive Index Metamaterials Based on Periodically L-C Loaded Transmission Lines." Workshop of Quantum Optics, Kavli Inst. of Theoretical Physics, University of Santa Barbara, July 2002 (invited).

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