TRUE LEFT-HANDED METAMATERIALS

  Left-handed materials and negative refraction phenomena have been studied extensively in recent years due to their unique physical properties and   novel applications. Negative refraction of electromagnetic waves is the most interesting physical phenomena behind the left-handed metamaterial   structures. The reversal of Doppler shift and backward Cerenkov radiation are also unusual physical characteristics arising from left-handed materials.

  The electric and magnetic properties of materials are determined by two important material parameters, dielectric permittivity and magnetic   permeability. Together the permeability and the permittivity determine the response of the material to the electromagnetic radiation. Generally, ε and μ   are both positive in ordinary materials. While ε could be negative in some materials (for instance, ε posses negative values below the plasma frequency of   metals), no natural materials with negative μ are known. However, for certain structures, which are called left-handed materials (LHM), both the   effective permittivity, εeff and permeability, μeff possess negative values. In such materials the index of refraction, n, is less than zero, and therefore,   phase and group velocity of an electromagnetic (EM) wave can propagate in opposite directions such that the direction of propagation is reversed with   respect to the direction of energy flow [1].

  This phenomenon is called the negative index of refraction and was first theoretically proposed by Veselago in 1968, who also investigated various   interesting optical properties of the negative index structures [1].

  Negative effective permittivity in the microwave frequency range can be achieved by using periodic thin wire media. Dielectric permittivity takes   negative values and EM waves cannot propagate inside the medium below the plasma frequency [2]. Electric charge is responsible for a large electric   response in dielectric materials. Because of the lack of magnetic charge analogous to electric charge, it is more difficult to obtain a material with negative   magnetic permeability. Pendry et al. suggested that a periodic array of artificial structures called split ring resonators (SRRs) exhibit negative effective μ   for frequencies close to the magnetic resonance frequency [3].Smith et al. reported the experimental demonstration of left-handed materials by stacking   SRR and thin wire structures [4].    

  The split ring resonator has a large magnetic response against electromagnetic waves over certain frequencies. The magnetic resonance of SRR   structure does not allow EM waves to propagate through a periodic medium composed of SRRs, hence a stop band occurs. SRR structures have also   electric resonances at certain frequencies where EM waves cannot propagate inside the medium due to negative effective permittivity. Hence, a bandgap   in the transmission spectrum of periodic SRR medium may be due to the negative permittivity or the negative permeability or to the periodicity.

Fig. 1. Schematics of (a) a single split ring resonator (SRR) (b) a ring resonator with splits closed (CSRR) (c) Periodic CMM composed of SRRs on one side, wires on the other side of dielectric board.

The ambiguity can be removed by using a structure in which the splits in the ring resonators are closed (closed SRR). Closing the splits of ring resonator, will destroy the magnetic resonance but still keep the electric resonance. Therefore we expect to have a transmission band instead of a bandgap at frequencies of interest for    negative magnetic permeability. Figure 2 shows the measured transmission spectra of periodic SRRs (solid line) and CSRRs (dashed line) between 3-14    GHz. The first bandgap (3.55-4.05 GHz) of the SRR medium is not present in the CSRR medium, indicating μ < 0. The second bandgap (8.1-11.9    GHz)  is present for both the SRR medium and CSRR medium. This measurement clearly shows that the stop bands of an SRR medium can not be    automatically assumed as “negative μ” behaviour. Some of the observed gaps could also originate from the electrical response of the SRRs or from    Bragg gaps due to periodicity.

  Fig. 2. Measured transmission spectra of a periodic SRR medium (red) and periodic CSRR medium (blue)   between 3-14 GHz.

Fig. 3. Measured transmission spectra of wires (red) and closed CMM (blue) composed by arranging closed SRRs and wires periodically.

   SRRs, in addition to their resonant magnetic response at wm, exhibit a second resonant response at a higher frequency wo that has electric character. As a result, the SRRs contribute to the effective permittivity of the CMM, causing a downward shift on the plasma frequency determined solely from wire structures. To   demonstrate this effect, a CMM consisting of periodic alternating layers of CSRRs and wires is used. Figure 3 displays the measured transmission   spectra of wire only medium and CMM consisting of CSRR and wire layers. The wp of the wire-only structure around 8 GHz, is reduced down to 5.3   GHz within the closed CMM structure. As seen in Fig. 3, wp of the CMM is lower than that of the wire-only medium alone. It is crucial to determine   whether the shift in plasma cut-off frequency covers the magnetic resonance gap, which would render the CMM as a right-handed medium.

Fig. 4. Transmission spectra of SRRs (solid line), wires (dashed line) and open CMM (bold solid line)

  The CMM structure allows propagation of EM waves between 3.6 and 4.1 GHz, where both e and μ are negative. The CMM pass band exactly   coincides with the stop band of SRR. The transmission peak at 3.9 GHz is -1.2 dB, which is a significantly high value for a material made of metals.   Similarly, the simulations predict a transmission peak at 3.92 GHz of -1.5 dB. We stress that, a similar transmission band is not present for a CMM   composed of CSRRs and wires (Fig. 3). The electric response contribution of SRRs is also evident here: If the wp of the wire-only structure (dashed line   in Fig. 4(a)) were used to identify the e < 0 regime for the CMM, the transmission between 5.3 – 8 GHz would have occured in a regime with e < 0 and   μ > 0, which is not possible. However, as Fig. 3 suggests, the e > 0 regime of the combined electric response of SRRs and wires starts at 5.3 GHz.

      REFERENCES   

  1.       V. G. Veselago, Sov. Phys. Usp. 10, 504 (1968).

  2.       J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, J. Phys.: Condens. Matter 10, 4785 (1998).

  3.       J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).

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

  Related Group Publications:

  1. Koray Aydin, Kaan Guven, L. Zhang, M. Kafesaki, C. M. Soukoulis, and Ekmel Ozbay, “Experimental observation of true left-handed transmission   peak in metamaterials,” Optics Letters, vol. 26, p. 2625, 2004

  2. Koray Aydin, Kaan Guven, N. Katsarakis, C. M. Soukoulis, and Ekmel Ozbay, “Effect of disorder on magnetic resonance band gap of split-ring   resonator structures,” Optics Express, vol. 12, p. 5896, 2004.

   True Left-Handed Metamaterials

   Labyrint Based Left Handed Metamaterials

   Negative Refraction and Subwavelength Focusing Using Composite Metamaterials

   Millimeter Wave Scale Left-Handed Metamaterials

   Plasmonic Structures With Highly Directional Beaming Properties

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