LABYRINTH BASED LEFT HANDED METAMATERIALS

_The electromagnetic properties of materials are described by the use of two parameters: permittivity and permeability. The permittivities of known   naturally occurring materials can attain positive and negative values. On the other hand, the permeabilities of known naturally occurring materials are   known to be positive. However, there is no fundamental reason implied by the laws of electromagnetism that may restrict the values of permittivities and   permeabilities to positive values [1]. As a matter of fact, it has been shown that when a medium attains negative permittivity and permeability,   simultaneously, it may exhibit certain very exciting properties such as negative refraction [2-4], left-handed transmission, reverse Doppler shift [1, 5], and   subwavelength focusing [6-9]. While nature does not provide us with a material with simultaneous negative permittivity and permeability, this obstacle has   been overcome by the use of metamaterials. By use of the metamaterials, which are artificially created structures, we may now engineer the ""properties _of   a medium so that the medium exhibits the desired permittivities and permeabilities.

_Split ring resonator (SRR) is a commonly used structure in order to obtain negative permeability [11-15]. While SRR structure provides negative   permeability and can be used to obtain negative refraction, it has several disadvantages. One of these disadvantages is the bianisotropy[16-18]. Second,   it has been shown that the magnetic resonance of the SRR structure can be excited via electric fields [19]. These two disadvantages make it difficult to   obtain isotropic, homogeneous two or three dimensional negative refraction media by using SRRs for negative permeability. We proposed the labyrinth   structure in order to overcome these specific disadvantages of the SRR structure. The labyrinth structure consists of four rings instead of two. The unit   cell of the fabricated structure is shown in Fig. 1. The structures are fabricated by using the standard printed circuit board manufacturing methods.

Figure 1

a) Schematics of the labyrinth structure. r1=1.35 mm, r2=1.8 mm, r3=2.25 mm, r4=2.7 mm, g=0.15 mm, w=0.3 mm, and d=0.15 mm.

b) The unit cell of the actual, fabricated structure and the coordinate system that we used throughout the paper.

_The transmission properties of a single labyrinth structure were characterized by using a HP 8510C vector network analyzer and two monopole   antennas as the receiver and transmitter antennas. The measured and calculated transmission spectrum of plane EM waves through a single layer of a   labyrinth structure is shown in Fig. 2(a). The directions of the electric field, magnetic field, and wave vector of the incident EM waves are shown in the   insets of Figs. 2(a) and (b). First of all, the transmission spectrum of a single labyrinth structure exhibits a resonance around 6.2 GHz with a transmission   of -25 dB (Fig. 2(a)). Second, the closed labyrinth structure does not exhibit this resonance in the transmission spectrum. As a result, the transmission   spectrum shown in Fig. 2(a) clearly demonstrates that the labyrinth structure exhibits a magnetic resonance around 6.2 GHz. Note that for the case of   incidence configuration shown in Fig. 2(b) the magnetic resonance of the SRR structure can be excited by electric fields. The measurement and   calculation results for a single labyrinth structure are shown in Fig. 2(b) for the incidence configuration when the magnetic resonance of an SRR structure   can be excited by electric coupling. The transmission spectrum does not exhibit any resonant feature for this incidence configuration. Hence, these results   show that the magnetic resonance of the labyrinth structure cannot be excited by electric coupling.

Figure 2

a) Measured transmission through a single labyrinth structure (A), a single closed labyrinth structure (B). Calculated transmission through a single labyrinth structure (C), a single closed labyrinth structure (D).

b) Measured (E) and calculated (F) transmission through a single labyrinth structure.

_The left-handed composite metamaterial (CMM) structure that we used in our study was composed of a one-dimensional periodic arrangement of   labyrinth structures and wire structures. The transmission spectrum of the wire only medium is shown in Fig. 4(a). The wire medium has a plasma   frequency of approximately 10.45 GHz. The transmission spectrum for 5 and 10 layers of CMM unit cells along the propagation direction is shown in   Fig. 4(b). Figure 4(b) shows that the transmission spectrum of the CMM medium exhibits a transmission band between 5.9 GHz and 6.55 GHz. We   measured the transmission spectrum of the closed CMM medium in order to check whether the transmission band observed between 5.9 GHz and 6.55   GHz is left-handed. The transmission spectrum of the closed CMM medium is shown in Fig. 4(c). First of all, the transmission spectrum of the closed   CMM medium did not exhibit a transmission band between 5.9 GHz and 6.55 GHz. These results, therefore, show that the transmission band of the   CMM medium is left-handed.

Figure 4

  a) The transmission spectrum of electromagnetic waves through the wire medium.

  b) The measured transmission spectrum of electromagnetic waves through the CMM medium.

  c) The measured transmission spectrum of electromagnetic wave through the closed CMM medium.

_Pendry predicted that a slab of ε=-1, µ=-1 may recover the evanescent components of the field emitted from a source [6]. In addition, due to   negative _refraction, such a medium focuses the propagating components of the source field. As a result, it may be possible to focus all of the Fourier   components _of the field emitted from a source. We checked the possibility of sub-wavelength focusing by use of the two dimensional labyrinth based   left-handed _medium. The two dimensional structure that was a periodic arrangement of wires and labyrinth structures in a two dimensional square lattice.   The lattice _constant was 8 mm along both of the lattice vectors of the square lattice. The unit cell of the two dimensional structure is shown in Fig. 5(a).   The width _of the wire stripes was 2.5 mm. The width of the structure was around one wavelength. The height of the structure was 20 layers long. The   transmission _spectrum of the structure is shown in Fig. 5(b). There is a left-handed transmission band between 6 GHz and 6.4 GHz.

Figure 5

  a) The unit cell of the two-dimensional labyrinth based left-handed metamaterial.

  b) The transmission spectrum of two dimensional left-handed metamaterial medium.

_We placed the source monopole antenna in front of the surface of the labyrinth based metamaterial. The axis of the source and receiver antennas   were _arranged parallel to the z-axis. We measured the electric field intensities on the output side of the left-handed metamaterial in steps of 2.5 mm. The   measurements were carried out for two different source distances to the input surface, 10 mm and 20 mm. The measurement results for source distances   of 20 mm and 10 mm are shown in Figs. 6(a) and (b) for 6.3 GHz, respectively. The images of the source fields are clearly observed in Figs. 6(a) and   (b). The maximum field intensity along the y axes was observed at 10 mm when the source was 20 mm away from the input surface, in which it was 17.5   mm when the source was 10 mm away. The half widths of the intensity profiles along the y axis for both cases were 19 mm. On the other hand, the half   width of the intensity profile on the output side of the metamaterial along the x axes was 12 mm, ≈ λ/4, when the source distance was 10 mm. The   measured half width of the intensity profile in free space, without the metamaterial in between, was 40 mm, ≈ λ. Without the metamaterial, even at such a   close distance, the source field could not be resolved with a resolution below the wavelength. However, it was possible to the resolve the source field   with a resolution below the wavelength when the metamaterial was inserted in between the source and receiver antennas.

Figure 6

_The measured electric field intensities on the output side of the metamaterial when the source was 2 cm away (a) and 1 cm away (b) from the input _surface of the metamaterial.The three dimensional metamaterial that we used in this present study is shown in Fig. 7(a) While the structure is an extension _of the two dimensional   labyrinth based metamaterial to three dimensions, the fabrication of the structure is itself quite complicated. Particular attention _was paid during the design   process in order to avoid intersecting wires. Such an intersection would evidently yield to a cut-wire medium. If not avoided, _the cut-wire medium would   cause us to loose the plasma-like behavior of a continuous wire medium. The results of the transmission measurements for _TE and TM polarized   electromagnetic waves, shown in Fig. 7(b), show the evidence of a left-handed transmission band between x-y GHz. The _transmission of TE waves is   weak when compared to TM polarized waves. This difference in the transmission properties of TE-TM polarized waves _indicates the presence of strong   anisotropy. Such anisotropy is expected as the unit cell of the structure lacks the electrical symmetries in certain _directions. Nonetheless, there is a   left-handed transmission band for both TE and TM polarized waves that overlap in the frequency range.

Figure 7

  a) The photographs of the three dimensional structure.

  b) The measured transmission spectrum of TE and TM polarized waves through the labyrinth based three dimensional left-handed structure.

_In order to study the refraction properties of the 3D structure at the frequencies corresponding to the left-handed transmission band, we used   electromagnetic waves incident on the structure at various angles. The setup that we used consists of transmitting horn antennas and receiving monopole   antennas. The horn antenna was tilted such that the angles of incidence with respect to the normal vector of the structure were 15 and 30 degrees. The   transmitted waves on the other side of the surface were measured by using the monopole antennas over a rectangular mesh. The results of our   measurements are shown in Figs. 8 (a) and (b) for incidence angles of 15 and 30 degrees, respectively. The output surface was parallel to the x axis. In   addition, the waves were incident on the negative side with respect to the surface normal. Electromagnetic waves leave the output surface from the side   of the surface normal that they were incident on. Hence, electromagnetic waves that are negatively refracted by the 3D labyrinth based metamaterial.

Figure 8

  a) The measured electric field intensities for the incidence angle of 15 degrees.

  b) The measured electric field intensities for the incidence angle of 30 degrees.

_Since our 3D structure exhibited negative refraction, we next checked the focusing properties of the structure. We placed a monopole antenna in front   of the input surface of the structure and measured the transmitted signal on the output side over a rectangular mesh by using a receiving monopole   antenna. The results are shown in Figs. 9(a) and (b) for source distances of 15 mm and 5 mm to the input surface, respectively. First of all, one can   clearly observe the images of the source field at the output side. In addition, the image of the source appears at a closer distance to the output surface for   the source distance of 15 mm when compared to the source distance of 5 mm. This result is expected for a metamaterial medium with simultaneously _negative permittivity and permeability.

Figure 9

  a) The measured electric field intensities for a source distance of 15 mm.

  b) The measured electric field intensities for a source distance of 5 mm.

_In conclusion, we studied the properties of one, two, and three dimensional labyrinth based left-handed metamaterials. Our studies revealed that the   labyrinth based medium overcomes the bianisotropy issue inherent to the split ring resonator based mediums. We were able to achieve sub-wavelength   focusing by use of a two dimensional labyrinth based left-handed medium. Moreover, negative refraction of electromagnetic waves was demonstrated by   the use of a 3D labyrinth based structure. In addition, we demonstrated the focusing of electromagnetic waves by use of a three dimensional flat lens. To   our knowledge, this is the first experimental demonstration of a three dimensional left-handed medium that is based on resonant structures.

   References

  [1] V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).

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

  [3] C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, Phys. Rev. Lett. 90, 107401 (2003).

  [4] A. A. Houck, J. B. Brock, and I. L. Chuang, Phys. Rev. Lett. 90,137401 (2003).

  [5] A.M. Belyantsev and A. B. Kozyrev, Tech. Phys. 47, 1477 (2002).

  [6] J.B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).

  [7] Koray Aydin, Irfan Bulu, Ekmel Ozbay, Optics Express 13, 7645-7652 (2005).

  [8] Irfan Bulu, Humeyra Caglayan, Ekmel Ozbay, Opt. Lett. 31, 814-816 (2006).

  [9] A. Grbic and G. V. Eleftheriades, Appl. Phys. Lett. 82, 1815 (2003).

  [10] Irfan Bulu, Humeyra Caglayan, Ekmel Ozbay, Optics Express 13,  10238 (2005).

  [11] J. B. Pendry, A. J. Holden, D. J. Robins, and W. J. Stewart, IEEE Trans. Microwave Theory Technol. 47, 2075 (1999).

  [12] P. Markos and C. M. Soukoulis, Phys. Rev. B 65, 033401 (2001).

  [13] Mehmet Bayindir, K. Aydin, E. Ozbay, P. Marko, and C. M. Soukoulis, Appl. Phys. Lett. 81, 120 (2002).

  [14] Philippe Gay-Balmaz and Olivier J. F. Martin, J. Appl. Phys. 92, 2929 (2002).

  [15] Philippe Gay-Balmaz and Olivier J. F. Martin, Appl. Phys. Lett. 81, 939 (2002).

  [16] Xudong Chen, Bae-Ian Wu, Jin Au Kong, and Tomasz M. Grzegorczyk, Phys. Rev. E 71, 046610 (2005).

  [17] R. Marques, F. Mesa, J. Martel, and F. Medina, IEEE Trans. Antennas Propag. 51, 2572 (2003)..

  [18] R. Marques, F. Medina, and R. Rafii-El-Idrissi, Phys. Rev. B  65, 144440 (2002).

  [19] N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, Appl. Phys. Lett. 84, 2943 (2004).

   True Left-Handed Metamaterials

   Left-Handed Transmission, Negative Refraction and Sub-Wavelength Resolution by Labyrinth-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

© Copyright - com.web.tr. This page is best viewed with IE v.5.0 or higher, at minimum 1024x768 resolution.