Abstract

In this present work, we propose and demonstrate a resonant structure that solves two major problems related to the split-ring resonator structure. One of the problems related to the split-ring resonator structure is the bianisotropy, and the other problem is the electric coupling to the magnetic resonance of the split-ring resonator structure. These two problems introduce difficulties in obtaining isotropic left-handed metamaterial mediums. The resonant structure that we propose here solves both of these problems. We further show that in addition to the magnetic resonance, when combined with a suitable wire medium, the structure that we propose exhibits left-handed transmission band. We believe that the structure we proposed may have important consequences in the design of isotropic negative index metamaterial mediums.

© 2005 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  38. N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Electric coupling to the magnetic resonance of split ring resonators," Appl. Phys. Lett. 84, 2943 (2004)
    [CrossRef]
  39. R. Marques, F. Medina, and R. Rafii-El-Idrissi, Comment on "Electromagnetic resonances in individual and coupled split-ring resonators" [J. Appl. Phys. 92, 2929 (2002)] J. Appl. Phys. 94, 2770 (2003)
    [CrossRef]
  40. Koray Aydin, Kaan Guven, Maria Kafesaki, Lei Zhang, Costas M. Soukoulis, and Ekmel Ozbay, "Experimental observation of true left-handed transmission peaks in metamaterials," Opt. Lett. 29, 2623 (2004)
    [CrossRef] [PubMed]

Appl. Phys. Lett.

Mehmet Bayindir, K. Aydin, E. Ozbay, P. Marko, and C. M. Soukoulis, "Transmission properties of composite metamaterials in free space," Appl. Phys. Lett. 81, 120 (2002)
[CrossRef]

Philippe Gay-Balmaz and Olivier J. F. Martin, "Efficient isotropic magnetic resonators," Appl. Phys. Lett. 81, 939 (2002)
[CrossRef]

D. R. Smith, D. C. Vier, N. Kroll, and S. Schultz, "Direct calculation of permeability and permittivity for a left-handed metamaterial," Appl. Phys. Lett. 77, 2246 (2000).
[CrossRef]

Koray Aydin, Kaan Guven, Costas M. Soukoulis, and Ekmel Ozbay, "Observation of negative refraction and negative phase velocity in left-handed metamaterials," Appl. Phys. Lett. 86, 124102 (2005).
[CrossRef]

N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Electric coupling to the magnetic resonance of split ring resonators," Appl. Phys. Lett. 84, 2943 (2004)
[CrossRef]

Electromagnetics

B. Sauviac, C.R. Simovski, S.A. Tretyakov, "Double split-ring resonators: Analytical modeling and numerical simulations," Electromagnetics 24, 317 (2004).
[CrossRef]

IEEE Trans. Antennas Propag.

R. Marques, F. Mesa, J. Martel, and F. Medina, "Comparative analysis of edge- and broadside- coupled split ring resonators for metamaterial design - theory and experiments," IEEE Trans. Antennas Propag. 51, 2572 (2003).
[CrossRef]

IEEE Trans. Microw. Theory Tech.

J.D. Baena, J. Bonache, F. Martin, R. M. Sillero, F. Falcone, T. Lopetegi, M.A.G. Laso, J. Garcia-Garcia, I. Gil, M. F. Portillo, M. Sorolla, "Equivalent-circuit models for split-ring resonators and complementary split-ring resonators coupled to planar transmission lines," IEEE Trans. Microw. Theory Tech. 53, 1451 (2005).
[CrossRef]

IEEE Trans. Microwave Theory Technol.

J. B. Pendry, A. J. Holden, D. J. Robins, andW. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Technol. 47, 2075 (1999).
[CrossRef]

J. Appl. Phys.

Philippe Gay-Balmaz and Olivier J. F. Martin, "Electromagnetic resonances in individual and coupled split-ring resonators," J. Appl. Phys. 92, 2929 (2002)
[CrossRef]

Yi-Jang Hsu, Yen-Chun Huang, Jiann-Shing Lih, and Jyh-Long Chern, "Electromagnetic resonance in deformed split ring resonators of left-handed meta-materials," J. Appl. Phys. 96, 1979 (2004)
[CrossRef]

M. Shamonin, E. Shamonina, V. Kalinin, and L. Solymar, "Properties of a metamaterial element: Analytical solutions and numerical simulations for a singly split double ring," J. Appl. Phys. 95, 3778 (2004)
[CrossRef]

R. Marques, F. Medina, and R. Rafii-El-Idrissi, Comment on "Electromagnetic resonances in individual and coupled split-ring resonators" [J. Appl. Phys. 92, 2929 (2002)] J. Appl. Phys. 94, 2770 (2003)
[CrossRef]

L. Ran, J. Huangfu, H. Chen, X. Zhang, K. Chen, T. M. Grzegorczyk, and J. A. Kong, "Beam shifting experiment for the characterization of left-handed properties," J. Appl. Phys. 95, 2238 (2004).
[CrossRef]

Jpn. J. Appl. Phys.

Yen-Chun Huang, Yi-Jang Hsu, Jiann-Shing Lih, and Jyh-Long Chern, "Transmission Characteristics of Deformed Split-Ring Resonators ," Jpn. J. Appl. Phys., Part 2 43, L190 (2004)
[CrossRef]

Microwave Opt. Technol. Lett.

S.I. Maslovski, S.A. Tretyakov, P.A. Belov, "Wire media with negative effective permittivity: A quasi-static model," Microwave Opt. Technol. Lett. 35, 47 (2002).
[CrossRef]

Opt. Lett.

Phys. Rev B

C. Poulton, S. Guenneau, A. B. Movchan, "Noncommuting limits and effective properties for oblique propagation of electromagnetic waves through an array of aligned fibres," Phys. Rev B 69, 195112, (2004).
[CrossRef]

Phys. Rev. B

P. Markos and C. M. Soukoulis, "Transmission studies of left-handed materials," Phys. Rev. B 65, 033401 (2001)
[CrossRef]

A. B. Movchan and S. Guenneau, "Split-ring resonators and localized modes," Phys. Rev. B 70, 125116 (2004)
[CrossRef]

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B 65, 195104 (2002)
[CrossRef]

R. Marques, F. Medina, and R. Rafii-El-Idrissi, "Role of bianisotropy in negative permeability and left-handed metamaterials," Phys. Rev. B 65, 144440 (2002).
[CrossRef]

K. Guven, K. Aydin, K. B. Alici, C. M. Soukoulis, and E. Ozbay, "Spectral negative refraction and focusing analysis of a two-dimensional left-handed photonic crystal lens," Phys. Rev. B 70, 205125 (2004).
[CrossRef]

Th. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials," Phys. Rev. B 71, 245105 (2005)
[CrossRef]

Phys. Rev. E

T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, "Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 68, 065602 (2003)
[CrossRef]

Z. G. Dong, S. N. Zhu, H. Liu, J. Zhu, and W. Cao, "Numerical simulations of negative-index refraction in wedge-shaped metamaterials ," Phys. Rev. E 72, 016607 (2005)
[CrossRef]

Xudong Chen, Tomasz M. Grzegorczyk, Bae-Ian Wu, Joe Pacheco, Jr., and Jin Au Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Phys. Rev. E 70, 016608 (2004)
[CrossRef]

Xudong Chen, Bae-Ian Wu, Jin Au Kong, and Tomasz M. Grzegorczyk, "Retrieval of the effective constitutive parameters of bianisotropic metamaterials," Phys. Rev. E 71, 046610 (2005)
[CrossRef]

C. R. Simovski and B. Sauviac, "Role of wave interaction of wires and split-ring resonators for the losses in a left-handed composite," Phys. Rev. E 70, 046607 (2004)
[CrossRef]

Phys. Rev. Lett.

T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Effective Medium Theory of Left-Handed Materials," Phys. Rev. Lett. 93, 107402 (2004)
[CrossRef] [PubMed]

R. Marques, J. Martel, F. Mesa, and F. Medina, "Left-Handed-Media Simulation and Transmission of EMWaves in Subwavelength Split-Ring-Resonator-Loaded Metallic Waveguides," Phys. Rev. Lett. 89, 183901 (2002)
[CrossRef] [PubMed]

D. F. Sievenpiper, M. E. Sickmiller, and E. Yablonovitch, "3D Wire Mesh Photonic Crystals," Phys. Rev. Lett. 76, 2480 (1996).
[CrossRef] [PubMed]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely Low Frequency Plasmons in Metallic Mesostructures," Phys. Rev. Lett. 76, 4773 (1996).
[CrossRef] [PubMed]

D. R. Smith, Willie J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite Medium with Simultaneously Negative Permeability and Permittivity," Phys. Rev. Lett. 84, 4184 (2000)
[CrossRef] [PubMed]

Andrew A. Houck, Jeffrey B. Brock, and Isaac L. Chuang, "Experimental Observations of a Left-Handed Material That Obeys Snell's Law," Phys. Rev. Lett. 90, 137401 (2003)
[CrossRef] [PubMed]

A. A. Houck, J. B. Brock, and I. L. Chuang, "Experimental Observations of a Left-Handed Material That Obeys Snell's Law," Phys. Rev. Lett. 90, 137401 (2003)
[CrossRef] [PubMed]

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental Verification and Simulation of Negative Index of Refraction Using Snell's Law," Phys. Rev. Lett. 90, 107401 (2003).
[CrossRef] [PubMed]

Science

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77 (2001).
[CrossRef] [PubMed]

Sov. Phys. Usp.

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of permittivity and permeability," Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Waves In Rand. Med.

D. Felbacq, G. Bouchitte, "Homogenization of a set of parallel fibres," Waves In Rand. Med. 7, 245 (1997).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

(Color online) 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 use throughout the paper.

Fig. 2.
Fig. 2.

(Color online) 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) Induced surface current density at 6.2 GHz. c) Measured (E) and calculated (F) transmission through a single labyrinth structure. d) Induced surface current density at 6.2 GHz.

Fig. 3.
Fig. 3.

a) Measured transmission spectrum of the z-component of the electric field through (A) the labyrinth metamaterial medium and (B) through the closed labyrinth metamaterial medium. Only the z-component of the incident electric field was nonzero. b) Measured transmission spectrum of the x-component of the electric field through (C) free space and through (D) the labyrinth metamaterial medium. Only the z-component of the incident electric field was nonzero.

Fig. 4.
Fig. 4.

a) Transmission spectrum of electromagnetic waves through the wire medium. b) Measured transmission spectrum of electromagnetic waves through the CMM medium. c) Measured transmission spectrum of electromagnetic wave through the closed CMM medium.

Equations (2)

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D ¯ = ε ̿ E ¯ + ζ ̿ H ¯
H ¯ = μ̿ H ¯ + ζ ̿ E ¯

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