Abstract

We present a systematic study of a close-ring pair based freestanding metamaterial fabricated by double-layer, self-aligned photolithography. Terahertz time-domain spectroscopy transmission measurements and numerical simulations have revealed negative index of refraction in the frequency range of 0.66-0.90 THz under normal wave incidence. The observed resonance behaviors can be well explained by a theoretical circuit model. The electromagnetic properties and the figure of merit of such close-ring metamaterials are also explored in terms of geometrical parameters of the unit cell with a goal of providing optimized design for three-dimensional metamaterials and potential device applications.

© 2009 OSA

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2009

R. Singh, C. Rockstuhl, C. Menzel, T. P. Meyrath, M. He, H. Giessen, F. Lederer, and W. Zhang, “Spiral-type terahertz antennas and the manifestation of the Mushiake principle,” Opt. Express 17(12), 9971–9980 (2009).
[CrossRef] [PubMed]

G. Donzelli, A. Vallecchi, F. Capolino, and A. Schuchinsky, “Metamaterial made of paired planar conductors: Particle resonances, phenomena and properties,” Metamaterials (Amst.) 3(1), 10–27 (2009).
[CrossRef]

A. Vallecchi, F. Capolino, and A. G. Schuchinsky, “2-D isotropic effective negative refractive index metamaterial in planar technology,” IEEE Microw.Wireless Compon. Lett. 19(5), 269–271 (2009).
[CrossRef]

J. Han, J. Gu, X. Lu, M. He, Q. Xing, and W. Zhang, “Broadband resonant terahertz transmission in a composite metal-dielectric structure,” Opt. Express 17(19), 16527–16534 (2009).
[CrossRef] [PubMed]

2008

2007

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Negative-index metamaterial at 780 nm wavelength,” Opt. Lett. 32(1), 53–55 (2007).
[CrossRef]

Z. Hao, M. C. Martin, B. Harteneck, S. Cabrini, and E. H. Anderson, “Negative index of refraction observed in a single layer of closed ring magnetic dipole resonators,” Appl. Phys. Lett. 91(25), 253119 (2007).
[CrossRef]

2006

J. Zhou, E. N. Economon, T. Koschny, and C. M. Soukoulis, “Unifying approach to left-handed material design,” Opt. Lett. 31(24), 3620–3622 (2006).
[CrossRef] [PubMed]

A. K. Azad, J. M. Dai, and W. Zhang, “Transmission properties of terahertz pulses through subwavelength double split-ring resonators,” Opt. Lett. 31(5), 634–636 (2006).
[CrossRef] [PubMed]

M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-Harmonic Generation from Magnetic Metamaterials,” Science 313(5786), 502–504 (2006).
[CrossRef] [PubMed]

R. W. Ziolkowski and A. Erentok, “Metamaterial-based efficient electrically small antennas,” IEEE Trans. Antenn. Propag. 54(7), 2113–2130 (2006).
[CrossRef]

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial Electromagnetic Cloak at Microwave Frequencies,” Science 314(5801), 977–980 (2006).
[CrossRef] [PubMed]

2005

2004

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz Magnetic Response from Artificial Materials,” Science 303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[CrossRef] [PubMed]

2000

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite Medium with Simultaneously Negative Permeability and Permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

1999

B. Wood and J. B. Pendry, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

1990

1968

V. G. Veselago, “The Electrodynamics of Substances with Simultaneously Negative Values of ε and µ,” Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Anderson, E. H.

Z. Hao, M. C. Martin, B. Harteneck, S. Cabrini, and E. H. Anderson, “Negative index of refraction observed in a single layer of closed ring magnetic dipole resonators,” Appl. Phys. Lett. 91(25), 253119 (2007).
[CrossRef]

Averitt, R. D.

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[CrossRef] [PubMed]

Awad, M.

Azad, A. K.

Basov, D. N.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz Magnetic Response from Artificial Materials,” Science 303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

Beigang, R.

Brener, I.

Brueck, S. R.

Cabrini, S.

Z. Hao, M. C. Martin, B. Harteneck, S. Cabrini, and E. H. Anderson, “Negative index of refraction observed in a single layer of closed ring magnetic dipole resonators,” Appl. Phys. Lett. 91(25), 253119 (2007).
[CrossRef]

Cai, W.

Capolino, F.

G. Donzelli, A. Vallecchi, F. Capolino, and A. Schuchinsky, “Metamaterial made of paired planar conductors: Particle resonances, phenomena and properties,” Metamaterials (Amst.) 3(1), 10–27 (2009).
[CrossRef]

A. Vallecchi, F. Capolino, and A. G. Schuchinsky, “2-D isotropic effective negative refractive index metamaterial in planar technology,” IEEE Microw.Wireless Compon. Lett. 19(5), 269–271 (2009).
[CrossRef]

Chen, H. T.

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[CrossRef] [PubMed]

Chen, X.

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[CrossRef] [PubMed]

Chettiar, U. K.

Cui, J.

Cummer, S. A.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial Electromagnetic Cloak at Microwave Frequencies,” Science 314(5801), 977–980 (2006).
[CrossRef] [PubMed]

Dai, J. M.

Dolling, G.

Donzelli, G.

G. Donzelli, A. Vallecchi, F. Capolino, and A. Schuchinsky, “Metamaterial made of paired planar conductors: Particle resonances, phenomena and properties,” Metamaterials (Amst.) 3(1), 10–27 (2009).
[CrossRef]

Drachev, V. P.

Du, C.

Economon, E. N.

Enkrich, C.

M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-Harmonic Generation from Magnetic Metamaterials,” Science 313(5786), 502–504 (2006).
[CrossRef] [PubMed]

Erentok, A.

R. W. Ziolkowski and A. Erentok, “Metamaterial-based efficient electrically small antennas,” IEEE Trans. Antenn. Propag. 54(7), 2113–2130 (2006).
[CrossRef]

Exter, M.

Fan, W.

Fang, N.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-Diffraction-Limited Optical Imaging with a Silver Superlens,” Science 308(5721), 534–537 (2005).
[CrossRef] [PubMed]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz Magnetic Response from Artificial Materials,” Science 303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

Fattinger, C.

Giessen, H.

Gossard, A. C.

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[CrossRef] [PubMed]

Grischkowsky, D.

Grzegorczyk, T. M.

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[CrossRef] [PubMed]

Gu, J.

Han, J.

Hao, Z.

Z. Hao, M. C. Martin, B. Harteneck, S. Cabrini, and E. H. Anderson, “Negative index of refraction observed in a single layer of closed ring magnetic dipole resonators,” Appl. Phys. Lett. 91(25), 253119 (2007).
[CrossRef]

Harteneck, B.

Z. Hao, M. C. Martin, B. Harteneck, S. Cabrini, and E. H. Anderson, “Negative index of refraction observed in a single layer of closed ring magnetic dipole resonators,” Appl. Phys. Lett. 91(25), 253119 (2007).
[CrossRef]

He, M.

Imhof, C.

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial Electromagnetic Cloak at Microwave Frequencies,” Science 314(5801), 977–980 (2006).
[CrossRef] [PubMed]

Keiding, S.

Kildishev, A. V.

Klein, M. W.

M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-Harmonic Generation from Magnetic Metamaterials,” Science 313(5786), 502–504 (2006).
[CrossRef] [PubMed]

Kong, J. A.

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[CrossRef] [PubMed]

Koschny, T.

Kurz, H.

Lederer, F.

Lee, H.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-Diffraction-Limited Optical Imaging with a Silver Superlens,” Science 308(5721), 534–537 (2005).
[CrossRef] [PubMed]

Linden, S.

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Negative-index metamaterial at 780 nm wavelength,” Opt. Lett. 32(1), 53–55 (2007).
[CrossRef]

M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-Harmonic Generation from Magnetic Metamaterials,” Science 313(5786), 502–504 (2006).
[CrossRef] [PubMed]

Lu, X.

Luo, X.

Ma, J.

Malloy, K. J.

Martin, M. C.

Z. Hao, M. C. Martin, B. Harteneck, S. Cabrini, and E. H. Anderson, “Negative index of refraction observed in a single layer of closed ring magnetic dipole resonators,” Appl. Phys. Lett. 91(25), 253119 (2007).
[CrossRef]

Menzel, C.

Meyrath, T. P.

Mock, J. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial Electromagnetic Cloak at Microwave Frequencies,” Science 314(5801), 977–980 (2006).
[CrossRef] [PubMed]

Nagel, M.

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite Medium with Simultaneously Negative Permeability and Permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

O’Hara, J. F.

Osgood, R. M.

Pacheco, J.

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[CrossRef] [PubMed]

Padilla, W. J.

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[CrossRef] [PubMed]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz Magnetic Response from Artificial Materials,” Science 303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite Medium with Simultaneously Negative Permeability and Permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Panoiu, N. C.

Paul, O.

Pendry, J. B.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial Electromagnetic Cloak at Microwave Frequencies,” Science 314(5801), 977–980 (2006).
[CrossRef] [PubMed]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz Magnetic Response from Artificial Materials,” Science 303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

B. Wood and J. B. Pendry, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

Reinhard, B.

Rockstuhl, C.

Sarychev, A. K.

Schuchinsky, A.

G. Donzelli, A. Vallecchi, F. Capolino, and A. Schuchinsky, “Metamaterial made of paired planar conductors: Particle resonances, phenomena and properties,” Metamaterials (Amst.) 3(1), 10–27 (2009).
[CrossRef]

Schuchinsky, A. G.

A. Vallecchi, F. Capolino, and A. G. Schuchinsky, “2-D isotropic effective negative refractive index metamaterial in planar technology,” IEEE Microw.Wireless Compon. Lett. 19(5), 269–271 (2009).
[CrossRef]

Schultz, S.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite Medium with Simultaneously Negative Permeability and Permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Schurig, D.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial Electromagnetic Cloak at Microwave Frequencies,” Science 314(5801), 977–980 (2006).
[CrossRef] [PubMed]

Shalaev, V. M.

Singh, R.

Smirnova, E.

Smith, D. R.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial Electromagnetic Cloak at Microwave Frequencies,” Science 314(5801), 977–980 (2006).
[CrossRef] [PubMed]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz Magnetic Response from Artificial Materials,” Science 303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite Medium with Simultaneously Negative Permeability and Permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Soukoulis, C. M.

Starr, A. F.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial Electromagnetic Cloak at Microwave Frequencies,” Science 314(5801), 977–980 (2006).
[CrossRef] [PubMed]

Sun, C.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-Diffraction-Limited Optical Imaging with a Silver Superlens,” Science 308(5721), 534–537 (2005).
[CrossRef] [PubMed]

Taylor, A. J.

J. F. O’Hara, R. Singh, I. Brener, E. Smirnova, J. Han, A. J. Taylor, and W. Zhang, “Thin-film sensing with planar terahertz metamaterials: sensitivity and limitations,” Opt. Express 16(3), 1786–1795 (2008).
[CrossRef] [PubMed]

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature 444(7119), 597–600 (2006).
[CrossRef] [PubMed]

Vallecchi, A.

A. Vallecchi, F. Capolino, and A. G. Schuchinsky, “2-D isotropic effective negative refractive index metamaterial in planar technology,” IEEE Microw.Wireless Compon. Lett. 19(5), 269–271 (2009).
[CrossRef]

G. Donzelli, A. Vallecchi, F. Capolino, and A. Schuchinsky, “Metamaterial made of paired planar conductors: Particle resonances, phenomena and properties,” Metamaterials (Amst.) 3(1), 10–27 (2009).
[CrossRef]

Veselago, V. G.

V. G. Veselago, “The Electrodynamics of Substances with Simultaneously Negative Values of ε and µ,” Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Vier, D. C.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz Magnetic Response from Artificial Materials,” Science 303(5663), 1494–1496 (2004).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite Medium with Simultaneously Negative Permeability and Permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Wang, C.

Wegener, M.

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Negative-index metamaterial at 780 nm wavelength,” Opt. Lett. 32(1), 53–55 (2007).
[CrossRef]

M. W. Klein, C. Enkrich, M. Wegener, and S. Linden, “Second-Harmonic Generation from Magnetic Metamaterials,” Science 313(5786), 502–504 (2006).
[CrossRef] [PubMed]

Wood, B.

B. Wood and J. B. Pendry, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

Wu, B. I.

X. Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[CrossRef] [PubMed]

Xing, Q.

Xu, T.

Yen, T. J.

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic of a CRP unit cell with typical dimensions of l = 60 µm, w = 5 µm, and h = 22 µm. The arrows in the rings represent surface current induced at the resonance frequency. (b) Effective circuit model of the unit cell. (c) Measured (solid curve) and simulated (dotted curve) of a single-layer CRP metamaterial. The dashed curve illustrates the measured transmission of corresponding Al rings patterned only on one side of Mylar. (d) Measured transmissions of multi-layer CRPs. A Mylar film of 50 µm is used as the spacer in the multi-layer CRPs.

Fig. 3
Fig. 3

Dependence of the CRP resonance on geometrical dimensions. (a), (c) and (e): measured (solid curves) and simulated (dotted curves) transmissions with (a) l = 40 (black), 60 (red) and 80 (blue) µm, (c) w = 5 (black), 10 (red) and 20 (blue) µm, and (e) d = 4 (black), 20 (red), and 40 (blue) µm, respectively. (b), (d) and (f): predicted (solid curves, by the circuit model) and simulated (squares) resonance frequencies.

Fig. 2
Fig. 2

Retrieved parameters of a single-layer CRP. The real and imaginary parts of the parameters are represented by the red and blue curves, respectively.

Fig. 4
Fig. 4

Figure of Merit of the CRPs with various lengths (a) and wire widths (b). The x-axis is normalized to the resonance frequency.

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