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 (4)

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]

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]

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 (4)

2007 (2)

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 (6)

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]

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]

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]

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]

2005 (3)

2004 (2)

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]

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]

2000 (1)

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 (1)

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 (1)

1968 (1)

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.

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]

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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