Abstract

We present the design, fabrication, and measurement of a dual-band planar metamaterial with two distinct electric resonances at 1.0 and 1.2 THz, as a step towards the development of frequency agile or broadband THz materials and devices. A method of defining the effective thickness of the metamaterial layer is introduced to simplify the material design and characterization. Good agreement between the simulated and measured transmission is obtained for the fabricated sample by treating the sample as multi-layer system, i. e. the effective metamaterial layer plus the rest of the substrate, as well as properly modeling the loss of the substrate. The methods introduced in this paper can be extended to planar metamaterial structures operating in infrared and optical frequency ranges.

© 2008 Optical Society of America

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  1. V. G. Veselago, "The electrodynamics of substance with simultaneously negative value of ? and ?," Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
  2. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely Low Frequency Plasmons in Metallic Mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
    [CrossRef] [PubMed]
  3. J. B. Pendry, A. J. Holden, D. J. Robbins, andW. J. Stewart, "Magnetism fromconductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
    [CrossRef]
  4. 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, 4184-4187 (2000).
    [CrossRef] [PubMed]
  5. R. A. Shelby, D. R. Smith, and S. Shultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
    [CrossRef] [PubMed]
  6. S. A. Cummer and B. I. Popa, "Wave fields measured inside a negative refractive index metamaterial," Appl. Phys. Lett. 85, 4564-4566 (2004).
    [CrossRef]
  7. Y. Yuan, L. Ran, H. Chen, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, "Backward coupling waveguide coupler using left-handed material," Appl. Phys. Lett. 88, 211903 (2006).
    [CrossRef]
  8. H. Chen, B. I. Wu, L. Ran, T. M. Grzegorczyk, and J. A. Kong, "Controllable left-handed metamaterial and its application to a steerable antenna," Appl. Phys. Lett. 89, 053509 (2006).
    [CrossRef]
  9. 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, 1494-1496 (2004).
    [CrossRef] [PubMed]
  10. H. O. Moser, B. D. F. Casse, O. Wilhelmi, and B. T. Saw, "Terahertz response of a microfabricated rod-splitring-resonator electromagnetic metamaterial," Phys. Rev. Lett. 94, 063901 (2005).
    [CrossRef] [PubMed]
  11. W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, "Dynamical electric and magnetic metamaterial response at terahertz frequencies," Phys. Rev. Lett. 96, 107401 (2006).
    [CrossRef] [PubMed]
  12. 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, 597-600 (2006)
    [CrossRef] [PubMed]
  13. 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]
  14. J. Garc?a-Garc?a, F. Mart?n, J. D. Baena, R. Maques, and L. Jelinek, "On the resonances and polarizabilities of split ring resonators," J. Appl. Phys. 98, 033103 (2005).
    [CrossRef]
  15. K. A. McIntosh, E. R. Brown, K. B. Nichols, O. B. McMahon, W. F. DiNatale, and T. M. Lyszczarz, "Terahertz measurements of resonant planar antennas coupled to low-temperature-grown GaAs photomixers," Appl. Phys. Lett. 69, 3632-3634 (1996).
    [CrossRef]
  16. T. Driscoll, D. N. Basov, W. J. Padilla, J. J. Mock, and D. R. Smith, "Electromagnetic characterization of planar metamaterials by oblique angle spectroscopic measurements," Phys. Rev. B 75, 115114 (2007).
    [CrossRef]
  17. T. Driscoll, G. O. Andreev, D. N. Basov, S. Palit, Tong Ren, Jack Mock, Sang-Yeon Cho, Nan Marie Jokerst, and D. R. Smith, "Quantitative investigation of terahertz artificial magnetic resonance using oblique angle spectroscopy," Appl. Phys. Lett. 90, 092508 (2007).
    [CrossRef]
  18. B. Popa and S. A. Cummer, "Determining the effective electromagnetic properties of negative-refractive-index metamaterials from internal fields," Phys. Rev. B 72, 165102 (2005).
    [CrossRef]
  19. M. Gorkunov, M. Lapine, E. Shamonina, and K. H. Ringhofer, "Effective magnetic properties of a composite material with circular conductive elements," Eur. Phys. J. B 28, 263-269 (2002).
    [CrossRef]
  20. D. R. Smith, S. Schultz, P. Marko, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B 65, 195104 (2002).
    [CrossRef]
  21. 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 70, 016608 (2004).
    [CrossRef]
  22. D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Phys. Rev. E 71, 036617 (2005).
    [CrossRef]

2007 (2)

T. Driscoll, D. N. Basov, W. J. Padilla, J. J. Mock, and D. R. Smith, "Electromagnetic characterization of planar metamaterials by oblique angle spectroscopic measurements," Phys. Rev. B 75, 115114 (2007).
[CrossRef]

T. Driscoll, G. O. Andreev, D. N. Basov, S. Palit, Tong Ren, Jack Mock, Sang-Yeon Cho, Nan Marie Jokerst, and D. R. Smith, "Quantitative investigation of terahertz artificial magnetic resonance using oblique angle spectroscopy," Appl. Phys. Lett. 90, 092508 (2007).
[CrossRef]

2006 (4)

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, "Dynamical electric and magnetic metamaterial response at terahertz frequencies," Phys. Rev. Lett. 96, 107401 (2006).
[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, 597-600 (2006)
[CrossRef] [PubMed]

Y. Yuan, L. Ran, H. Chen, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, "Backward coupling waveguide coupler using left-handed material," Appl. Phys. Lett. 88, 211903 (2006).
[CrossRef]

H. Chen, B. I. Wu, L. Ran, T. M. Grzegorczyk, and J. A. Kong, "Controllable left-handed metamaterial and its application to a steerable antenna," Appl. Phys. Lett. 89, 053509 (2006).
[CrossRef]

2005 (4)

J. Garc?a-Garc?a, F. Mart?n, J. D. Baena, R. Maques, and L. Jelinek, "On the resonances and polarizabilities of split ring resonators," J. Appl. Phys. 98, 033103 (2005).
[CrossRef]

B. Popa and S. A. Cummer, "Determining the effective electromagnetic properties of negative-refractive-index metamaterials from internal fields," Phys. Rev. B 72, 165102 (2005).
[CrossRef]

H. O. Moser, B. D. F. Casse, O. Wilhelmi, and B. T. Saw, "Terahertz response of a microfabricated rod-splitring-resonator electromagnetic metamaterial," Phys. Rev. Lett. 94, 063901 (2005).
[CrossRef] [PubMed]

D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Phys. Rev. E 71, 036617 (2005).
[CrossRef]

2004 (3)

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 70, 016608 (2004).
[CrossRef]

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, 1494-1496 (2004).
[CrossRef] [PubMed]

S. A. Cummer and B. I. Popa, "Wave fields measured inside a negative refractive index metamaterial," Appl. Phys. Lett. 85, 4564-4566 (2004).
[CrossRef]

2002 (3)

M. Gorkunov, M. Lapine, E. Shamonina, and K. H. Ringhofer, "Effective magnetic properties of a composite material with circular conductive elements," Eur. Phys. J. B 28, 263-269 (2002).
[CrossRef]

D. R. Smith, S. Schultz, P. Marko, 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]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Shultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[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, 4184-4187 (2000).
[CrossRef] [PubMed]

1999 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, andW. J. Stewart, "Magnetism fromconductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

1996 (2)

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely Low Frequency Plasmons in Metallic Mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

K. A. McIntosh, E. R. Brown, K. B. Nichols, O. B. McMahon, W. F. DiNatale, and T. M. Lyszczarz, "Terahertz measurements of resonant planar antennas coupled to low-temperature-grown GaAs photomixers," Appl. Phys. Lett. 69, 3632-3634 (1996).
[CrossRef]

1968 (1)

V. G. Veselago, "The electrodynamics of substance with simultaneously negative value of ? and ?," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Andreev, G. O.

T. Driscoll, G. O. Andreev, D. N. Basov, S. Palit, Tong Ren, Jack Mock, Sang-Yeon Cho, Nan Marie Jokerst, and D. R. Smith, "Quantitative investigation of terahertz artificial magnetic resonance using oblique angle spectroscopy," Appl. Phys. Lett. 90, 092508 (2007).
[CrossRef]

Averitt, R. D.

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, "Dynamical electric and magnetic metamaterial response at terahertz frequencies," Phys. Rev. Lett. 96, 107401 (2006).
[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, 597-600 (2006)
[CrossRef] [PubMed]

Baena, J. D.

J. Garc?a-Garc?a, F. Mart?n, J. D. Baena, R. Maques, and L. Jelinek, "On the resonances and polarizabilities of split ring resonators," J. Appl. Phys. 98, 033103 (2005).
[CrossRef]

Basov, D. N.

T. Driscoll, D. N. Basov, W. J. Padilla, J. J. Mock, and D. R. Smith, "Electromagnetic characterization of planar metamaterials by oblique angle spectroscopic measurements," Phys. Rev. B 75, 115114 (2007).
[CrossRef]

T. Driscoll, G. O. Andreev, D. N. Basov, S. Palit, Tong Ren, Jack Mock, Sang-Yeon Cho, Nan Marie Jokerst, and D. R. Smith, "Quantitative investigation of terahertz artificial magnetic resonance using oblique angle spectroscopy," Appl. Phys. Lett. 90, 092508 (2007).
[CrossRef]

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, 1494-1496 (2004).
[CrossRef] [PubMed]

Brown, E. R.

K. A. McIntosh, E. R. Brown, K. B. Nichols, O. B. McMahon, W. F. DiNatale, and T. M. Lyszczarz, "Terahertz measurements of resonant planar antennas coupled to low-temperature-grown GaAs photomixers," Appl. Phys. Lett. 69, 3632-3634 (1996).
[CrossRef]

Casse, B. D. F.

H. O. Moser, B. D. F. Casse, O. Wilhelmi, and B. T. Saw, "Terahertz response of a microfabricated rod-splitring-resonator electromagnetic metamaterial," Phys. Rev. Lett. 94, 063901 (2005).
[CrossRef] [PubMed]

Chen, H.

Y. Yuan, L. Ran, H. Chen, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, "Backward coupling waveguide coupler using left-handed material," Appl. Phys. Lett. 88, 211903 (2006).
[CrossRef]

H. Chen, B. I. Wu, L. Ran, T. M. Grzegorczyk, and J. A. Kong, "Controllable left-handed metamaterial and its application to a steerable antenna," Appl. Phys. Lett. 89, 053509 (2006).
[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, 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 70, 016608 (2004).
[CrossRef]

Cummer, S. A.

B. Popa and S. A. Cummer, "Determining the effective electromagnetic properties of negative-refractive-index metamaterials from internal fields," Phys. Rev. B 72, 165102 (2005).
[CrossRef]

S. A. Cummer and B. I. Popa, "Wave fields measured inside a negative refractive index metamaterial," Appl. Phys. Lett. 85, 4564-4566 (2004).
[CrossRef]

DiNatale, W. F.

K. A. McIntosh, E. R. Brown, K. B. Nichols, O. B. McMahon, W. F. DiNatale, and T. M. Lyszczarz, "Terahertz measurements of resonant planar antennas coupled to low-temperature-grown GaAs photomixers," Appl. Phys. Lett. 69, 3632-3634 (1996).
[CrossRef]

Driscoll, T.

T. Driscoll, D. N. Basov, W. J. Padilla, J. J. Mock, and D. R. Smith, "Electromagnetic characterization of planar metamaterials by oblique angle spectroscopic measurements," Phys. Rev. B 75, 115114 (2007).
[CrossRef]

T. Driscoll, G. O. Andreev, D. N. Basov, S. Palit, Tong Ren, Jack Mock, Sang-Yeon Cho, Nan Marie Jokerst, and D. R. Smith, "Quantitative investigation of terahertz artificial magnetic resonance using oblique angle spectroscopy," Appl. Phys. Lett. 90, 092508 (2007).
[CrossRef]

Fang, 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, 1494-1496 (2004).
[CrossRef] [PubMed]

Garcia-Garcia, J.

J. Garc?a-Garc?a, F. Mart?n, J. D. Baena, R. Maques, and L. Jelinek, "On the resonances and polarizabilities of split ring resonators," J. Appl. Phys. 98, 033103 (2005).
[CrossRef]

Gorkunov, M.

M. Gorkunov, M. Lapine, E. Shamonina, and K. H. Ringhofer, "Effective magnetic properties of a composite material with circular conductive elements," Eur. Phys. J. B 28, 263-269 (2002).
[CrossRef]

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, 597-600 (2006)
[CrossRef] [PubMed]

Grzegorczyk, T. M.

H. Chen, B. I. Wu, L. Ran, T. M. Grzegorczyk, and J. A. Kong, "Controllable left-handed metamaterial and its application to a steerable antenna," Appl. Phys. Lett. 89, 053509 (2006).
[CrossRef]

Y. Yuan, L. Ran, H. Chen, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, "Backward coupling waveguide coupler using left-handed material," Appl. Phys. Lett. 88, 211903 (2006).
[CrossRef]

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 70, 016608 (2004).
[CrossRef]

Highstrete, C.

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, "Dynamical electric and magnetic metamaterial response at terahertz frequencies," Phys. Rev. Lett. 96, 107401 (2006).
[CrossRef] [PubMed]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, andW. J. Stewart, "Magnetism fromconductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely Low Frequency Plasmons in Metallic Mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Huangfu, J.

Y. Yuan, L. Ran, H. Chen, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, "Backward coupling waveguide coupler using left-handed material," Appl. Phys. Lett. 88, 211903 (2006).
[CrossRef]

Jelinek, L.

J. Garc?a-Garc?a, F. Mart?n, J. D. Baena, R. Maques, and L. Jelinek, "On the resonances and polarizabilities of split ring resonators," J. Appl. Phys. 98, 033103 (2005).
[CrossRef]

Kong, J. A.

Y. Yuan, L. Ran, H. Chen, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, "Backward coupling waveguide coupler using left-handed material," Appl. Phys. Lett. 88, 211903 (2006).
[CrossRef]

H. Chen, B. I. Wu, L. Ran, T. M. Grzegorczyk, and J. A. Kong, "Controllable left-handed metamaterial and its application to a steerable antenna," Appl. Phys. Lett. 89, 053509 (2006).
[CrossRef]

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 70, 016608 (2004).
[CrossRef]

Koschny, Th.

D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Phys. Rev. E 71, 036617 (2005).
[CrossRef]

Lapine, M.

M. Gorkunov, M. Lapine, E. Shamonina, and K. H. Ringhofer, "Effective magnetic properties of a composite material with circular conductive elements," Eur. Phys. J. B 28, 263-269 (2002).
[CrossRef]

Lee, M.

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, "Dynamical electric and magnetic metamaterial response at terahertz frequencies," Phys. Rev. Lett. 96, 107401 (2006).
[CrossRef] [PubMed]

Lyszczarz, T. M.

K. A. McIntosh, E. R. Brown, K. B. Nichols, O. B. McMahon, W. F. DiNatale, and T. M. Lyszczarz, "Terahertz measurements of resonant planar antennas coupled to low-temperature-grown GaAs photomixers," Appl. Phys. Lett. 69, 3632-3634 (1996).
[CrossRef]

Maques, R.

J. Garc?a-Garc?a, F. Mart?n, J. D. Baena, R. Maques, and L. Jelinek, "On the resonances and polarizabilities of split ring resonators," J. Appl. Phys. 98, 033103 (2005).
[CrossRef]

Marko, P.

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

Marques, R.

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]

Martin, F.

J. Garc?a-Garc?a, F. Mart?n, J. D. Baena, R. Maques, and L. Jelinek, "On the resonances and polarizabilities of split ring resonators," J. Appl. Phys. 98, 033103 (2005).
[CrossRef]

McIntosh, K. A.

K. A. McIntosh, E. R. Brown, K. B. Nichols, O. B. McMahon, W. F. DiNatale, and T. M. Lyszczarz, "Terahertz measurements of resonant planar antennas coupled to low-temperature-grown GaAs photomixers," Appl. Phys. Lett. 69, 3632-3634 (1996).
[CrossRef]

McMahon, O. B.

K. A. McIntosh, E. R. Brown, K. B. Nichols, O. B. McMahon, W. F. DiNatale, and T. M. Lyszczarz, "Terahertz measurements of resonant planar antennas coupled to low-temperature-grown GaAs photomixers," Appl. Phys. Lett. 69, 3632-3634 (1996).
[CrossRef]

Medina, F.

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]

Mock, J. J.

T. Driscoll, D. N. Basov, W. J. Padilla, J. J. Mock, and D. R. Smith, "Electromagnetic characterization of planar metamaterials by oblique angle spectroscopic measurements," Phys. Rev. B 75, 115114 (2007).
[CrossRef]

Moser, H. O.

H. O. Moser, B. D. F. Casse, O. Wilhelmi, and B. T. Saw, "Terahertz response of a microfabricated rod-splitring-resonator electromagnetic metamaterial," Phys. Rev. Lett. 94, 063901 (2005).
[CrossRef] [PubMed]

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, 4184-4187 (2000).
[CrossRef] [PubMed]

Nichols, K. B.

K. A. McIntosh, E. R. Brown, K. B. Nichols, O. B. McMahon, W. F. DiNatale, and T. M. Lyszczarz, "Terahertz measurements of resonant planar antennas coupled to low-temperature-grown GaAs photomixers," Appl. Phys. Lett. 69, 3632-3634 (1996).
[CrossRef]

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 70, 016608 (2004).
[CrossRef]

Padilla, W. J.

T. Driscoll, D. N. Basov, W. J. Padilla, J. J. Mock, and D. R. Smith, "Electromagnetic characterization of planar metamaterials by oblique angle spectroscopic measurements," Phys. Rev. B 75, 115114 (2007).
[CrossRef]

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, "Dynamical electric and magnetic metamaterial response at terahertz frequencies," Phys. Rev. Lett. 96, 107401 (2006).
[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, 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, 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, 4184-4187 (2000).
[CrossRef] [PubMed]

Palit, S.

T. Driscoll, G. O. Andreev, D. N. Basov, S. Palit, Tong Ren, Jack Mock, Sang-Yeon Cho, Nan Marie Jokerst, and D. R. Smith, "Quantitative investigation of terahertz artificial magnetic resonance using oblique angle spectroscopy," Appl. Phys. Lett. 90, 092508 (2007).
[CrossRef]

Pendry, J. B.

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, 1494-1496 (2004).
[CrossRef] [PubMed]

J. B. Pendry, A. J. Holden, D. J. Robbins, andW. J. Stewart, "Magnetism fromconductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely Low Frequency Plasmons in Metallic Mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Popa, B.

B. Popa and S. A. Cummer, "Determining the effective electromagnetic properties of negative-refractive-index metamaterials from internal fields," Phys. Rev. B 72, 165102 (2005).
[CrossRef]

Popa, B. I.

S. A. Cummer and B. I. Popa, "Wave fields measured inside a negative refractive index metamaterial," Appl. Phys. Lett. 85, 4564-4566 (2004).
[CrossRef]

Rafii-El-Idrissi, R.

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]

Ran, L.

Y. Yuan, L. Ran, H. Chen, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, "Backward coupling waveguide coupler using left-handed material," Appl. Phys. Lett. 88, 211903 (2006).
[CrossRef]

H. Chen, B. I. Wu, L. Ran, T. M. Grzegorczyk, and J. A. Kong, "Controllable left-handed metamaterial and its application to a steerable antenna," Appl. Phys. Lett. 89, 053509 (2006).
[CrossRef]

Ringhofer, K. H.

M. Gorkunov, M. Lapine, E. Shamonina, and K. H. Ringhofer, "Effective magnetic properties of a composite material with circular conductive elements," Eur. Phys. J. B 28, 263-269 (2002).
[CrossRef]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, andW. J. Stewart, "Magnetism fromconductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Saw, B. T.

H. O. Moser, B. D. F. Casse, O. Wilhelmi, and B. T. Saw, "Terahertz response of a microfabricated rod-splitring-resonator electromagnetic metamaterial," Phys. Rev. Lett. 94, 063901 (2005).
[CrossRef] [PubMed]

Schultz, S.

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

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, 4184-4187 (2000).
[CrossRef] [PubMed]

Shamonina, E.

M. Gorkunov, M. Lapine, E. Shamonina, and K. H. Ringhofer, "Effective magnetic properties of a composite material with circular conductive elements," Eur. Phys. J. B 28, 263-269 (2002).
[CrossRef]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Shultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Shultz, S.

R. A. Shelby, D. R. Smith, and S. Shultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Smith, D. R.

T. Driscoll, D. N. Basov, W. J. Padilla, J. J. Mock, and D. R. Smith, "Electromagnetic characterization of planar metamaterials by oblique angle spectroscopic measurements," Phys. Rev. B 75, 115114 (2007).
[CrossRef]

D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Phys. Rev. E 71, 036617 (2005).
[CrossRef]

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, 1494-1496 (2004).
[CrossRef] [PubMed]

D. R. Smith, S. Schultz, P. Marko, 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. A. Shelby, D. R. Smith, and S. Shultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[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, 4184-4187 (2000).
[CrossRef] [PubMed]

Soukoulis, C. M.

D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Phys. Rev. E 71, 036617 (2005).
[CrossRef]

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

Stewart, W. J.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely Low Frequency Plasmons in Metallic Mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Taylor, A. 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, 597-600 (2006)
[CrossRef] [PubMed]

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, "Dynamical electric and magnetic metamaterial response at terahertz frequencies," Phys. Rev. Lett. 96, 107401 (2006).
[CrossRef] [PubMed]

Veselago, V. G.

V. G. Veselago, "The electrodynamics of substance with simultaneously negative value of ? and ?," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Vier, D. C.

D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Phys. Rev. E 71, 036617 (2005).
[CrossRef]

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, 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, 4184-4187 (2000).
[CrossRef] [PubMed]

Wilhelmi, O.

H. O. Moser, B. D. F. Casse, O. Wilhelmi, and B. T. Saw, "Terahertz response of a microfabricated rod-splitring-resonator electromagnetic metamaterial," Phys. Rev. Lett. 94, 063901 (2005).
[CrossRef] [PubMed]

Wu, B. I.

H. Chen, B. I. Wu, L. Ran, T. M. Grzegorczyk, and J. A. Kong, "Controllable left-handed metamaterial and its application to a steerable antenna," Appl. Phys. Lett. 89, 053509 (2006).
[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 70, 016608 (2004).
[CrossRef]

Yen, T. J.

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, 1494-1496 (2004).
[CrossRef] [PubMed]

Youngs, I.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely Low Frequency Plasmons in Metallic Mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Yuan, Y.

Y. Yuan, L. Ran, H. Chen, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, "Backward coupling waveguide coupler using left-handed material," Appl. Phys. Lett. 88, 211903 (2006).
[CrossRef]

Zhang, X.

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, 1494-1496 (2004).
[CrossRef] [PubMed]

Zide, J. M. O.

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, 597-600 (2006)
[CrossRef] [PubMed]

Appl. Phys. Lett. (5)

S. A. Cummer and B. I. Popa, "Wave fields measured inside a negative refractive index metamaterial," Appl. Phys. Lett. 85, 4564-4566 (2004).
[CrossRef]

Y. Yuan, L. Ran, H. Chen, J. Huangfu, T. M. Grzegorczyk, and J. A. Kong, "Backward coupling waveguide coupler using left-handed material," Appl. Phys. Lett. 88, 211903 (2006).
[CrossRef]

H. Chen, B. I. Wu, L. Ran, T. M. Grzegorczyk, and J. A. Kong, "Controllable left-handed metamaterial and its application to a steerable antenna," Appl. Phys. Lett. 89, 053509 (2006).
[CrossRef]

K. A. McIntosh, E. R. Brown, K. B. Nichols, O. B. McMahon, W. F. DiNatale, and T. M. Lyszczarz, "Terahertz measurements of resonant planar antennas coupled to low-temperature-grown GaAs photomixers," Appl. Phys. Lett. 69, 3632-3634 (1996).
[CrossRef]

T. Driscoll, G. O. Andreev, D. N. Basov, S. Palit, Tong Ren, Jack Mock, Sang-Yeon Cho, Nan Marie Jokerst, and D. R. Smith, "Quantitative investigation of terahertz artificial magnetic resonance using oblique angle spectroscopy," Appl. Phys. Lett. 90, 092508 (2007).
[CrossRef]

Eur. Phys. J. B (1)

M. Gorkunov, M. Lapine, E. Shamonina, and K. H. Ringhofer, "Effective magnetic properties of a composite material with circular conductive elements," Eur. Phys. J. B 28, 263-269 (2002).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, andW. J. Stewart, "Magnetism fromconductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

J. Appl. Phys. (1)

J. Garc?a-Garc?a, F. Mart?n, J. D. Baena, R. Maques, and L. Jelinek, "On the resonances and polarizabilities of split ring resonators," J. Appl. Phys. 98, 033103 (2005).
[CrossRef]

Nature (1)

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, 597-600 (2006)
[CrossRef] [PubMed]

Phys. Rev. B (4)

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]

B. Popa and S. A. Cummer, "Determining the effective electromagnetic properties of negative-refractive-index metamaterials from internal fields," Phys. Rev. B 72, 165102 (2005).
[CrossRef]

T. Driscoll, D. N. Basov, W. J. Padilla, J. J. Mock, and D. R. Smith, "Electromagnetic characterization of planar metamaterials by oblique angle spectroscopic measurements," Phys. Rev. B 75, 115114 (2007).
[CrossRef]

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

Phys. Rev. E (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 70, 016608 (2004).
[CrossRef]

D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis, "Electromagnetic parameter retrieval from inhomogeneous metamaterials," Phys. Rev. E 71, 036617 (2005).
[CrossRef]

Phys. Rev. Lett. (4)

H. O. Moser, B. D. F. Casse, O. Wilhelmi, and B. T. Saw, "Terahertz response of a microfabricated rod-splitring-resonator electromagnetic metamaterial," Phys. Rev. Lett. 94, 063901 (2005).
[CrossRef] [PubMed]

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, "Dynamical electric and magnetic metamaterial response at terahertz frequencies," Phys. Rev. Lett. 96, 107401 (2006).
[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, 4184-4187 (2000).
[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, 4773-4776 (1996).
[CrossRef] [PubMed]

Science (2)

R. A. Shelby, D. R. Smith, and S. Shultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[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, 1494-1496 (2004).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

V. G. Veselago, "The electrodynamics of substance with simultaneously negative value of ? and ?," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Photomicrograph of the fabricated dual symmetrical SRR sample. A unit cell of the metamaterial is shown in the highlighted, white-edged box, and inset is the simulated SRRs, polarization of the incident wave included. Lattice constants of the unit cell a=112 µm and b=60 µm, and geometric parameters of the SRRs are: w 1=16 µm, h 1=w 2=h 2=20 µm, w=4 µm, and g=3 µm.

Fig. 2.
Fig. 2.

(a) Simulated transmission (in dB) of the dual-band electric metamaterial (solid line), and of the individual symmetrical SRRs (dashed lines). (b) Surface current circulation on the symmetrical SRRs near f o,1, and (c) surface current circulation on the symmetrical SRRs near f o,2.

Fig. 3.
Fig. 3.

Retrieved permittivity for the dual-band electric metamaterial, based on incidence from the symmetrical SRRs side (forward, blue lines), and from the substrate side (backward, red lines).

Fig. 4.
Fig. 4.

Measured transmission for the fabricated sample (solid red line), and the simulated transmission spectrum for the modified models. In the modified simulation, the loss tangent of the extra GaAs substrate was swept: 0.06 (dashed blue line), 0.07 (solid pink line), and 0.08 (dashed green line).

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