Abstract

Terahertz time-domain spectroscopy was used to investigate the bianisotropic response of microfabricated split-ring resonators (SRRs) and the in-plane SRR–wire metamaterials. We observed a strong polarization dependence of the transmission with a polarized incident terahertz electromagnetic wave. Two transmission minima, one from the bianisotropic contribution and the other from the anisotropic plasmonic contribution, are discussed. The evolution of the two transmission minima as a function of polarization angle is also demonstrated. The effective-medium theory combined with the dispersion relations in metamaterials is employed to elucidate the experimental data effectively.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. Inoue and K. Ohtaka, Photonic Crystals: Physics, Fabrication and Applications (Springer, 2004).
  2. V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of epsi and μ," Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
  3. D. R. Smith, P. Kolinko, and D. Schurig, "Negative refraction in indefinite media," J. Opt. Soc. Am. B 21, 1032-1043 (2004).
    [CrossRef]
  4. J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  5. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
    [CrossRef]
  6. 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]
  7. 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]
  8. R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
    [CrossRef] [PubMed]
  9. 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, 107401-1-107401-4 (2003).
    [CrossRef]
  10. T. M. Grzegorczyk, Z. M. Thomas, and J. A. Kong, "Inversion of critical angle and Brewster angle in anisotropic left-handed metamaterials," Appl. Phys. Lett. 86, 251909-1-251909-3 (2005).
    [CrossRef]
  11. 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]
  12. D. M. Wu, N. Fang, C. Sun, and X. Zhang, "Terahertz plasmonic high pass filter," Appl. Phys. Lett. 83, 201-203 (2003).
    [CrossRef]
  13. S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100THz," Science 306, 1351-1353 (2004).
    [CrossRef] [PubMed]
  14. H. O. Moser, B. D. F. Casse, O. Wilhelmi, and B. T. Saw, "Terahertz response of a microfabricated rod-split-ring-resonator electromagnetic metamaterial," Phys. Rev. Lett. 94, 063901-1-063901-4 (2005).
    [CrossRef]
  15. B. Ferguson and X.-C. Zhang, "Materials for terahertz science and technology," Nat. Mater. 1, 26-33 (2002).
    [CrossRef]
  16. R. Marqués, F. Medina, and R. Rafii-El-Idrissi, "Role of bianisotropy in negative permeability and left-handed metamaterials," Phys. Rev. B 65, 144440-1-144440-6 (2002).
    [CrossRef]
  17. D. Grischkowsky, S. Keiding, M. Van Exter, and Ch. Fattinger, "Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors," J. Opt. Soc. Am. B 7, 2006-2014 (1990).
    [CrossRef]
  18. M. Schall, M. Walther, and P. U. Jepsen, "Fundamental and second-order phonon processes in CdTe and ZnTe," Phys. Rev. B 64, 094301-1-094301-5 (2001).
    [CrossRef]
  19. M. V. Exter, C. Fattinger, and D. Grischkowsky, "Terahertz time-domain spectroscopy of water vapor," Opt. Lett. 14, 1128-1130 (1989).
    [CrossRef] [PubMed]
  20. P. Y. Han, M. Tani, M. Usami, S. Kono, R. Kersting, and X.-C. Zhang, "A direct comparison between terahertz time-domain spectroscopy and far-infrared Fourier transform spectroscopy," J. Appl. Phys. 89, 2357-2359 (2001).
    [CrossRef]
  21. X. Chen, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, "Retrieval of the effective constitutive parameters of bianisotropic metamaterials," Phys. Rev. E 71, 046610-1-046610-9 (2005).
    [CrossRef]
  22. 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, 2943-2945 (2004).
    [CrossRef]
  23. T. Koschny, M. Kafesakis, E. N. Economou, and C. M. Soukoulis, "Effective medium theory of left-handed materials," Phys. Rev. Lett. 93, 107402-1-107402-4 (2004).
    [CrossRef]
  24. N. Katsarakis, G. Konstantinidis, A. Kostopoulos, R. S. Penciu, T. F. Gundogdu, Th. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Magnetic response of split-ring resonators in the far-infrared frequency regime," Opt. Lett. 30, 1348-1350 (2005).
    [CrossRef] [PubMed]
  25. P. Gay-Balmaz and O. J. F. Martin, "Electromagnetic resonances in individual and coupled split-ring resonators," J. Appl. Phys. 92, 2929-2936 (2002).
    [CrossRef]
  26. 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, 3778-3784 (2004).
    [CrossRef]
  27. Y.-J. Hsu, Y.-C. Huang, J.-S. Lih, and J.-L. Chern, "Electromagnetic resonance in deformed split ring resonators of left-handed meta-materials," J. Appl. Phys. 96, 1979-1982 (2004).
    [CrossRef]
  28. J. A. Kong, Electromagnetic Wave Theory (Wiley, 1975).
  29. T. M. Grzegorcyk, X. Chen, J. Pacheco, Jr., J. Chen, B.-I. Wu, and J. A. Kong, "Reflection coefficients and Goos-Hänchen shifts in anisotropic and bianisotropic left-handed metamaterials," Prog. Electromagn. Res. 51, 83-113 (2005).
    [CrossRef]

2005

T. M. Grzegorczyk, Z. M. Thomas, and J. A. Kong, "Inversion of critical angle and Brewster angle in anisotropic left-handed metamaterials," Appl. Phys. Lett. 86, 251909-1-251909-3 (2005).
[CrossRef]

H. O. Moser, B. D. F. Casse, O. Wilhelmi, and B. T. Saw, "Terahertz response of a microfabricated rod-split-ring-resonator electromagnetic metamaterial," Phys. Rev. Lett. 94, 063901-1-063901-4 (2005).
[CrossRef]

X. Chen, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, "Retrieval of the effective constitutive parameters of bianisotropic metamaterials," Phys. Rev. E 71, 046610-1-046610-9 (2005).
[CrossRef]

T. M. Grzegorcyk, X. Chen, J. Pacheco, Jr., J. Chen, B.-I. Wu, and J. A. Kong, "Reflection coefficients and Goos-Hänchen shifts in anisotropic and bianisotropic left-handed metamaterials," Prog. Electromagn. Res. 51, 83-113 (2005).
[CrossRef]

N. Katsarakis, G. Konstantinidis, A. Kostopoulos, R. S. Penciu, T. F. Gundogdu, Th. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Magnetic response of split-ring resonators in the far-infrared frequency regime," Opt. Lett. 30, 1348-1350 (2005).
[CrossRef] [PubMed]

2004

D. R. Smith, P. Kolinko, and D. Schurig, "Negative refraction in indefinite media," J. Opt. Soc. Am. B 21, 1032-1043 (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, 3778-3784 (2004).
[CrossRef]

Y.-J. Hsu, Y.-C. Huang, J.-S. Lih, and J.-L. Chern, "Electromagnetic resonance in deformed split ring resonators of left-handed meta-materials," J. Appl. Phys. 96, 1979-1982 (2004).
[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, 2943-2945 (2004).
[CrossRef]

T. Koschny, M. Kafesakis, E. N. Economou, and C. M. Soukoulis, "Effective medium theory of left-handed materials," Phys. Rev. Lett. 93, 107402-1-107402-4 (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. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100THz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

2003

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, 107401-1-107401-4 (2003).
[CrossRef]

D. M. Wu, N. Fang, C. Sun, and X. Zhang, "Terahertz plasmonic high pass filter," Appl. Phys. Lett. 83, 201-203 (2003).
[CrossRef]

2002

P. Gay-Balmaz and O. J. F. Martin, "Electromagnetic resonances in individual and coupled split-ring resonators," J. Appl. Phys. 92, 2929-2936 (2002).
[CrossRef]

B. Ferguson and X.-C. Zhang, "Materials for terahertz science and technology," Nat. Mater. 1, 26-33 (2002).
[CrossRef]

R. Marqués, F. Medina, and R. Rafii-El-Idrissi, "Role of bianisotropy in negative permeability and left-handed metamaterials," Phys. Rev. B 65, 144440-1-144440-6 (2002).
[CrossRef]

2001

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

M. Schall, M. Walther, and P. U. Jepsen, "Fundamental and second-order phonon processes in CdTe and ZnTe," Phys. Rev. B 64, 094301-1-094301-5 (2001).
[CrossRef]

P. Y. Han, M. Tani, M. Usami, S. Kono, R. Kersting, and X.-C. Zhang, "A direct comparison between terahertz time-domain spectroscopy and far-infrared Fourier transform spectroscopy," J. Appl. Phys. 89, 2357-2359 (2001).
[CrossRef]

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

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

1999

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

1996

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]

1990

1989

1968

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of epsi and μ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

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

Casse, B. D. F.

H. O. Moser, B. D. F. Casse, O. Wilhelmi, and B. T. Saw, "Terahertz response of a microfabricated rod-split-ring-resonator electromagnetic metamaterial," Phys. Rev. Lett. 94, 063901-1-063901-4 (2005).
[CrossRef]

Chen, J.

T. M. Grzegorcyk, X. Chen, J. Pacheco, Jr., J. Chen, B.-I. Wu, and J. A. Kong, "Reflection coefficients and Goos-Hänchen shifts in anisotropic and bianisotropic left-handed metamaterials," Prog. Electromagn. Res. 51, 83-113 (2005).
[CrossRef]

Chen, X.

T. M. Grzegorcyk, X. Chen, J. Pacheco, Jr., J. Chen, B.-I. Wu, and J. A. Kong, "Reflection coefficients and Goos-Hänchen shifts in anisotropic and bianisotropic left-handed metamaterials," Prog. Electromagn. Res. 51, 83-113 (2005).
[CrossRef]

X. Chen, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, "Retrieval of the effective constitutive parameters of bianisotropic metamaterials," Phys. Rev. E 71, 046610-1-046610-9 (2005).
[CrossRef]

Chern, J.-L.

Y.-J. Hsu, Y.-C. Huang, J.-S. Lih, and J.-L. Chern, "Electromagnetic resonance in deformed split ring resonators of left-handed meta-materials," J. Appl. Phys. 96, 1979-1982 (2004).
[CrossRef]

Economou, E. N.

N. Katsarakis, G. Konstantinidis, A. Kostopoulos, R. S. Penciu, T. F. Gundogdu, Th. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Magnetic response of split-ring resonators in the far-infrared frequency regime," Opt. Lett. 30, 1348-1350 (2005).
[CrossRef] [PubMed]

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, 2943-2945 (2004).
[CrossRef]

T. Koschny, M. Kafesakis, E. N. Economou, and C. M. Soukoulis, "Effective medium theory of left-handed materials," Phys. Rev. Lett. 93, 107402-1-107402-4 (2004).
[CrossRef]

Enkrich, C.

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100THz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Exter, M. V.

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]

D. M. Wu, N. Fang, C. Sun, and X. Zhang, "Terahertz plasmonic high pass filter," Appl. Phys. Lett. 83, 201-203 (2003).
[CrossRef]

Fattinger, C.

Fattinger, Ch.

Ferguson, B.

B. Ferguson and X.-C. Zhang, "Materials for terahertz science and technology," Nat. Mater. 1, 26-33 (2002).
[CrossRef]

Gay-Balmaz, P.

P. Gay-Balmaz and O. J. F. Martin, "Electromagnetic resonances in individual and coupled split-ring resonators," J. Appl. Phys. 92, 2929-2936 (2002).
[CrossRef]

Greegor, R. B.

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, 107401-1-107401-4 (2003).
[CrossRef]

Grischkowsky, D.

Grzegorcyk, T. M.

T. M. Grzegorcyk, X. Chen, J. Pacheco, Jr., J. Chen, B.-I. Wu, and J. A. Kong, "Reflection coefficients and Goos-Hänchen shifts in anisotropic and bianisotropic left-handed metamaterials," Prog. Electromagn. Res. 51, 83-113 (2005).
[CrossRef]

Grzegorczyk, T. M.

T. M. Grzegorczyk, Z. M. Thomas, and J. A. Kong, "Inversion of critical angle and Brewster angle in anisotropic left-handed metamaterials," Appl. Phys. Lett. 86, 251909-1-251909-3 (2005).
[CrossRef]

X. Chen, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, "Retrieval of the effective constitutive parameters of bianisotropic metamaterials," Phys. Rev. E 71, 046610-1-046610-9 (2005).
[CrossRef]

Gundogdu, T. F.

Han, P. Y.

P. Y. Han, M. Tani, M. Usami, S. Kono, R. Kersting, and X.-C. Zhang, "A direct comparison between terahertz time-domain spectroscopy and far-infrared Fourier transform spectroscopy," J. Appl. Phys. 89, 2357-2359 (2001).
[CrossRef]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors 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]

Hsu, Y.-J.

Y.-J. Hsu, Y.-C. Huang, J.-S. Lih, and J.-L. Chern, "Electromagnetic resonance in deformed split ring resonators of left-handed meta-materials," J. Appl. Phys. 96, 1979-1982 (2004).
[CrossRef]

Huang, Y.-C.

Y.-J. Hsu, Y.-C. Huang, J.-S. Lih, and J.-L. Chern, "Electromagnetic resonance in deformed split ring resonators of left-handed meta-materials," J. Appl. Phys. 96, 1979-1982 (2004).
[CrossRef]

Inoue, K.

K. Inoue and K. Ohtaka, Photonic Crystals: Physics, Fabrication and Applications (Springer, 2004).

Jepsen, P. U.

M. Schall, M. Walther, and P. U. Jepsen, "Fundamental and second-order phonon processes in CdTe and ZnTe," Phys. Rev. B 64, 094301-1-094301-5 (2001).
[CrossRef]

Kafesaki, M.

Kafesakis, M.

T. Koschny, M. Kafesakis, E. N. Economou, and C. M. Soukoulis, "Effective medium theory of left-handed materials," Phys. Rev. Lett. 93, 107402-1-107402-4 (2004).
[CrossRef]

Kalinin, V.

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, 3778-3784 (2004).
[CrossRef]

Katsarakis, N.

Keiding, S.

Kersting, R.

P. Y. Han, M. Tani, M. Usami, S. Kono, R. Kersting, and X.-C. Zhang, "A direct comparison between terahertz time-domain spectroscopy and far-infrared Fourier transform spectroscopy," J. Appl. Phys. 89, 2357-2359 (2001).
[CrossRef]

Kolinko, P.

Koltenbah, B. E. C.

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, 107401-1-107401-4 (2003).
[CrossRef]

Kong, J. A.

T. M. Grzegorczyk, Z. M. Thomas, and J. A. Kong, "Inversion of critical angle and Brewster angle in anisotropic left-handed metamaterials," Appl. Phys. Lett. 86, 251909-1-251909-3 (2005).
[CrossRef]

X. Chen, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, "Retrieval of the effective constitutive parameters of bianisotropic metamaterials," Phys. Rev. E 71, 046610-1-046610-9 (2005).
[CrossRef]

T. M. Grzegorcyk, X. Chen, J. Pacheco, Jr., J. Chen, B.-I. Wu, and J. A. Kong, "Reflection coefficients and Goos-Hänchen shifts in anisotropic and bianisotropic left-handed metamaterials," Prog. Electromagn. Res. 51, 83-113 (2005).
[CrossRef]

J. A. Kong, Electromagnetic Wave Theory (Wiley, 1975).

Kono, S.

P. Y. Han, M. Tani, M. Usami, S. Kono, R. Kersting, and X.-C. Zhang, "A direct comparison between terahertz time-domain spectroscopy and far-infrared Fourier transform spectroscopy," J. Appl. Phys. 89, 2357-2359 (2001).
[CrossRef]

Konstantinidis, G.

Koschny, T.

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, 2943-2945 (2004).
[CrossRef]

T. Koschny, M. Kafesakis, E. N. Economou, and C. M. Soukoulis, "Effective medium theory of left-handed materials," Phys. Rev. Lett. 93, 107402-1-107402-4 (2004).
[CrossRef]

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100THz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Koschny, Th.

Kostopoulos, A.

Li, K.

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, 107401-1-107401-4 (2003).
[CrossRef]

Lih, J.-S.

Y.-J. Hsu, Y.-C. Huang, J.-S. Lih, and J.-L. Chern, "Electromagnetic resonance in deformed split ring resonators of left-handed meta-materials," J. Appl. Phys. 96, 1979-1982 (2004).
[CrossRef]

Linden, S.

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100THz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Marqués, R.

R. Marqués, F. Medina, and R. Rafii-El-Idrissi, "Role of bianisotropy in negative permeability and left-handed metamaterials," Phys. Rev. B 65, 144440-1-144440-6 (2002).
[CrossRef]

Martin, O. J. F.

P. Gay-Balmaz and O. J. F. Martin, "Electromagnetic resonances in individual and coupled split-ring resonators," J. Appl. Phys. 92, 2929-2936 (2002).
[CrossRef]

Medina, F.

R. Marqués, F. Medina, and R. Rafii-El-Idrissi, "Role of bianisotropy in negative permeability and left-handed metamaterials," Phys. Rev. B 65, 144440-1-144440-6 (2002).
[CrossRef]

Moser, H. O.

H. O. Moser, B. D. F. Casse, O. Wilhelmi, and B. T. Saw, "Terahertz response of a microfabricated rod-split-ring-resonator electromagnetic metamaterial," Phys. Rev. Lett. 94, 063901-1-063901-4 (2005).
[CrossRef]

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]

Ohtaka, K.

K. Inoue and K. Ohtaka, Photonic Crystals: Physics, Fabrication and Applications (Springer, 2004).

Pacheco, J.

T. M. Grzegorcyk, X. Chen, J. Pacheco, Jr., J. Chen, B.-I. Wu, and J. A. Kong, "Reflection coefficients and Goos-Hänchen shifts in anisotropic and bianisotropic left-handed metamaterials," Prog. Electromagn. Res. 51, 83-113 (2005).
[CrossRef]

Padilla, W. 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]

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]

Parazzoli, C. G.

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, 107401-1-107401-4 (2003).
[CrossRef]

Penciu, R. S.

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, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors 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]

Rafii-El-Idrissi, R.

R. Marqués, F. Medina, and R. Rafii-El-Idrissi, "Role of bianisotropy in negative permeability and left-handed metamaterials," Phys. Rev. B 65, 144440-1-144440-6 (2002).
[CrossRef]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors 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-split-ring-resonator electromagnetic metamaterial," Phys. Rev. Lett. 94, 063901-1-063901-4 (2005).
[CrossRef]

Schall, M.

M. Schall, M. Walther, and P. U. Jepsen, "Fundamental and second-order phonon processes in CdTe and ZnTe," Phys. Rev. B 64, 094301-1-094301-5 (2001).
[CrossRef]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, "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]

Schurig, D.

Shamonin, M.

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, 3778-3784 (2004).
[CrossRef]

Shamonina, E.

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, 3778-3784 (2004).
[CrossRef]

Shelby, R. A.

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

Smith, D. R.

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, P. Kolinko, and D. Schurig, "Negative refraction in indefinite media," J. Opt. Soc. Am. B 21, 1032-1043 (2004).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, "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]

Solymar, L.

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, 3778-3784 (2004).
[CrossRef]

Soukoulis, C. M.

N. Katsarakis, G. Konstantinidis, A. Kostopoulos, R. S. Penciu, T. F. Gundogdu, Th. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, "Magnetic response of split-ring resonators in the far-infrared frequency regime," Opt. Lett. 30, 1348-1350 (2005).
[CrossRef] [PubMed]

T. Koschny, M. Kafesakis, E. N. Economou, and C. M. Soukoulis, "Effective medium theory of left-handed materials," Phys. Rev. Lett. 93, 107402-1-107402-4 (2004).
[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, 2943-2945 (2004).
[CrossRef]

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100THz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors 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]

Sun, C.

D. M. Wu, N. Fang, C. Sun, and X. Zhang, "Terahertz plasmonic high pass filter," Appl. Phys. Lett. 83, 201-203 (2003).
[CrossRef]

Tani, M.

P. Y. Han, M. Tani, M. Usami, S. Kono, R. Kersting, and X.-C. Zhang, "A direct comparison between terahertz time-domain spectroscopy and far-infrared Fourier transform spectroscopy," J. Appl. Phys. 89, 2357-2359 (2001).
[CrossRef]

Tanielian, M.

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, 107401-1-107401-4 (2003).
[CrossRef]

Thomas, Z. M.

T. M. Grzegorczyk, Z. M. Thomas, and J. A. Kong, "Inversion of critical angle and Brewster angle in anisotropic left-handed metamaterials," Appl. Phys. Lett. 86, 251909-1-251909-3 (2005).
[CrossRef]

Usami, M.

P. Y. Han, M. Tani, M. Usami, S. Kono, R. Kersting, and X.-C. Zhang, "A direct comparison between terahertz time-domain spectroscopy and far-infrared Fourier transform spectroscopy," J. Appl. Phys. 89, 2357-2359 (2001).
[CrossRef]

Van Exter, M.

Veselago, V. G.

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of epsi and μ," Sov. Phys. Usp. 10, 509-514 (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, 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]

Walther, M.

M. Schall, M. Walther, and P. U. Jepsen, "Fundamental and second-order phonon processes in CdTe and ZnTe," Phys. Rev. B 64, 094301-1-094301-5 (2001).
[CrossRef]

Wegener, M.

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100THz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Wilhelmi, O.

H. O. Moser, B. D. F. Casse, O. Wilhelmi, and B. T. Saw, "Terahertz response of a microfabricated rod-split-ring-resonator electromagnetic metamaterial," Phys. Rev. Lett. 94, 063901-1-063901-4 (2005).
[CrossRef]

Wu, B.-I.

X. Chen, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, "Retrieval of the effective constitutive parameters of bianisotropic metamaterials," Phys. Rev. E 71, 046610-1-046610-9 (2005).
[CrossRef]

T. M. Grzegorcyk, X. Chen, J. Pacheco, Jr., J. Chen, B.-I. Wu, and J. A. Kong, "Reflection coefficients and Goos-Hänchen shifts in anisotropic and bianisotropic left-handed metamaterials," Prog. Electromagn. Res. 51, 83-113 (2005).
[CrossRef]

Wu, D. M.

D. M. Wu, N. Fang, C. Sun, and X. Zhang, "Terahertz plasmonic high pass filter," Appl. Phys. Lett. 83, 201-203 (2003).
[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]

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]

D. M. Wu, N. Fang, C. Sun, and X. Zhang, "Terahertz plasmonic high pass filter," Appl. Phys. Lett. 83, 201-203 (2003).
[CrossRef]

Zhang, X.-C.

B. Ferguson and X.-C. Zhang, "Materials for terahertz science and technology," Nat. Mater. 1, 26-33 (2002).
[CrossRef]

P. Y. Han, M. Tani, M. Usami, S. Kono, R. Kersting, and X.-C. Zhang, "A direct comparison between terahertz time-domain spectroscopy and far-infrared Fourier transform spectroscopy," J. Appl. Phys. 89, 2357-2359 (2001).
[CrossRef]

Zhou, J. F.

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100THz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Appl. Phys. Lett.

T. M. Grzegorczyk, Z. M. Thomas, and J. A. Kong, "Inversion of critical angle and Brewster angle in anisotropic left-handed metamaterials," Appl. Phys. Lett. 86, 251909-1-251909-3 (2005).
[CrossRef]

D. M. Wu, N. Fang, C. Sun, and X. Zhang, "Terahertz plasmonic high pass filter," Appl. Phys. Lett. 83, 201-203 (2003).
[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, 2943-2945 (2004).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

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

J. Appl. Phys.

P. Y. Han, M. Tani, M. Usami, S. Kono, R. Kersting, and X.-C. Zhang, "A direct comparison between terahertz time-domain spectroscopy and far-infrared Fourier transform spectroscopy," J. Appl. Phys. 89, 2357-2359 (2001).
[CrossRef]

P. Gay-Balmaz and O. J. F. Martin, "Electromagnetic resonances in individual and coupled split-ring resonators," J. Appl. Phys. 92, 2929-2936 (2002).
[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, 3778-3784 (2004).
[CrossRef]

Y.-J. Hsu, Y.-C. Huang, J.-S. Lih, and J.-L. Chern, "Electromagnetic resonance in deformed split ring resonators of left-handed meta-materials," J. Appl. Phys. 96, 1979-1982 (2004).
[CrossRef]

J. Opt. Soc. Am. B

Nat. Mater.

B. Ferguson and X.-C. Zhang, "Materials for terahertz science and technology," Nat. Mater. 1, 26-33 (2002).
[CrossRef]

Opt. Lett.

Phys. Rev. B

M. Schall, M. Walther, and P. U. Jepsen, "Fundamental and second-order phonon processes in CdTe and ZnTe," Phys. Rev. B 64, 094301-1-094301-5 (2001).
[CrossRef]

R. Marqués, F. Medina, and R. Rafii-El-Idrissi, "Role of bianisotropy in negative permeability and left-handed metamaterials," Phys. Rev. B 65, 144440-1-144440-6 (2002).
[CrossRef]

Phys. Rev. E

X. Chen, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, "Retrieval of the effective constitutive parameters of bianisotropic metamaterials," Phys. Rev. E 71, 046610-1-046610-9 (2005).
[CrossRef]

Phys. Rev. Lett.

H. O. Moser, B. D. F. Casse, O. Wilhelmi, and B. T. Saw, "Terahertz response of a microfabricated rod-split-ring-resonator electromagnetic metamaterial," Phys. Rev. Lett. 94, 063901-1-063901-4 (2005).
[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]

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, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[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, 107401-1-107401-4 (2003).
[CrossRef]

T. Koschny, M. Kafesakis, E. N. Economou, and C. M. Soukoulis, "Effective medium theory of left-handed materials," Phys. Rev. Lett. 93, 107402-1-107402-4 (2004).
[CrossRef]

Prog. Electromagn. Res.

T. M. Grzegorcyk, X. Chen, J. Pacheco, Jr., J. Chen, B.-I. Wu, and J. A. Kong, "Reflection coefficients and Goos-Hänchen shifts in anisotropic and bianisotropic left-handed metamaterials," Prog. Electromagn. Res. 51, 83-113 (2005).
[CrossRef]

Science

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]

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

S. Linden, C. Enkrich, M. Wegener, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100THz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Sov. Phys. Usp.

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of epsi and μ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Other

K. Inoue and K. Ohtaka, Photonic Crystals: Physics, Fabrication and Applications (Springer, 2004).

J. A. Kong, Electromagnetic Wave Theory (Wiley, 1975).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

(a) Schematic of a SRR on a quartz slab. (b) Schematic of in-plane SRR–wire metamaterials on a quartz slab. (c) The Cartesian coordinate system ( x , y , z ) is chosen in our experiment with the sample located in the x , y plane and the incident wave is along the z axis. The electric vector is along the x axis. The gap-bearing sides of the SRR is along the x axis. (d) Typical THz time-domain wave; the arrow indicates the peak of the THz wave.

Fig. 2
Fig. 2

(a) Angular dependence of the transmission of a THz peak signal through the SRR sample. (b) Transmission through the SRR sample as a function of frequency at different polarization orientations ( 0 ° , 30 ° , 60 ° , and 90 ° ).

Fig. 3
Fig. 3

(a) Angular dependence of the transmission of a THz peak signal through the in-plane SRR–wire metamaterials. (b) Transmission through the in-plane SRR–wire metamaterials as a function of frequency at different polarization orientations ( 0 ° , 30 ° , 60 ° , and 90 ° ).

Fig. 4
Fig. 4

Simulation of the transmission through the SRR sample as a function of frequency at different polarization orientations ( 0 ° , 30 ° , 60 ° , and 90 ° ).

Fig. 5
Fig. 5

Simulation of the transmission through the in-plane SRR–wire metamaterials as a function of frequency at different polarization orientations ( 0 ° , 30 ° , 60 ° , and 90 ° ).

Tables (1)

Tables Icon

Table 1 Theoretical Simulation Parameters for the Data Presented in Figs. 4, 5 a

Equations (33)

Equations on this page are rendered with MathJax. Learn more.

D = ε 0 ε ̿ E + 1 c ξ ̿ H ,
B = μ 0 μ ̿ H + 1 c χ ̿ E ,
k × E = ω B ,
k × H = ω D ,
k B = 0 ,
k D = 0 ,
[ ω 2 c 2 ( ε ̿ ξ ̿ μ ̿ 1 χ ̿ ) + ω c ( ξ ̿ μ ̿ 1 k K ̿ k K ̿ μ ̿ 1 ξ ̿ ) + k K ̿ μ ̿ 1 k K ̿ ] E = 0 ,
k K ̿ = [ 0 k z k y k z 0 k x k y k x 0 ] .
ε ̿ = [ ε x x 0 0 0 ε y y 0 0 0 ε z z ] , μ ̿ = [ μ x x 0 0 0 μ y y 0 0 0 μ z z ] ,
ξ ̿ = [ 0 0 i ξ x z 0 0 0 0 0 0 ] , χ ̿ = [ 0 0 0 0 0 0 i ξ x z 0 0 ] ,
[ ω 2 ε x x c 2 ω 2 ξ x z 2 c 2 μ z z k z 2 μ y y k y 2 μ z z , k x k y μ z z i ω k x ξ x z c μ z z , k x k z μ y y k x k y μ z z + i ω k x ξ x z c μ z z , ω 2 ε y y c 2 k z 2 μ x x k x 2 μ z z , k y k z μ x x k x k z μ y y , k y k z μ x x , ω 2 ε z z c 2 k y 2 μ x x k x 2 μ y y ] = 0 .
k z 2 = ω 2 c 2 ε y y μ x x ,
k z 2 = ω 2 c 2 ε x x μ y y ω 2 μ y y c 2 μ z z ξ x z 2 ,
E i = y ̂ E 0 e i k x x + i k z z ,
E r = y ̂ R TE E 0 e i k r x x i k r z z ,
E t = y ̂ T TE E 0 e i k t x x + i k t z z ,
H i = x ̂ k z E 0 μ 0 ω e i k x x + i k z z + z ̂ k x E 0 μ 0 ω e i k x x + i k z z ,
H r = x ̂ k r z E 0 μ 0 ω R TE e i k r x x i k r z z + z ̂ k r x E 0 μ 0 ω R TE e i k r x x i k r z z ,
H t = x ̂ k t z E 0 μ 0 μ x x ω T TE e i k t x x + i k t z z + z ̂ k t x E 0 μ 0 μ z z ω T TE e i k t x x + i k t z z .
n × ( E 1 E 2 ) = 0 ,
n × ( H 1 H 2 ) = 0 .
T TE = 2 1 + k t z ( k 0 μ x x ) ,
R TE = 1 2 1 + k t z ( k 0 μ x x ) .
T TM = 2 1 + k t z ( k 0 ε x x ) ,
R TE = 1 2 1 + k t z ( k 0 ε x x ) .
T TE = 2 μ x x ( μ x x + ε y y μ x x ) ,
T TM = 2 ε x x ( ε x x + ε x x μ y y μ y y μ z z ξ x z 2 ) ,
R TE = 1 2 μ x x ( μ x x + ε y y μ x x ) ,
R TM = 1 2 ε x x ( ε x x + ε x x μ y y μ y y μ z z ξ x z 2 ) .
μ x x = μ y y = μ z z = 1 , ε x x ( ω ) = ε x x 0 ω p 1 2 ω 01 2 ω 2 ω 01 2 + i ω γ 1 ,
ε y y ( ω ) = ε y y 0 ω p 2 2 ω 02 2 ω 2 ω 02 2 + i ω γ 2 ,
ξ x z ( ω ) = ξ x z 0 ω m 1 2 ω m 2 2 ω 2 ω m 2 2 + i ω γ 3 ,
ε wire ( ω ) = ε 0 wire ω p 3 2 ( ω 2 + i ω γ 4 ) .

Metrics