Abstract

We established a novel method to evaluate effective optical constants by terahertz (THz) time domain spectroscopy and suggested a strict definition of optical constants and an expression for electromagnetic energy loss following the second law of thermodynamics. We deduced the effective optical constants of phosphor bronze wire grids in the THz region experimentally and theoretically. The results depend strongly on the polarization of the THz waves. When the electric field is parallel to the wires, we observed Drude-like electric permittivities with a plasma frequency reduced by a factor of 10-3, whereas when the field is perpendicular, the sample behaved as a simple dielectric film. We also observed unexpected magnetic permeabilities, which originate from the non-resonant real magnetic response of finite size-conductors.

© 2008 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  28. T. Driscoll, G. O. Andreev, D. N. Basov, S. Palit, T. Ren, J. Mock, S.-Y. Cho, N. M. Jokerst, and D. R. Smith, "Quantitative investigation of terahertz artificial magnetic resonance using oblique angle spectroscopy," Appl. Phys. Lett. 90, 092508 (2007).
    [CrossRef]
  29. B.-I. 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]
  30. E. Gornov, K.-E. Peiponen, Y. Svirko, Y. Ino, and M. Kuwata-Gonokami, "Efficient dispersion relations for terahertz spectroscopy," Appl. Phys. Lett. 89, 142903 (2006).
    [CrossRef]
  31. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
    [CrossRef]

2007 (8)

E. Saenzz, P. M. T. Ikonen, R. Gonzalo, and S. A. Tretyakov, "On the definition of effective permittivity and permeability for thin composite layers," J. Appl. Phys. 101, 114910 (2007).
[CrossRef]

W. J. Padilla, M. T. Aronsson, C. Highstrete, M. Lee, A. J. Taylor, and R. D. Averitt, "Electrically resonant terahertz metamaterials: Theoretical and experimental investigations," Phys. Rev. B 75, 041102 (2007).
[CrossRef]

T. Driscoll, D. N. Basov, E. 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, T. Ren, J. Mock, S.-Y. Cho, N. M. Jokerst, and D. R. Smith, "Quantitative investigation of terahertz artificial magnetic resonance using oblique angle spectroscopy," Appl. Phys. Lett. 90, 092508 (2007).
[CrossRef]

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

H.-Tong Chen, J. F. O’Hara, A. J. Taylor, R. D. Averitt, C. Highstrete, M. Lee, and W. J. Padilla, "Complementary planar terahertz metamaterials," Opt. Express 15, 1084-1095 (2007).
[CrossRef] [PubMed]

M. Iwanaga, "Effective optical constants in stratified metal-dielectric metamaterial," Opt. Lett. 32, 1314-1316 (2007).
[CrossRef] [PubMed]

H.-Tong Chen, W. J. Padilla, J. M. O. Zide, S. R. Bank, A. C. Gossard, A. J. Taylor, and R. D. Averitt, "Ultrafast optical switching of terahertz metamaterials fabricated on ErAs/GaAs nanoisland superlattices," Opt. lett. 32, 1620-1622 (2007).
[CrossRef] [PubMed]

2006 (3)

E. Gornov, K.-E. Peiponen, Y. Svirko, Y. Ino, and M. Kuwata-Gonokami, "Efficient dispersion relations for terahertz spectroscopy," Appl. Phys. Lett. 89, 142903 (2006).
[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.-Tong 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]

2005 (3)

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]

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

2004 (5)

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]

A. F. Starr, P. M. Rye, D. R. Smith, and S. Nemat-Nasser, "Fabrication and characterization o a negative-refractive-index composite metamaterial," Phys. Rev. B 70, 113102 (2004).
[CrossRef]

R. A. Depine and A. Lakhtakia, "Comment I on Resonant and antiresonant frequency dependence of the effective parameters of metamaterials", Phys. Rev. E 70, 048601 (2004).
[CrossRef]

A. L. Efros, "Comment II on Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 70, 048602 (2004).
[CrossRef]

T. Koschny, P. Markos, D. R. Smith, and C. Soukoulis, "Reply to Comments on Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 70, 048603 (2004).
[CrossRef]

2003 (2)

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

P. Markos and C. M. Soukoulis, "Transmission properties and effective electromagnetic parameters of double negative metamaterials," Opt. Express 11, 649-661 (2003).
[CrossRef] [PubMed]

2002 (1)

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

2001 (1)

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

1998 (3)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Low frequency plasmons in thin-wire structures," J. Phys.: Condens. Matter 104785-4809 (1998).
[CrossRef]

K. Ohataka, T. Ueta, and K. Amemiya "Calculation of photonic bands using vector cylindrical waves and reflectivity of light for an array of dielectric rods," Phys Rev. B 57, 2550-2568 (1998).
[CrossRef]

1974 (1)

W. B. Weir, "Automatic Measurement of complex dielectric constant and permeability at microwave frequencies," Proc. IEEE 62, 33-36 (1974).
[CrossRef]

1970 (1)

A. M. Nicolson and G. F. Ross, "Measurement of the intrinsic properties of material by time-domain techniques," IEEE Trans. Instrum. Meas. IM-19, 377-382 (1970).
[CrossRef]

1968 (1)

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

Amemiya, K.

K. Ohataka, T. Ueta, and K. Amemiya "Calculation of photonic bands using vector cylindrical waves and reflectivity of light for an array of dielectric rods," Phys Rev. B 57, 2550-2568 (1998).
[CrossRef]

Andreev, G. O.

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

Aronsson, M. T.

W. J. Padilla, M. T. Aronsson, C. Highstrete, M. Lee, A. J. Taylor, and R. D. Averitt, "Electrically resonant terahertz metamaterials: Theoretical and experimental investigations," Phys. Rev. B 75, 041102 (2007).
[CrossRef]

Averitt, R. D.

W. J. Padilla, M. T. Aronsson, C. Highstrete, M. Lee, A. J. Taylor, and R. D. Averitt, "Electrically resonant terahertz metamaterials: Theoretical and experimental investigations," Phys. Rev. B 75, 041102 (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]

Basov, D. N.

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

T. Driscoll, D. N. Basov, E. 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. 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]

Cho, S.-Y.

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

Cummer, S. A.

B.-I. 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]

Depine, R. A.

R. A. Depine and A. Lakhtakia, "Comment I on Resonant and antiresonant frequency dependence of the effective parameters of metamaterials", Phys. Rev. E 70, 048601 (2004).
[CrossRef]

Dolling, G.

Driscoll, T.

T. Driscoll, D. N. Basov, E. 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, T. Ren, J. Mock, S.-Y. Cho, N. M. Jokerst, and D. R. Smith, "Quantitative investigation of terahertz artificial magnetic resonance using oblique angle spectroscopy," Appl. Phys. Lett. 90, 092508 (2007).
[CrossRef]

Ebbesen, T. W.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Economou, E. N.

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

Efros, A. L.

A. L. Efros, "Comment II on Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 70, 048602 (2004).
[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]

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Gonzalo, R.

E. Saenzz, P. M. T. Ikonen, R. Gonzalo, and S. A. Tretyakov, "On the definition of effective permittivity and permeability for thin composite layers," J. Appl. Phys. 101, 114910 (2007).
[CrossRef]

Gornov, E.

E. Gornov, K.-E. Peiponen, Y. Svirko, Y. Ino, and M. Kuwata-Gonokami, "Efficient dispersion relations for terahertz spectroscopy," Appl. Phys. Lett. 89, 142903 (2006).
[CrossRef]

Highstrete, C.

W. J. Padilla, M. T. Aronsson, C. Highstrete, M. Lee, A. J. Taylor, and R. D. Averitt, "Electrically resonant terahertz metamaterials: Theoretical and experimental investigations," Phys. Rev. B 75, 041102 (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]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Low frequency plasmons in thin-wire structures," J. Phys.: Condens. Matter 104785-4809 (1998).
[CrossRef]

Ikonen, P. M. T.

E. Saenzz, P. M. T. Ikonen, R. Gonzalo, and S. A. Tretyakov, "On the definition of effective permittivity and permeability for thin composite layers," J. Appl. Phys. 101, 114910 (2007).
[CrossRef]

Ino, Y.

E. Gornov, K.-E. Peiponen, Y. Svirko, Y. Ino, and M. Kuwata-Gonokami, "Efficient dispersion relations for terahertz spectroscopy," Appl. Phys. Lett. 89, 142903 (2006).
[CrossRef]

Iwanaga, M.

Jokerst, N. M.

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

Koschny, T.

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

T. Koschny, P. Markos, D. R. Smith, and C. Soukoulis, "Reply to Comments on Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 70, 048603 (2004).
[CrossRef]

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

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]

Kuwata-Gonokami, M.

E. Gornov, K.-E. Peiponen, Y. Svirko, Y. Ino, and M. Kuwata-Gonokami, "Efficient dispersion relations for terahertz spectroscopy," Appl. Phys. Lett. 89, 142903 (2006).
[CrossRef]

Lakhtakia, A.

R. A. Depine and A. Lakhtakia, "Comment I on Resonant and antiresonant frequency dependence of the effective parameters of metamaterials", Phys. Rev. E 70, 048601 (2004).
[CrossRef]

Lee, M.

W. J. Padilla, M. T. Aronsson, C. Highstrete, M. Lee, A. J. Taylor, and R. D. Averitt, "Electrically resonant terahertz metamaterials: Theoretical and experimental investigations," Phys. Rev. B 75, 041102 (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]

Lezec, H. J.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Linden, S.

Markos, P.

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

T. Koschny, P. Markos, D. R. Smith, and C. Soukoulis, "Reply to Comments on Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 70, 048603 (2004).
[CrossRef]

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

P. Markos and C. M. Soukoulis, "Transmission properties and effective electromagnetic parameters of double negative metamaterials," Opt. Express 11, 649-661 (2003).
[CrossRef] [PubMed]

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

Mock, J.

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

Mock, J. J.

T. Driscoll, D. N. Basov, E. 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]

Nemat-Nasser, S.

A. F. Starr, P. M. Rye, D. R. Smith, and S. Nemat-Nasser, "Fabrication and characterization o a negative-refractive-index composite metamaterial," Phys. Rev. B 70, 113102 (2004).
[CrossRef]

Nicolson, A. M.

A. M. Nicolson and G. F. Ross, "Measurement of the intrinsic properties of material by time-domain techniques," IEEE Trans. Instrum. Meas. IM-19, 377-382 (1970).
[CrossRef]

Ohataka, K.

K. Ohataka, T. Ueta, and K. Amemiya "Calculation of photonic bands using vector cylindrical waves and reflectivity of light for an array of dielectric rods," Phys Rev. B 57, 2550-2568 (1998).
[CrossRef]

Padilla, E. J.

T. Driscoll, D. N. Basov, E. 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]

Padilla, W. J.

W. J. Padilla, M. T. Aronsson, C. Highstrete, M. Lee, A. J. Taylor, and R. D. Averitt, "Electrically resonant terahertz metamaterials: Theoretical and experimental investigations," Phys. Rev. B 75, 041102 (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]

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]

Palit, S.

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

Peiponen, K.-E.

E. Gornov, K.-E. Peiponen, Y. Svirko, Y. Ino, and M. Kuwata-Gonokami, "Efficient dispersion relations for terahertz spectroscopy," Appl. Phys. Lett. 89, 142903 (2006).
[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, and W. J. Stewart, "Low frequency plasmons in thin-wire structures," J. Phys.: Condens. Matter 104785-4809 (1998).
[CrossRef]

Popa, B.-I.

B.-I. 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]

Ren, T.

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

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Low frequency plasmons in thin-wire structures," J. Phys.: Condens. Matter 104785-4809 (1998).
[CrossRef]

Ross, G. F.

A. M. Nicolson and G. F. Ross, "Measurement of the intrinsic properties of material by time-domain techniques," IEEE Trans. Instrum. Meas. IM-19, 377-382 (1970).
[CrossRef]

Rye, P. M.

A. F. Starr, P. M. Rye, D. R. Smith, and S. Nemat-Nasser, "Fabrication and characterization o a negative-refractive-index composite metamaterial," Phys. Rev. B 70, 113102 (2004).
[CrossRef]

Saenzz, E.

E. Saenzz, P. M. T. Ikonen, R. Gonzalo, and S. A. Tretyakov, "On the definition of effective permittivity and permeability for thin composite layers," J. Appl. Phys. 101, 114910 (2007).
[CrossRef]

Schultz, S.

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

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

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

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

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]

A. F. Starr, P. M. Rye, D. R. Smith, and S. Nemat-Nasser, "Fabrication and characterization o a negative-refractive-index composite metamaterial," Phys. Rev. B 70, 113102 (2004).
[CrossRef]

T. Koschny, P. Markos, D. R. Smith, and C. Soukoulis, "Reply to Comments on Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 70, 048603 (2004).
[CrossRef]

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

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

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

Soukoulis, C.

T. Koschny, P. Markos, D. R. Smith, and C. Soukoulis, "Reply to Comments on Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 70, 048603 (2004).
[CrossRef]

Soukoulis, C. M.

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, "Negative-index metamaterial at 780 nm wavelength," Opt. Lett. 32, 53-55 (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. Koschny, P. Markos, E. N. Economou, D. R. Smith, D. C. Vier, and C. M. Soukoulis, "Impact of inherent periodic structure on effective medium description of left-handed and related metamaterials," Phys. Rev. B 71, 245105 (2005).
[CrossRef]

P. Markos and C. M. Soukoulis, "Transmission properties and effective electromagnetic parameters of double negative metamaterials," Opt. Express 11, 649-661 (2003).
[CrossRef] [PubMed]

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

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

Starr, A. F.

A. F. Starr, P. M. Rye, D. R. Smith, and S. Nemat-Nasser, "Fabrication and characterization o a negative-refractive-index composite metamaterial," Phys. Rev. B 70, 113102 (2004).
[CrossRef]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Low frequency plasmons in thin-wire structures," J. Phys.: Condens. Matter 104785-4809 (1998).
[CrossRef]

Svirko, Y.

E. Gornov, K.-E. Peiponen, Y. Svirko, Y. Ino, and M. Kuwata-Gonokami, "Efficient dispersion relations for terahertz spectroscopy," Appl. Phys. Lett. 89, 142903 (2006).
[CrossRef]

Taylor, A. J.

W. J. Padilla, M. T. Aronsson, C. Highstrete, M. Lee, A. J. Taylor, and R. D. Averitt, "Electrically resonant terahertz metamaterials: Theoretical and experimental investigations," Phys. Rev. B 75, 041102 (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]

Thio, T.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Tretyakov, S. A.

E. Saenzz, P. M. T. Ikonen, R. Gonzalo, and S. A. Tretyakov, "On the definition of effective permittivity and permeability for thin composite layers," J. Appl. Phys. 101, 114910 (2007).
[CrossRef]

Ueta, T.

K. Ohataka, T. Ueta, and K. Amemiya "Calculation of photonic bands using vector cylindrical waves and reflectivity of light for an array of dielectric rods," Phys Rev. B 57, 2550-2568 (1998).
[CrossRef]

Veselago, V. G.

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

Vier, D. C.

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

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]

Wegener, M.

Weir, W. B.

W. B. Weir, "Automatic Measurement of complex dielectric constant and permeability at microwave frequencies," Proc. IEEE 62, 33-36 (1974).
[CrossRef]

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[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]

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]

Appl. Phys. Lett. (2)

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

E. Gornov, K.-E. Peiponen, Y. Svirko, Y. Ino, and M. Kuwata-Gonokami, "Efficient dispersion relations for terahertz spectroscopy," Appl. Phys. Lett. 89, 142903 (2006).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

A. M. Nicolson and G. F. Ross, "Measurement of the intrinsic properties of material by time-domain techniques," IEEE Trans. Instrum. Meas. IM-19, 377-382 (1970).
[CrossRef]

J. Appl. Phys. (1)

E. Saenzz, P. M. T. Ikonen, R. Gonzalo, and S. A. Tretyakov, "On the definition of effective permittivity and permeability for thin composite layers," J. Appl. Phys. 101, 114910 (2007).
[CrossRef]

J. Phys.: Condens. Matter (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Low frequency plasmons in thin-wire structures," J. Phys.: Condens. Matter 104785-4809 (1998).
[CrossRef]

Nature (2)

H.-Tong 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. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Phys Rev. B (1)

K. Ohataka, T. Ueta, and K. Amemiya "Calculation of photonic bands using vector cylindrical waves and reflectivity of light for an array of dielectric rods," Phys Rev. B 57, 2550-2568 (1998).
[CrossRef]

Phys. Rev. B (6)

A. F. Starr, P. M. Rye, D. R. Smith, and S. Nemat-Nasser, "Fabrication and characterization o a negative-refractive-index composite metamaterial," Phys. Rev. B 70, 113102 (2004).
[CrossRef]

W. J. Padilla, M. T. Aronsson, C. Highstrete, M. Lee, A. J. Taylor, and R. D. Averitt, "Electrically resonant terahertz metamaterials: Theoretical and experimental investigations," Phys. Rev. B 75, 041102 (2007).
[CrossRef]

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

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

T. Driscoll, D. N. Basov, E. 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]

Phys. Rev. E (5)

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

R. A. Depine and A. Lakhtakia, "Comment I on Resonant and antiresonant frequency dependence of the effective parameters of metamaterials", Phys. Rev. E 70, 048601 (2004).
[CrossRef]

A. L. Efros, "Comment II on Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 70, 048602 (2004).
[CrossRef]

T. Koschny, P. Markos, D. R. Smith, and C. Soukoulis, "Reply to Comments on Resonant and antiresonant frequency dependence of the effective parameters of metamaterials," Phys. Rev. E 70, 048603 (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. (1)

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]

Proc. IEEE (1)

W. B. Weir, "Automatic Measurement of complex dielectric constant and permeability at microwave frequencies," Proc. IEEE 62, 33-36 (1974).
[CrossRef]

Science (2)

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]

Sov. Phys. Usp. (1)

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

Other (2)

K. Cho, "Model-independent derivation of macroscopic Maxwell equations from microscopic basis: Beyond the "ε and μ" description," arXiv:cond-mat/0611235v4 [cond-mat.mtrl-sci] http://arxiv.org/abs/cond-mat/0611235v4.

L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media 2nd ed. (Elsevier, New York, 1984).

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Figures (7)

Fig. 1.
Fig. 1.

Schematic diagrams of (a) the transmission-type THz-TDS and (b) the reflection-type THz-TDS.

Fig. 2.
Fig. 2.

Phosphor bronze wire grid structures.

Fig. 3.
Fig. 3.

Power transmittance of four samples.

Fig. 4.
Fig. 4.

Complex transmission and reflection coefficients of sample A in the (a) parallel and (b) perpendicular configuration; the power transmittances and reflectances (middle), their addition (top), and the phase shifts (bottom). The doted curves are the computed results. The vertical dashed orange lines indicate νa .

Fig. 5.
Fig. 5.

Effective optical constants derived from the experiments (solid curves) and computations (dotted curves) conducted on sample A in the parallel configuration. The vertical dashed orange lines indicate νa .

Fig. 6.
Fig. 6.

Effective optical constants derived from the experiments (solid curves) and computations (dotted curves) conducted on sample A in the perpendicular configuration. The vertical dashed orange lines indicate νa .

Fig. 7.
Fig. 7.

Energy absorption spectrum calculated from the effective optical constants of sample A.

Tables (1)

Tables Icon

Table 1. Dimensions of the samples. α denotes the geometrical factor for the transmission area.

Equations (17)

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

{ n = k · s ̂ c ω e = z 0 z h × s ̂ ,
S ¯ = 1 2 Re ( e × h * )
= z 0 Re ( z ) 2 h 2 s ̂ ,
Q = · S U t ,
Q ¯ = · S ¯
= · Re ( 1 2 e × h * )
= 1 2 · s ̂ h 2 z 0 Re z
= Im ( n ) Re ( z ) ω µ 0 h 2 ,
Q ¯ = ω ε 0 2 e 2 µ ( [ ε µ + µ ε ] ) .
{ T = 4 z ( z + 1 ) 2 exp ( i ( n 1 ) ω d c ) 1 ( z 1 z + 1 ) 2 exp ( 2 in ω d c ) R = z 1 z + 1 4 z ( 1 z ) ( z + 1 ) 3 exp ( 2 in ω d c ) 1 ( z 1 z + 1 ) 2 exp ( 2 in ω d c ) ,
z 2 = T 2 ( 1 + R ) 2 T 2 ( 1 R ) 2 ,
n = c i ω d ln ( 1 + z ) R ( 1 z ) T + 1 T ,
{ ε = n z µ = nz .
ε ( ω ) = ε ω p 2 ω ( ω + i γ )
ω p 2 = π c 2 ad [ ln ( a ld ) + ld 2 a 2 1 2 ] , γ = a ω p 2 lc 2 µ 0 σ ( ω ) ,
ε ( ω ) = ε ( 0 ) a C ε 0 ,
α = 2 π r 2 ,

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