Abstract

Terahertz time-domain spectroscopy (THz-TDS) offers a new perspective for extraction of negative refractive index of low-loss metamaterials directly. We present the detailed extraction procedure how to obtain the negative refractive index of metamaterials through THz-TDS measurement. The basic equations are deduced to obtain the negative index through comparison of THz data measured for the sample and reference, respectively. Further simulation examples matching the practical experimental cases are given, which verifies that the extraction procedure is reliable. This approach demonstrates the potential use of THz-TDS in study of metamaterials and is helpful for design of metamaterial devices.

©2008 Optical Society of America

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  1. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968).
    [Crossref]
  2. 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]
  3. J. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
    [Crossref] [PubMed]
  4. C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104/1–4 (2002).
    [Crossref]
  5. B. C. Gupta and Z. Ye, “Disorder effects on the imaging of a negative refractive lens made by arrays of dielectric cylinders,” J. Appl. Phys 94, 2173–2176 (2003).
    [Crossref]
  6. Z. Ye, “Optical transmission and reflection of perfect lenses by left handed materials,” Phys. Rev. B 67, 193106/1–4 (2003).
    [Crossref]
  7. S. A. Cummer, “Dynamics of causal beam refraction in negative refractive index materials,” Appl. Phys. Lett. 82, 2008–2010 (2003).
    [Crossref]
  8. J. Pendry, “Electromagnetic materials enter the negative age,” Phys. World 14, 47–51 (2001).
  9. J. Pendry, A. J. Holden, D. D. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
    [Crossref]
  10. 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]
  11. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
    [Crossref] [PubMed]
  12. A. K. Azad, J. Dai, and W. Zhang, “Transmission properties of terahertz pulses through subwavelength double split-ring resonators,” Opt. Lett. 31, 634–636 (2006).
    [Crossref] [PubMed]
  13. 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, 107401/1–4 (2006).
    [Crossref] [PubMed]
  14. S. Linden, C. Enkrich, M. Wegener, J. Zhou, Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306, 1351–1353 (2004).
    [Crossref] [PubMed]
  15. B. Ferguson and X. C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1, 26–33 (2002).
    [Crossref]
  16. D. Grischkowsky, S. Keiding, M. van Exter, and Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B 7, 2006–2015 (1990).
    [Crossref]
  17. W. Zhang, A. K. Azad, and D. Grischkowsky, “Terahertz studies of carrier dynamics and dielectric response of n-type freestanding epitaxial GaN,” Appl. Phys. Lett. 82, 2841–2843 (2003).
    [Crossref]
  18. M. Born and E. Wolf, Principles of Optics (Fifth Edition, Pergamon Press, 1975), Chap. 1.
  19. L. Duvillaret, F. Garet, and J. L. Coutaz, “A reliable method for extraction of material parameters in terahertz time-domain spectroscopy,” IEEE J. Sel. Opt. Quantum Electron. 2, 739–746(1996).
    [Crossref]
  20. R. W. Ziolkowski and N. Enghetz, “Introduction, history and selected topics in fundamental theories of metamaterials” in Metamaterials: Physics and Engineering Explorations, (John Wiley and Sons, 2006).
  21. L. Duvillaret, F. Garet, and J. L. Coutaz, “Influence of noise on the characterization of materials by terahertz time-domain spectroscopy,” J. Opt. Soc. Am. B 17, 452–461 (2000).
    [Crossref]

2006 (2)

A. K. Azad, J. Dai, and W. Zhang, “Transmission properties of terahertz pulses through subwavelength double split-ring resonators,” Opt. Lett. 31, 634–636 (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, 107401/1–4 (2006).
[Crossref] [PubMed]

2004 (2)

S. Linden, C. Enkrich, M. Wegener, J. Zhou, Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306, 1351–1353 (2004).
[Crossref] [PubMed]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303, 1494–1496 (2004).
[Crossref] [PubMed]

2003 (4)

W. Zhang, A. K. Azad, and D. Grischkowsky, “Terahertz studies of carrier dynamics and dielectric response of n-type freestanding epitaxial GaN,” Appl. Phys. Lett. 82, 2841–2843 (2003).
[Crossref]

B. C. Gupta and Z. Ye, “Disorder effects on the imaging of a negative refractive lens made by arrays of dielectric cylinders,” J. Appl. Phys 94, 2173–2176 (2003).
[Crossref]

Z. Ye, “Optical transmission and reflection of perfect lenses by left handed materials,” Phys. Rev. B 67, 193106/1–4 (2003).
[Crossref]

S. A. Cummer, “Dynamics of causal beam refraction in negative refractive index materials,” Appl. Phys. Lett. 82, 2008–2010 (2003).
[Crossref]

2002 (2)

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104/1–4 (2002).
[Crossref]

B. Ferguson and X. C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1, 26–33 (2002).
[Crossref]

2001 (2)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[Crossref] [PubMed]

J. Pendry, “Electromagnetic materials enter the negative age,” Phys. World 14, 47–51 (2001).

2000 (3)

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. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[Crossref] [PubMed]

L. Duvillaret, F. Garet, and J. L. Coutaz, “Influence of noise on the characterization of materials by terahertz time-domain spectroscopy,” J. Opt. Soc. Am. B 17, 452–461 (2000).
[Crossref]

1999 (1)

J. Pendry, A. J. Holden, D. D. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
[Crossref]

1996 (1)

L. Duvillaret, F. Garet, and J. L. Coutaz, “A reliable method for extraction of material parameters in terahertz time-domain spectroscopy,” IEEE J. Sel. Opt. Quantum Electron. 2, 739–746(1996).
[Crossref]

1990 (1)

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968).
[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, 107401/1–4 (2006).
[Crossref] [PubMed]

Azad, A. K.

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

W. Zhang, A. K. Azad, and D. Grischkowsky, “Terahertz studies of carrier dynamics and dielectric response of n-type freestanding epitaxial GaN,” Appl. Phys. Lett. 82, 2841–2843 (2003).
[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]

Born, M.

M. Born and E. Wolf, Principles of Optics (Fifth Edition, Pergamon Press, 1975), Chap. 1.

Coutaz, J. L.

L. Duvillaret, F. Garet, and J. L. Coutaz, “Influence of noise on the characterization of materials by terahertz time-domain spectroscopy,” J. Opt. Soc. Am. B 17, 452–461 (2000).
[Crossref]

L. Duvillaret, F. Garet, and J. L. Coutaz, “A reliable method for extraction of material parameters in terahertz time-domain spectroscopy,” IEEE J. Sel. Opt. Quantum Electron. 2, 739–746(1996).
[Crossref]

Cummer, S. A.

S. A. Cummer, “Dynamics of causal beam refraction in negative refractive index materials,” Appl. Phys. Lett. 82, 2008–2010 (2003).
[Crossref]

Dai, J.

Duvillaret, L.

L. Duvillaret, F. Garet, and J. L. Coutaz, “Influence of noise on the characterization of materials by terahertz time-domain spectroscopy,” J. Opt. Soc. Am. B 17, 452–461 (2000).
[Crossref]

L. Duvillaret, F. Garet, and J. L. Coutaz, “A reliable method for extraction of material parameters in terahertz time-domain spectroscopy,” IEEE J. Sel. Opt. Quantum Electron. 2, 739–746(1996).
[Crossref]

Enghetz, N.

R. W. Ziolkowski and N. Enghetz, “Introduction, history and selected topics in fundamental theories of metamaterials” in Metamaterials: Physics and Engineering Explorations, (John Wiley and Sons, 2006).

Enkrich, C.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306, 1351–1353 (2004).
[Crossref] [PubMed]

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]

Fattinger,

Ferguson, B.

B. Ferguson and X. C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1, 26–33 (2002).
[Crossref]

Garet, F.

L. Duvillaret, F. Garet, and J. L. Coutaz, “Influence of noise on the characterization of materials by terahertz time-domain spectroscopy,” J. Opt. Soc. Am. B 17, 452–461 (2000).
[Crossref]

L. Duvillaret, F. Garet, and J. L. Coutaz, “A reliable method for extraction of material parameters in terahertz time-domain spectroscopy,” IEEE J. Sel. Opt. Quantum Electron. 2, 739–746(1996).
[Crossref]

Grischkowsky, D.

W. Zhang, A. K. Azad, and D. Grischkowsky, “Terahertz studies of carrier dynamics and dielectric response of n-type freestanding epitaxial GaN,” Appl. Phys. Lett. 82, 2841–2843 (2003).
[Crossref]

D. Grischkowsky, S. Keiding, M. van Exter, and Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B 7, 2006–2015 (1990).
[Crossref]

Gupta, B. C.

B. C. Gupta and Z. Ye, “Disorder effects on the imaging of a negative refractive lens made by arrays of dielectric cylinders,” J. Appl. Phys 94, 2173–2176 (2003).
[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, 107401/1–4 (2006).
[Crossref] [PubMed]

Holden, A. J.

J. Pendry, A. J. Holden, D. D. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
[Crossref]

Joannopoulos, J. D.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104/1–4 (2002).
[Crossref]

Johnson, S. G.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104/1–4 (2002).
[Crossref]

Keiding, S.

Koschny,

S. Linden, C. Enkrich, M. Wegener, J. Zhou, Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306, 1351–1353 (2004).
[Crossref] [PubMed]

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, 107401/1–4 (2006).
[Crossref] [PubMed]

Linden, S.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306, 1351–1353 (2004).
[Crossref] [PubMed]

Luo, C.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104/1–4 (2002).
[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]

Padilla, W. J.

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, 107401/1–4 (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]

Pendry, J.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104/1–4 (2002).
[Crossref]

J. Pendry, “Electromagnetic materials enter the negative age,” Phys. World 14, 47–51 (2001).

J. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[Crossref] [PubMed]

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

Robbins, D. D.

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

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

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]

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]

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. M.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306, 1351–1353 (2004).
[Crossref] [PubMed]

Stewart, W. J.

J. Pendry, A. J. Holden, D. D. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
[Crossref]

Taylor, A. J.

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, 107401/1–4 (2006).
[Crossref] [PubMed]

van Exter, M.

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. 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]

Wegener, M.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306, 1351–1353 (2004).
[Crossref] [PubMed]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Fifth Edition, Pergamon Press, 1975), Chap. 1.

Ye, Z.

B. C. Gupta and Z. Ye, “Disorder effects on the imaging of a negative refractive lens made by arrays of dielectric cylinders,” J. Appl. Phys 94, 2173–2176 (2003).
[Crossref]

Z. Ye, “Optical transmission and reflection of perfect lenses by left handed materials,” Phys. Rev. B 67, 193106/1–4 (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]

Zhang, W.

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

W. Zhang, A. K. Azad, and D. Grischkowsky, “Terahertz studies of carrier dynamics and dielectric response of n-type freestanding epitaxial GaN,” Appl. Phys. Lett. 82, 2841–2843 (2003).
[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]

Zhang, X. C.

B. Ferguson and X. C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1, 26–33 (2002).
[Crossref]

Zhou, J.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306, 1351–1353 (2004).
[Crossref] [PubMed]

Ziolkowski, R. W.

R. W. Ziolkowski and N. Enghetz, “Introduction, history and selected topics in fundamental theories of metamaterials” in Metamaterials: Physics and Engineering Explorations, (John Wiley and Sons, 2006).

Appl. Phys. Lett. (2)

S. A. Cummer, “Dynamics of causal beam refraction in negative refractive index materials,” Appl. Phys. Lett. 82, 2008–2010 (2003).
[Crossref]

W. Zhang, A. K. Azad, and D. Grischkowsky, “Terahertz studies of carrier dynamics and dielectric response of n-type freestanding epitaxial GaN,” Appl. Phys. Lett. 82, 2841–2843 (2003).
[Crossref]

IEEE J. Sel. Opt. Quantum Electron. (1)

L. Duvillaret, F. Garet, and J. L. Coutaz, “A reliable method for extraction of material parameters in terahertz time-domain spectroscopy,” IEEE J. Sel. Opt. Quantum Electron. 2, 739–746(1996).
[Crossref]

IEEE Trans. Microwave Theory Tech. (1)

J. Pendry, A. J. Holden, D. D. 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 (1)

B. C. Gupta and Z. Ye, “Disorder effects on the imaging of a negative refractive lens made by arrays of dielectric cylinders,” J. Appl. Phys 94, 2173–2176 (2003).
[Crossref]

J. Opt. Soc. Am. B (2)

Nat. Mater. (1)

B. Ferguson and X. C. Zhang, “Materials for terahertz science and technology,” Nat. Mater. 1, 26–33 (2002).
[Crossref]

Opt. Lett. (1)

Phys. Rev. B (2)

Z. Ye, “Optical transmission and reflection of perfect lenses by left handed materials,” Phys. Rev. B 67, 193106/1–4 (2003).
[Crossref]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104/1–4 (2002).
[Crossref]

Phys. Rev. Lett. (3)

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. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[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, 107401/1–4 (2006).
[Crossref] [PubMed]

Phys. World (1)

J. Pendry, “Electromagnetic materials enter the negative age,” Phys. World 14, 47–51 (2001).

Science (3)

S. Linden, C. Enkrich, M. Wegener, J. Zhou, Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306, 1351–1353 (2004).
[Crossref] [PubMed]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303, 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)

M. Born and E. Wolf, Principles of Optics (Fifth Edition, Pergamon Press, 1975), Chap. 1.

R. W. Ziolkowski and N. Enghetz, “Introduction, history and selected topics in fundamental theories of metamaterials” in Metamaterials: Physics and Engineering Explorations, (John Wiley and Sons, 2006).

Supplementary Material (1)

» Media 1: AVI (1467 KB)     

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Figures (5)

Fig. 1.
Fig. 1. Sketch of THz-TDS measurement for reference and sample.
Fig. 2.
Fig. 2. Illustration of reflection and refraction of a p-polarization plane wave incidence upon the interface of DPS and DNG medium.
Fig. 3.
Fig. 3. Demonstration of theoretical simulated distributions of electric field intensity for THz TDS measurements on metamaterial sample (upper) and corresponding reference (lower), respectively.
Fig.4.
Fig.4. (a). Sketch of THz-TDS measurement on the free-standing sample. (b) Comparison of extracted refractive index (circles) and assigned value (triangles) dependence on frequency.
Fig. 5.
Fig. 5. Theoretical demonstration of DPS-DNG pair. Electric field intensity distributions simulated for the sample case (upper) and reference case (lower). The animated electric field magnitude as a function of phase of the simulated DPS-DNG pair is seen clearly from the video. (AVI video, figure_05.avi, 1.43 MBytes). [Media 1]

Equations (45)

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E R ( ω ) = E i ( ω ) t 10 t 03 exp ( i k R d ) 1 + r 10 r 03 exp ( 2 i k R d ) ,
E S ( ω ) = E i ( ω ) t 12 t 23 exp ( i k S d ) 1 + r 12 r 23 exp ( 2 i k S d ) ,
t ab s = 2 n a cos θ i n a cos θ i + n b cos θ t , r ab s = n a cos θ i n b cos θ t n a cos θ i + n b cos θ t ,
t ab p = 2 n a cos θ i n b cos θ i + n a cos θ t , r ab p = n b cos θ i n a cos θ i n b cos θ i + n a cos θ y .
E R ( ω ) = E i ( ω ) t 10 t 03 exp ( i k R d ) ,
E S ( ω ) = E i ( ω ) t 12 t 23 exp ( i k S d ) ,
t ab = 2 n a n a + n b .
T ( ω ) = E S ( ω ) E R ( ω )
= t 12 t 23 t 10 t 03 exp [ i ( k S ( ω ) k R ( ω ) ) d ] .
= t 12 t 23 t 10 t 03 exp [ i ω c ( n S ( ω ) n R ( ω ) ) d ]
T ( ω ) = E S ( ω ) E R ( ω )
= t 12 t 23 t 10 t 03 exp [ i ω c ( n ~ S ( ω ) n R ( ω ) ) d ] ,
= t 12 t 23 t 10 t 03 exp [ i ω c ( n S ( ω ) n R ( ω ) ) d ] · exp [ α ( ω ) 2 d ]
ε ( ω ) = ε r ( ω ) + i ε i ( ω ) = ( n S ( ω ) + i κ ( ω ) ) 2 ,
ε r = n S 2 ( α c 2 ω ) 2 ,
ε i = α n S c ω .
E i = E i 0 exp [ j ( k i · r ω t ) ]
= E i 0 ( cos θ i e ̂ x sin θ i e ̂ z ) exp [ j ( k 1 x sin θ i + k 1 z cos θ i ω t ) ] ,
H i = H i 0 exp [ j ( k i · r ω t ) ]
= ε 1 μ 1 E i 0 exp [ j ( k 1 x sin θ i + k 1 z cos θ i ω t ) ] e ̂ y ,
E r = E r 0 exp [ j ( k r · r ω t ) ]
= E r 0 ( cos θ i e ̂ x sin θ i e ̂ z ) exp [ j ( k 1 x sin θ i + k 1 z cos θ i ω t ) ] ,
H r = H r 0 exp [ j ( k r · r ω t ) ]
= ε 1 μ 1 E r 0 exp [ j ( k 1 x sin θ i + k 1 z cos θ i ω t ) ] e ̂ y .
E t = E t 0 exp [ j ( k t · r ω t ) ]
= E t 0 ( cos θ t e ̂ x sin θ t e ̂ z ) exp [ j ( k 2 x sin θ t + k 2 z cos θ t ω t ) ] ,
H t = H t 0 exp [ j ( k t · r ω t ) ]
= ε 2 μ 2 E t 0 exp [ j ( k 2 x sin θ t k 2 z cos θ t ω t ) ] e ̂ y ,
E i 0 cos θ i E r 0 cos θ i = E t 0 cos θ t ,
ε 1 μ 1 E i 0 + ε 1 μ 1 E r 0 = ε 2 μ 2 E t 0 .
r 12 = E r 0 E i 0 = ε 2 μ 2 cos θ i ε 1 μ 1 cos θ t ε 2 μ 2 cos θ i + ε 1 μ 1 cos θ t , t 12 = E t 0 E i 0 = 2 cos θ i ε 1 μ 1 ε 2 μ 2 cos θ i + ε 1 μ 1 cos θ t .
r 12 = E r 0 E i 0 = ε 2 μ 2 ε 1 μ 1 ε 2 μ 2 + ε 1 μ 1 , t 12 = E t 0 E i 0 = 2 ε 1 μ 1 ε 2 μ 2 + ε 1 μ 1 .
E R ( ω ) = E i ( ω ) t 10 t 03 exp ( i k R d ) = E i ( ω ) t 10 t 03 exp ( i ω c n R d ) ,
E S ( ω ) = E i ( ω ) t 12 t 23 exp ( i k S d ) = E i ( ω ) t 12 t 23 exp ( i ω c n S d )
= E i ( ω ) t 12 t 23 exp ( i ω c n S d ) ,
t 10 = 2 n 1 n 1 + n R , t 03 = 2 n R n 3 + n R , t 12 = 2 ε 1 μ 1 ε 1 μ 1 + ε 2 μ 2 , t 23 = 2 ε 2 μ 2 ε 2 μ 2 + ε 3 μ 3 .
t 12 = 2 n 1 ε 2 μ 2 + n 1 , t 23 = 2 ε 2 μ 2 ε 2 μ 2 + n 3 .
T ( ω ) = E S ( ω ) E R ( ω )
= t 12 t 23 t 10 t 03 exp [ i ( k S ( ω ) k S ( ω ) ) d ]
= t 12 t 23 t 10 t 03 exp [ i ω c ( n s ( ω ) n R ( ω ) ) d ] .
T ( ω ) = E S ( ω ) E R ( ω )
= t 12 t 23 t 10 t 03 exp [ i ( k S ( ω ) k S ( ω ) ) d ]
= t 12 t 23 t 10 t 03 exp [ i ω c ( n s ( ω ) n R ( ω ) ) d ] · exp [ α ( ω ) 2 d ] ,
n S ( ω ) = n R ( ω ) + Δ ϕ · c ω d .
κ ( ω ) = c ω d ln ( t 10 t 03 t 12 t 23 · T ( ω ) ) .

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