Abstract

We propose a scheme to design a new type of optical metamaterial that can mimic the functionality of four-state atomic systems of N-type energy-level configuration with electromagnetically induced transparency (EIT). We show that in such metamaterial a transition from a single EIT to a double EIT of terahertz radiation may be easily achieved by actively tuning the intensity of the infrared pump field or passively tuning the geometrical parameters of resonator structures. In addition, the group velocity of the terahertz radiation can be varied from subluminal to superluminal by changing the pump field intensity. The scheme suggested here may be used to construct chip-scale slow and fast light devices and to realize rapidly responded switching of terahertz radiation at room temperature.

© 2013 OSA

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  7. J. Gea-Banacloche, M. Mumba, and M. Xiao, “Optical switching in arrays of quantum dots with dipole-dipole interaction,” Phys. Rev. B74, 165330 (2006).
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    [CrossRef] [PubMed]
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  16. Z. Dong, H. Liu, J. Cao, T. Li, S. Wang, S. Zhu, and X. Zhang, “Enhanced sensing performance by the plasmonic analog of electromagnetically induced transparency in active metamaterials,” Appl. Phys. Lett.97, 114101 (2010).
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  24. G. S. Agarwal and S. Dasgupta, “Superluminal propagation via coherent manipulation of the Raman gain process,” Phys. Rev. A70, 023802 (2004).
    [CrossRef]
  25. C. Hang and G. Huang, “Giant Kerr nonlinearity and weak-light superluminal optical solitons in a four-state atomic system with gain doublet,” Opt. Express18, 2952–2966 (2010).
    [CrossRef] [PubMed]
  26. R. B. Li, L. Deng, and E. D. Hagley, “Fast, All-Optical, Zero to π Continuously Controllable Kerr Phase Gates,”, Phys. Rev. Lett.110, 113903 (2013).
    [CrossRef]
  27. D. Han, H. Guo, Y. Bai, and H. Sun, “Subluminal and superluminal propagation of light in an N-type medium,” Phys. Lett. A334, 243–248 (2005).
    [CrossRef]
  28. X. Liu, J. Gu, R. Singh, Y. Ma, J. Zhu, Z. Tian, M. He, J. Han, and W. Zhang, “Electromagnetically induced transparency in terahertz plasmonic metamaterials via dual excitation pathways of the dark mode,” Appl. Phys. Lett.100, 131101 (2012).
    [CrossRef]
  29. Z. Li, Y. Ma, R. Huang, R. Singh, J. Gu, Z. Tian, J. Han, and W. Zhang, “Manipulating the plasmon-induced transparency in terahertz metamaterials,” Opt. Express19, 8912–8919 (2011).
    [CrossRef] [PubMed]
  30. Y. Ma, Z. Li, Y. Yang, R. Huang, R. Singh, S. Zhang, J. Gu, Z. Tian, J. Han, and W. Zhang, “Plasmon-induced transparency in twisted Fano terahertz metamaterials,” Opt. Mat. Express1, 391–399 (2011).
    [CrossRef]
  31. Q. Bai, C. Liu, J. Chen, C. Cheng, M. Kang, and H.-T. Wang, “Tunable slow light in semiconductor metamaterial in a broad terahertz regime,” J. Appl. Phys.107(9), 093104 (2010).
    [CrossRef]
  32. Y. Lu, X. Jin, H. Zheng, Y. Lee, J. Y. Rhee, and W. H. Jang, “Plasmonic electromagnetically induced transparency in symmetric structures,” Opt. Express.18, 13396–13401 (2010).
    [CrossRef] [PubMed]
  33. Y. Lu, J. Rhee, W. Jang, and Y. Lee, “Active manipulation of plasmonic electromagnetically induced transparency based on magnetic plasmon resonance,” Opt. Express.1820912–20917 (2010).
    [CrossRef] [PubMed]
  34. V. T. T. Thuy, N. T. Tung, J. W. Park, V. D. Lam, Y. P. Lee, and J. Y. Rhee, “Highly dispersive transparency in coupled metamaterials,” J. Opt.12115102 (2010).
    [CrossRef]

2013 (1)

R. B. Li, L. Deng, and E. D. Hagley, “Fast, All-Optical, Zero to π Continuously Controllable Kerr Phase Gates,”, Phys. Rev. Lett.110, 113903 (2013).
[CrossRef]

2012 (4)

R. Taubert, M. Hentschel, J. Kästel, and H. Giessen, “Classical analog of electromagnetically induced absorption in plasmonics,” Nano Lett.12, 1367–1371 (2012).
[CrossRef] [PubMed]

X. Liu, J. Gu, R. Singh, Y. Ma, J. Zhu, Z. Tian, M. He, J. Han, and W. Zhang, “Electromagnetically induced transparency in terahertz plasmonic metamaterials via dual excitation pathways of the dark mode,” Appl. Phys. Lett.100, 131101 (2012).
[CrossRef]

S. Satpathy, A. Roy, and A. Mohapatra, “Fano interference in classical oscillators,” Eur. J. Phys.33, 863–871 (2012).
[CrossRef]

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H.-T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun.3, 1151 (2012).
[CrossRef] [PubMed]

2011 (4)

Z. Han and S. I. Bozhevolnyi, “Plasmon-induced transparency with detuned ultracompact Fabry-Perot resonators in integrated plasmonic devices,” Opt. Express19, 3251–3257 (2011).
[CrossRef] [PubMed]

Z. Li, Y. Ma, R. Huang, R. Singh, J. Gu, Z. Tian, J. Han, and W. Zhang, “Manipulating the plasmon-induced transparency in terahertz metamaterials,” Opt. Express19, 8912–8919 (2011).
[CrossRef] [PubMed]

Y. Ma, Z. Li, Y. Yang, R. Huang, R. Singh, S. Zhang, J. Gu, Z. Tian, J. Han, and W. Zhang, “Plasmon-induced transparency in twisted Fano terahertz metamaterials,” Opt. Mat. Express1, 391–399 (2011).
[CrossRef]

N. Liu, M. Hentschel, T. Weiss, A. P. Alivisators, and H. Giessen, “Three-dimensional plasmon rulers,” Science332, 1407–1410 (2011).
[CrossRef] [PubMed]

2010 (6)

Q. Bai, C. Liu, J. Chen, C. Cheng, M. Kang, and H.-T. Wang, “Tunable slow light in semiconductor metamaterial in a broad terahertz regime,” J. Appl. Phys.107(9), 093104 (2010).
[CrossRef]

Y. Lu, X. Jin, H. Zheng, Y. Lee, J. Y. Rhee, and W. H. Jang, “Plasmonic electromagnetically induced transparency in symmetric structures,” Opt. Express.18, 13396–13401 (2010).
[CrossRef] [PubMed]

Y. Lu, J. Rhee, W. Jang, and Y. Lee, “Active manipulation of plasmonic electromagnetically induced transparency based on magnetic plasmon resonance,” Opt. Express.1820912–20917 (2010).
[CrossRef] [PubMed]

V. T. T. Thuy, N. T. Tung, J. W. Park, V. D. Lam, Y. P. Lee, and J. Y. Rhee, “Highly dispersive transparency in coupled metamaterials,” J. Opt.12115102 (2010).
[CrossRef]

C. Hang and G. Huang, “Giant Kerr nonlinearity and weak-light superluminal optical solitons in a four-state atomic system with gain doublet,” Opt. Express18, 2952–2966 (2010).
[CrossRef] [PubMed]

Z. Dong, H. Liu, J. Cao, T. Li, S. Wang, S. Zhu, and X. Zhang, “Enhanced sensing performance by the plasmonic analog of electromagnetically induced transparency in active metamaterials,” Appl. Phys. Lett.97, 114101 (2010).
[CrossRef]

2009 (1)

2008 (2)

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett.101, 047401 (2008).
[CrossRef] [PubMed]

H. Wu, M. Xiao, and J. Gea-Banacloche, “Evidence of lasing without inversion in a hot rubidium vapor under electromagnetically induced transparency conditions,” Phys. Rev. A78, 041802(R) (2008).
[CrossRef]

2007 (1)

T. N. Dey and G. S. Agarwal, “Observable effects of Kerr nonlinearity on slow light,” Phys. Rev. A76, 015802 (2007).
[CrossRef]

2006 (1)

J. Gea-Banacloche, M. Mumba, and M. Xiao, “Optical switching in arrays of quantum dots with dipole-dipole interaction,” Phys. Rev. B74, 165330 (2006).
[CrossRef]

2005 (3)

G. Huang, L. Deng, and M. G. Payne, “Dynamics of ultraslow optical solitons in a cold three-state atomic system,” Phys. Rev. E72, 016617 (2005).
[CrossRef]

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys.77, 633–673 (2005).
[CrossRef]

D. Han, H. Guo, Y. Bai, and H. Sun, “Subluminal and superluminal propagation of light in an N-type medium,” Phys. Lett. A334, 243–248 (2005).
[CrossRef]

2004 (2)

G. S. Agarwal and S. Dasgupta, “Superluminal propagation via coherent manipulation of the Raman gain process,” Phys. Rev. A70, 023802 (2004).
[CrossRef]

Y. Wu and L. Deng, “Ultraslow Optical Solitons in a Cold Four-State Medium,” Phys. Rev. Lett.93, 143904 (2004).
[CrossRef] [PubMed]

2002 (3)

A. G. Litvak and M. D. Tokman, “Electromagnetically induced transparency in ensembles of classical oscillators,” Phys. Rev. Lett.88, 095003 (2002).
[CrossRef] [PubMed]

M. Fleischhauer and M. D. Lukin, “Quantum memory for photons: Dark-state polaritons,” Phys. Rev. A65, 022314 (2002).
[CrossRef]

C. L. G. Alzar, M. A. G. Martinez, and P. Nussenzveig, “Classical analog of electromagnetically induced transparency,” Am. J. Phys.70, 37–41 (2002).
[CrossRef]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental veritcation of a negative index of refraction,” Science292, 77–79 (2001).
[CrossRef] [PubMed]

2000 (2)

L. J. Wang, A. Kuzmich, and P. Pogariu, “Superluminal solitons in a Lambda-type atomic system with two-folded levels,” Nature (London)406, 277 (2000).
[CrossRef]

M. D. Lukin and A. Imamoglu, “Nonlinear Optics and Quantum Entanglement of Ultraslow Single Photons,” Phys. Rev. Lett.84, 1419 (2000).
[CrossRef] [PubMed]

1999 (2)

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A60, 3225–3228 (1999).
[CrossRef]

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]

Agarwal, G. S.

T. N. Dey and G. S. Agarwal, “Observable effects of Kerr nonlinearity on slow light,” Phys. Rev. A76, 015802 (2007).
[CrossRef]

G. S. Agarwal and S. Dasgupta, “Superluminal propagation via coherent manipulation of the Raman gain process,” Phys. Rev. A70, 023802 (2004).
[CrossRef]

Alivisators, A. P.

N. Liu, M. Hentschel, T. Weiss, A. P. Alivisators, and H. Giessen, “Three-dimensional plasmon rulers,” Science332, 1407–1410 (2011).
[CrossRef] [PubMed]

Alzar, C. L. G.

C. L. G. Alzar, M. A. G. Martinez, and P. Nussenzveig, “Classical analog of electromagnetically induced transparency,” Am. J. Phys.70, 37–41 (2002).
[CrossRef]

Azad, A. K.

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H.-T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun.3, 1151 (2012).
[CrossRef] [PubMed]

Bai, Q.

Q. Bai, C. Liu, J. Chen, C. Cheng, M. Kang, and H.-T. Wang, “Tunable slow light in semiconductor metamaterial in a broad terahertz regime,” J. Appl. Phys.107(9), 093104 (2010).
[CrossRef]

Bai, Y.

D. Han, H. Guo, Y. Bai, and H. Sun, “Subluminal and superluminal propagation of light in an N-type medium,” Phys. Lett. A334, 243–248 (2005).
[CrossRef]

Bozhevolnyi, S. I.

Cao, J.

Z. Dong, H. Liu, J. Cao, T. Li, S. Wang, S. Zhu, and X. Zhang, “Enhanced sensing performance by the plasmonic analog of electromagnetically induced transparency in active metamaterials,” Appl. Phys. Lett.97, 114101 (2010).
[CrossRef]

Chen, C.

Chen, H.-T.

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H.-T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun.3, 1151 (2012).
[CrossRef] [PubMed]

Chen, J.

Q. Bai, C. Liu, J. Chen, C. Cheng, M. Kang, and H.-T. Wang, “Tunable slow light in semiconductor metamaterial in a broad terahertz regime,” J. Appl. Phys.107(9), 093104 (2010).
[CrossRef]

Cheng, C.

Q. Bai, C. Liu, J. Chen, C. Cheng, M. Kang, and H.-T. Wang, “Tunable slow light in semiconductor metamaterial in a broad terahertz regime,” J. Appl. Phys.107(9), 093104 (2010).
[CrossRef]

Dasgupta, S.

G. S. Agarwal and S. Dasgupta, “Superluminal propagation via coherent manipulation of the Raman gain process,” Phys. Rev. A70, 023802 (2004).
[CrossRef]

Deng, L.

R. B. Li, L. Deng, and E. D. Hagley, “Fast, All-Optical, Zero to π Continuously Controllable Kerr Phase Gates,”, Phys. Rev. Lett.110, 113903 (2013).
[CrossRef]

G. Huang, L. Deng, and M. G. Payne, “Dynamics of ultraslow optical solitons in a cold three-state atomic system,” Phys. Rev. E72, 016617 (2005).
[CrossRef]

Y. Wu and L. Deng, “Ultraslow Optical Solitons in a Cold Four-State Medium,” Phys. Rev. Lett.93, 143904 (2004).
[CrossRef] [PubMed]

Dey, T. N.

T. N. Dey and G. S. Agarwal, “Observable effects of Kerr nonlinearity on slow light,” Phys. Rev. A76, 015802 (2007).
[CrossRef]

Dong, Z.

Z. Dong, H. Liu, J. Cao, T. Li, S. Wang, S. Zhu, and X. Zhang, “Enhanced sensing performance by the plasmonic analog of electromagnetically induced transparency in active metamaterials,” Appl. Phys. Lett.97, 114101 (2010).
[CrossRef]

Fleischhauer, M.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys.77, 633–673 (2005).
[CrossRef]

M. Fleischhauer and M. D. Lukin, “Quantum memory for photons: Dark-state polaritons,” Phys. Rev. A65, 022314 (2002).
[CrossRef]

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A60, 3225–3228 (1999).
[CrossRef]

Gea-Banacloche, J.

H. Wu, M. Xiao, and J. Gea-Banacloche, “Evidence of lasing without inversion in a hot rubidium vapor under electromagnetically induced transparency conditions,” Phys. Rev. A78, 041802(R) (2008).
[CrossRef]

J. Gea-Banacloche, M. Mumba, and M. Xiao, “Optical switching in arrays of quantum dots with dipole-dipole interaction,” Phys. Rev. B74, 165330 (2006).
[CrossRef]

Genov, D. A.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett.101, 047401 (2008).
[CrossRef] [PubMed]

Giessen, H.

R. Taubert, M. Hentschel, J. Kästel, and H. Giessen, “Classical analog of electromagnetically induced absorption in plasmonics,” Nano Lett.12, 1367–1371 (2012).
[CrossRef] [PubMed]

N. Liu, M. Hentschel, T. Weiss, A. P. Alivisators, and H. Giessen, “Three-dimensional plasmon rulers,” Science332, 1407–1410 (2011).
[CrossRef] [PubMed]

Gu, J.

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H.-T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun.3, 1151 (2012).
[CrossRef] [PubMed]

X. Liu, J. Gu, R. Singh, Y. Ma, J. Zhu, Z. Tian, M. He, J. Han, and W. Zhang, “Electromagnetically induced transparency in terahertz plasmonic metamaterials via dual excitation pathways of the dark mode,” Appl. Phys. Lett.100, 131101 (2012).
[CrossRef]

Y. Ma, Z. Li, Y. Yang, R. Huang, R. Singh, S. Zhang, J. Gu, Z. Tian, J. Han, and W. Zhang, “Plasmon-induced transparency in twisted Fano terahertz metamaterials,” Opt. Mat. Express1, 391–399 (2011).
[CrossRef]

Z. Li, Y. Ma, R. Huang, R. Singh, J. Gu, Z. Tian, J. Han, and W. Zhang, “Manipulating the plasmon-induced transparency in terahertz metamaterials,” Opt. Express19, 8912–8919 (2011).
[CrossRef] [PubMed]

Guo, H.

D. Han, H. Guo, Y. Bai, and H. Sun, “Subluminal and superluminal propagation of light in an N-type medium,” Phys. Lett. A334, 243–248 (2005).
[CrossRef]

Hagley, E. D.

R. B. Li, L. Deng, and E. D. Hagley, “Fast, All-Optical, Zero to π Continuously Controllable Kerr Phase Gates,”, Phys. Rev. Lett.110, 113903 (2013).
[CrossRef]

Han, D.

D. Han, H. Guo, Y. Bai, and H. Sun, “Subluminal and superluminal propagation of light in an N-type medium,” Phys. Lett. A334, 243–248 (2005).
[CrossRef]

Han, J.

X. Liu, J. Gu, R. Singh, Y. Ma, J. Zhu, Z. Tian, M. He, J. Han, and W. Zhang, “Electromagnetically induced transparency in terahertz plasmonic metamaterials via dual excitation pathways of the dark mode,” Appl. Phys. Lett.100, 131101 (2012).
[CrossRef]

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H.-T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun.3, 1151 (2012).
[CrossRef] [PubMed]

Y. Ma, Z. Li, Y. Yang, R. Huang, R. Singh, S. Zhang, J. Gu, Z. Tian, J. Han, and W. Zhang, “Plasmon-induced transparency in twisted Fano terahertz metamaterials,” Opt. Mat. Express1, 391–399 (2011).
[CrossRef]

Z. Li, Y. Ma, R. Huang, R. Singh, J. Gu, Z. Tian, J. Han, and W. Zhang, “Manipulating the plasmon-induced transparency in terahertz metamaterials,” Opt. Express19, 8912–8919 (2011).
[CrossRef] [PubMed]

Han, Z.

Hang, C.

He, M.

X. Liu, J. Gu, R. Singh, Y. Ma, J. Zhu, Z. Tian, M. He, J. Han, and W. Zhang, “Electromagnetically induced transparency in terahertz plasmonic metamaterials via dual excitation pathways of the dark mode,” Appl. Phys. Lett.100, 131101 (2012).
[CrossRef]

Hentschel, M.

R. Taubert, M. Hentschel, J. Kästel, and H. Giessen, “Classical analog of electromagnetically induced absorption in plasmonics,” Nano Lett.12, 1367–1371 (2012).
[CrossRef] [PubMed]

N. Liu, M. Hentschel, T. Weiss, A. P. Alivisators, and H. Giessen, “Three-dimensional plasmon rulers,” Science332, 1407–1410 (2011).
[CrossRef] [PubMed]

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]

Huang, G.

C. Hang and G. Huang, “Giant Kerr nonlinearity and weak-light superluminal optical solitons in a four-state atomic system with gain doublet,” Opt. Express18, 2952–2966 (2010).
[CrossRef] [PubMed]

G. Huang, L. Deng, and M. G. Payne, “Dynamics of ultraslow optical solitons in a cold three-state atomic system,” Phys. Rev. E72, 016617 (2005).
[CrossRef]

Huang, R.

Z. Li, Y. Ma, R. Huang, R. Singh, J. Gu, Z. Tian, J. Han, and W. Zhang, “Manipulating the plasmon-induced transparency in terahertz metamaterials,” Opt. Express19, 8912–8919 (2011).
[CrossRef] [PubMed]

Y. Ma, Z. Li, Y. Yang, R. Huang, R. Singh, S. Zhang, J. Gu, Z. Tian, J. Han, and W. Zhang, “Plasmon-induced transparency in twisted Fano terahertz metamaterials,” Opt. Mat. Express1, 391–399 (2011).
[CrossRef]

Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys.77, 633–673 (2005).
[CrossRef]

M. D. Lukin and A. Imamoglu, “Nonlinear Optics and Quantum Entanglement of Ultraslow Single Photons,” Phys. Rev. Lett.84, 1419 (2000).
[CrossRef] [PubMed]

Jang, W.

Y. Lu, J. Rhee, W. Jang, and Y. Lee, “Active manipulation of plasmonic electromagnetically induced transparency based on magnetic plasmon resonance,” Opt. Express.1820912–20917 (2010).
[CrossRef] [PubMed]

Jang, W. H.

Y. Lu, X. Jin, H. Zheng, Y. Lee, J. Y. Rhee, and W. H. Jang, “Plasmonic electromagnetically induced transparency in symmetric structures,” Opt. Express.18, 13396–13401 (2010).
[CrossRef] [PubMed]

Jin, X.

Y. Lu, X. Jin, H. Zheng, Y. Lee, J. Y. Rhee, and W. H. Jang, “Plasmonic electromagnetically induced transparency in symmetric structures,” Opt. Express.18, 13396–13401 (2010).
[CrossRef] [PubMed]

Kang, M.

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R. Taubert, M. Hentschel, J. Kästel, and H. Giessen, “Classical analog of electromagnetically induced absorption in plasmonics,” Nano Lett.12, 1367–1371 (2012).
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L. J. Wang, A. Kuzmich, and P. Pogariu, “Superluminal solitons in a Lambda-type atomic system with two-folded levels,” Nature (London)406, 277 (2000).
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V. T. T. Thuy, N. T. Tung, J. W. Park, V. D. Lam, Y. P. Lee, and J. Y. Rhee, “Highly dispersive transparency in coupled metamaterials,” J. Opt.12115102 (2010).
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Y. Lu, X. Jin, H. Zheng, Y. Lee, J. Y. Rhee, and W. H. Jang, “Plasmonic electromagnetically induced transparency in symmetric structures,” Opt. Express.18, 13396–13401 (2010).
[CrossRef] [PubMed]

Y. Lu, J. Rhee, W. Jang, and Y. Lee, “Active manipulation of plasmonic electromagnetically induced transparency based on magnetic plasmon resonance,” Opt. Express.1820912–20917 (2010).
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V. T. T. Thuy, N. T. Tung, J. W. Park, V. D. Lam, Y. P. Lee, and J. Y. Rhee, “Highly dispersive transparency in coupled metamaterials,” J. Opt.12115102 (2010).
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Z. Dong, H. Liu, J. Cao, T. Li, S. Wang, S. Zhu, and X. Zhang, “Enhanced sensing performance by the plasmonic analog of electromagnetically induced transparency in active metamaterials,” Appl. Phys. Lett.97, 114101 (2010).
[CrossRef]

Li, Z.

Z. Li, Y. Ma, R. Huang, R. Singh, J. Gu, Z. Tian, J. Han, and W. Zhang, “Manipulating the plasmon-induced transparency in terahertz metamaterials,” Opt. Express19, 8912–8919 (2011).
[CrossRef] [PubMed]

Y. Ma, Z. Li, Y. Yang, R. Huang, R. Singh, S. Zhang, J. Gu, Z. Tian, J. Han, and W. Zhang, “Plasmon-induced transparency in twisted Fano terahertz metamaterials,” Opt. Mat. Express1, 391–399 (2011).
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A. G. Litvak and M. D. Tokman, “Electromagnetically induced transparency in ensembles of classical oscillators,” Phys. Rev. Lett.88, 095003 (2002).
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Q. Bai, C. Liu, J. Chen, C. Cheng, M. Kang, and H.-T. Wang, “Tunable slow light in semiconductor metamaterial in a broad terahertz regime,” J. Appl. Phys.107(9), 093104 (2010).
[CrossRef]

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Z. Dong, H. Liu, J. Cao, T. Li, S. Wang, S. Zhu, and X. Zhang, “Enhanced sensing performance by the plasmonic analog of electromagnetically induced transparency in active metamaterials,” Appl. Phys. Lett.97, 114101 (2010).
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S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett.101, 047401 (2008).
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N. Liu, M. Hentschel, T. Weiss, A. P. Alivisators, and H. Giessen, “Three-dimensional plasmon rulers,” Science332, 1407–1410 (2011).
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J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H.-T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun.3, 1151 (2012).
[CrossRef] [PubMed]

X. Liu, J. Gu, R. Singh, Y. Ma, J. Zhu, Z. Tian, M. He, J. Han, and W. Zhang, “Electromagnetically induced transparency in terahertz plasmonic metamaterials via dual excitation pathways of the dark mode,” Appl. Phys. Lett.100, 131101 (2012).
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Y. Lu, X. Jin, H. Zheng, Y. Lee, J. Y. Rhee, and W. H. Jang, “Plasmonic electromagnetically induced transparency in symmetric structures,” Opt. Express.18, 13396–13401 (2010).
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J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H.-T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun.3, 1151 (2012).
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X. Liu, J. Gu, R. Singh, Y. Ma, J. Zhu, Z. Tian, M. He, J. Han, and W. Zhang, “Electromagnetically induced transparency in terahertz plasmonic metamaterials via dual excitation pathways of the dark mode,” Appl. Phys. Lett.100, 131101 (2012).
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Y. Ma, Z. Li, Y. Yang, R. Huang, R. Singh, S. Zhang, J. Gu, Z. Tian, J. Han, and W. Zhang, “Plasmon-induced transparency in twisted Fano terahertz metamaterials,” Opt. Mat. Express1, 391–399 (2011).
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Z. Li, Y. Ma, R. Huang, R. Singh, J. Gu, Z. Tian, J. Han, and W. Zhang, “Manipulating the plasmon-induced transparency in terahertz metamaterials,” Opt. Express19, 8912–8919 (2011).
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J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H.-T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun.3, 1151 (2012).
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J. Gea-Banacloche, M. Mumba, and M. Xiao, “Optical switching in arrays of quantum dots with dipole-dipole interaction,” Phys. Rev. B74, 165330 (2006).
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V. T. T. Thuy, N. T. Tung, J. W. Park, V. D. Lam, Y. P. Lee, and J. Y. Rhee, “Highly dispersive transparency in coupled metamaterials,” J. Opt.12115102 (2010).
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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).
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L. J. Wang, A. Kuzmich, and P. Pogariu, “Superluminal solitons in a Lambda-type atomic system with two-folded levels,” Nature (London)406, 277 (2000).
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Rhee, J.

Y. Lu, J. Rhee, W. Jang, and Y. Lee, “Active manipulation of plasmonic electromagnetically induced transparency based on magnetic plasmon resonance,” Opt. Express.1820912–20917 (2010).
[CrossRef] [PubMed]

Rhee, J. Y.

Y. Lu, X. Jin, H. Zheng, Y. Lee, J. Y. Rhee, and W. H. Jang, “Plasmonic electromagnetically induced transparency in symmetric structures,” Opt. Express.18, 13396–13401 (2010).
[CrossRef] [PubMed]

V. T. T. Thuy, N. T. Tung, J. W. Park, V. D. Lam, Y. P. Lee, and J. Y. Rhee, “Highly dispersive transparency in coupled metamaterials,” J. Opt.12115102 (2010).
[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).
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Roy, A.

S. Satpathy, A. Roy, and A. Mohapatra, “Fano interference in classical oscillators,” Eur. J. Phys.33, 863–871 (2012).
[CrossRef]

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S. Satpathy, A. Roy, and A. Mohapatra, “Fano interference in classical oscillators,” Eur. J. Phys.33, 863–871 (2012).
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M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A60, 3225–3228 (1999).
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R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental veritcation of a negative index of refraction,” Science292, 77–79 (2001).
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J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H.-T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun.3, 1151 (2012).
[CrossRef] [PubMed]

X. Liu, J. Gu, R. Singh, Y. Ma, J. Zhu, Z. Tian, M. He, J. Han, and W. Zhang, “Electromagnetically induced transparency in terahertz plasmonic metamaterials via dual excitation pathways of the dark mode,” Appl. Phys. Lett.100, 131101 (2012).
[CrossRef]

Y. Ma, Z. Li, Y. Yang, R. Huang, R. Singh, S. Zhang, J. Gu, Z. Tian, J. Han, and W. Zhang, “Plasmon-induced transparency in twisted Fano terahertz metamaterials,” Opt. Mat. Express1, 391–399 (2011).
[CrossRef]

Z. Li, Y. Ma, R. Huang, R. Singh, J. Gu, Z. Tian, J. Han, and W. Zhang, “Manipulating the plasmon-induced transparency in terahertz metamaterials,” Opt. Express19, 8912–8919 (2011).
[CrossRef] [PubMed]

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R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental veritcation of a negative index of refraction,” Science292, 77–79 (2001).
[CrossRef] [PubMed]

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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).
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D. Han, H. Guo, Y. Bai, and H. Sun, “Subluminal and superluminal propagation of light in an N-type medium,” Phys. Lett. A334, 243–248 (2005).
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Taubert, R.

R. Taubert, M. Hentschel, J. Kästel, and H. Giessen, “Classical analog of electromagnetically induced absorption in plasmonics,” Nano Lett.12, 1367–1371 (2012).
[CrossRef] [PubMed]

Taylor, A. J.

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H.-T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun.3, 1151 (2012).
[CrossRef] [PubMed]

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V. T. T. Thuy, N. T. Tung, J. W. Park, V. D. Lam, Y. P. Lee, and J. Y. Rhee, “Highly dispersive transparency in coupled metamaterials,” J. Opt.12115102 (2010).
[CrossRef]

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X. Liu, J. Gu, R. Singh, Y. Ma, J. Zhu, Z. Tian, M. He, J. Han, and W. Zhang, “Electromagnetically induced transparency in terahertz plasmonic metamaterials via dual excitation pathways of the dark mode,” Appl. Phys. Lett.100, 131101 (2012).
[CrossRef]

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H.-T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun.3, 1151 (2012).
[CrossRef] [PubMed]

Y. Ma, Z. Li, Y. Yang, R. Huang, R. Singh, S. Zhang, J. Gu, Z. Tian, J. Han, and W. Zhang, “Plasmon-induced transparency in twisted Fano terahertz metamaterials,” Opt. Mat. Express1, 391–399 (2011).
[CrossRef]

Z. Li, Y. Ma, R. Huang, R. Singh, J. Gu, Z. Tian, J. Han, and W. Zhang, “Manipulating the plasmon-induced transparency in terahertz metamaterials,” Opt. Express19, 8912–8919 (2011).
[CrossRef] [PubMed]

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A. G. Litvak and M. D. Tokman, “Electromagnetically induced transparency in ensembles of classical oscillators,” Phys. Rev. Lett.88, 095003 (2002).
[CrossRef] [PubMed]

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V. T. T. Thuy, N. T. Tung, J. W. Park, V. D. Lam, Y. P. Lee, and J. Y. Rhee, “Highly dispersive transparency in coupled metamaterials,” J. Opt.12115102 (2010).
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Q. Bai, C. Liu, J. Chen, C. Cheng, M. Kang, and H.-T. Wang, “Tunable slow light in semiconductor metamaterial in a broad terahertz regime,” J. Appl. Phys.107(9), 093104 (2010).
[CrossRef]

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L. J. Wang, A. Kuzmich, and P. Pogariu, “Superluminal solitons in a Lambda-type atomic system with two-folded levels,” Nature (London)406, 277 (2000).
[CrossRef]

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Z. Dong, H. Liu, J. Cao, T. Li, S. Wang, S. Zhu, and X. Zhang, “Enhanced sensing performance by the plasmonic analog of electromagnetically induced transparency in active metamaterials,” Appl. Phys. Lett.97, 114101 (2010).
[CrossRef]

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S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett.101, 047401 (2008).
[CrossRef] [PubMed]

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N. Liu, M. Hentschel, T. Weiss, A. P. Alivisators, and H. Giessen, “Three-dimensional plasmon rulers,” Science332, 1407–1410 (2011).
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H. Wu, M. Xiao, and J. Gea-Banacloche, “Evidence of lasing without inversion in a hot rubidium vapor under electromagnetically induced transparency conditions,” Phys. Rev. A78, 041802(R) (2008).
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[CrossRef]

J. Gea-Banacloche, M. Mumba, and M. Xiao, “Optical switching in arrays of quantum dots with dipole-dipole interaction,” Phys. Rev. B74, 165330 (2006).
[CrossRef]

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Y. Ma, Z. Li, Y. Yang, R. Huang, R. Singh, S. Zhang, J. Gu, Z. Tian, J. Han, and W. Zhang, “Plasmon-induced transparency in twisted Fano terahertz metamaterials,” Opt. Mat. Express1, 391–399 (2011).
[CrossRef]

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M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A60, 3225–3228 (1999).
[CrossRef]

Yen, T.

Zhang, S.

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H.-T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun.3, 1151 (2012).
[CrossRef] [PubMed]

Y. Ma, Z. Li, Y. Yang, R. Huang, R. Singh, S. Zhang, J. Gu, Z. Tian, J. Han, and W. Zhang, “Plasmon-induced transparency in twisted Fano terahertz metamaterials,” Opt. Mat. Express1, 391–399 (2011).
[CrossRef]

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett.101, 047401 (2008).
[CrossRef] [PubMed]

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J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H.-T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun.3, 1151 (2012).
[CrossRef] [PubMed]

X. Liu, J. Gu, R. Singh, Y. Ma, J. Zhu, Z. Tian, M. He, J. Han, and W. Zhang, “Electromagnetically induced transparency in terahertz plasmonic metamaterials via dual excitation pathways of the dark mode,” Appl. Phys. Lett.100, 131101 (2012).
[CrossRef]

Y. Ma, Z. Li, Y. Yang, R. Huang, R. Singh, S. Zhang, J. Gu, Z. Tian, J. Han, and W. Zhang, “Plasmon-induced transparency in twisted Fano terahertz metamaterials,” Opt. Mat. Express1, 391–399 (2011).
[CrossRef]

Z. Li, Y. Ma, R. Huang, R. Singh, J. Gu, Z. Tian, J. Han, and W. Zhang, “Manipulating the plasmon-induced transparency in terahertz metamaterials,” Opt. Express19, 8912–8919 (2011).
[CrossRef] [PubMed]

Zhang, X.

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H.-T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun.3, 1151 (2012).
[CrossRef] [PubMed]

Z. Dong, H. Liu, J. Cao, T. Li, S. Wang, S. Zhu, and X. Zhang, “Enhanced sensing performance by the plasmonic analog of electromagnetically induced transparency in active metamaterials,” Appl. Phys. Lett.97, 114101 (2010).
[CrossRef]

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett.101, 047401 (2008).
[CrossRef] [PubMed]

Zheng, H.

Y. Lu, X. Jin, H. Zheng, Y. Lee, J. Y. Rhee, and W. H. Jang, “Plasmonic electromagnetically induced transparency in symmetric structures,” Opt. Express.18, 13396–13401 (2010).
[CrossRef] [PubMed]

Zhu, J.

X. Liu, J. Gu, R. Singh, Y. Ma, J. Zhu, Z. Tian, M. He, J. Han, and W. Zhang, “Electromagnetically induced transparency in terahertz plasmonic metamaterials via dual excitation pathways of the dark mode,” Appl. Phys. Lett.100, 131101 (2012).
[CrossRef]

Zhu, S.

Z. Dong, H. Liu, J. Cao, T. Li, S. Wang, S. Zhu, and X. Zhang, “Enhanced sensing performance by the plasmonic analog of electromagnetically induced transparency in active metamaterials,” Appl. Phys. Lett.97, 114101 (2010).
[CrossRef]

Am. J. Phys. (1)

C. L. G. Alzar, M. A. G. Martinez, and P. Nussenzveig, “Classical analog of electromagnetically induced transparency,” Am. J. Phys.70, 37–41 (2002).
[CrossRef]

Appl. Phys. Lett. (2)

Z. Dong, H. Liu, J. Cao, T. Li, S. Wang, S. Zhu, and X. Zhang, “Enhanced sensing performance by the plasmonic analog of electromagnetically induced transparency in active metamaterials,” Appl. Phys. Lett.97, 114101 (2010).
[CrossRef]

X. Liu, J. Gu, R. Singh, Y. Ma, J. Zhu, Z. Tian, M. He, J. Han, and W. Zhang, “Electromagnetically induced transparency in terahertz plasmonic metamaterials via dual excitation pathways of the dark mode,” Appl. Phys. Lett.100, 131101 (2012).
[CrossRef]

Eur. J. Phys. (1)

S. Satpathy, A. Roy, and A. Mohapatra, “Fano interference in classical oscillators,” Eur. J. Phys.33, 863–871 (2012).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

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. (1)

Q. Bai, C. Liu, J. Chen, C. Cheng, M. Kang, and H.-T. Wang, “Tunable slow light in semiconductor metamaterial in a broad terahertz regime,” J. Appl. Phys.107(9), 093104 (2010).
[CrossRef]

J. Opt. (1)

V. T. T. Thuy, N. T. Tung, J. W. Park, V. D. Lam, Y. P. Lee, and J. Y. Rhee, “Highly dispersive transparency in coupled metamaterials,” J. Opt.12115102 (2010).
[CrossRef]

Nano Lett. (1)

R. Taubert, M. Hentschel, J. Kästel, and H. Giessen, “Classical analog of electromagnetically induced absorption in plasmonics,” Nano Lett.12, 1367–1371 (2012).
[CrossRef] [PubMed]

Nat. Commun. (1)

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H.-T. Chen, A. J. Taylor, J. Han, and W. Zhang, “Active control of electromagnetically induced transparency analogue in terahertz metamaterials,” Nat. Commun.3, 1151 (2012).
[CrossRef] [PubMed]

Nature (London) (1)

L. J. Wang, A. Kuzmich, and P. Pogariu, “Superluminal solitons in a Lambda-type atomic system with two-folded levels,” Nature (London)406, 277 (2000).
[CrossRef]

Opt. Express (4)

Opt. Express. (2)

Y. Lu, X. Jin, H. Zheng, Y. Lee, J. Y. Rhee, and W. H. Jang, “Plasmonic electromagnetically induced transparency in symmetric structures,” Opt. Express.18, 13396–13401 (2010).
[CrossRef] [PubMed]

Y. Lu, J. Rhee, W. Jang, and Y. Lee, “Active manipulation of plasmonic electromagnetically induced transparency based on magnetic plasmon resonance,” Opt. Express.1820912–20917 (2010).
[CrossRef] [PubMed]

Opt. Mat. Express (1)

Y. Ma, Z. Li, Y. Yang, R. Huang, R. Singh, S. Zhang, J. Gu, Z. Tian, J. Han, and W. Zhang, “Plasmon-induced transparency in twisted Fano terahertz metamaterials,” Opt. Mat. Express1, 391–399 (2011).
[CrossRef]

Phys. Lett. A (1)

D. Han, H. Guo, Y. Bai, and H. Sun, “Subluminal and superluminal propagation of light in an N-type medium,” Phys. Lett. A334, 243–248 (2005).
[CrossRef]

Phys. Rev. A (5)

G. S. Agarwal and S. Dasgupta, “Superluminal propagation via coherent manipulation of the Raman gain process,” Phys. Rev. A70, 023802 (2004).
[CrossRef]

H. Wu, M. Xiao, and J. Gea-Banacloche, “Evidence of lasing without inversion in a hot rubidium vapor under electromagnetically induced transparency conditions,” Phys. Rev. A78, 041802(R) (2008).
[CrossRef]

T. N. Dey and G. S. Agarwal, “Observable effects of Kerr nonlinearity on slow light,” Phys. Rev. A76, 015802 (2007).
[CrossRef]

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A60, 3225–3228 (1999).
[CrossRef]

M. Fleischhauer and M. D. Lukin, “Quantum memory for photons: Dark-state polaritons,” Phys. Rev. A65, 022314 (2002).
[CrossRef]

Phys. Rev. B (1)

J. Gea-Banacloche, M. Mumba, and M. Xiao, “Optical switching in arrays of quantum dots with dipole-dipole interaction,” Phys. Rev. B74, 165330 (2006).
[CrossRef]

Phys. Rev. E (1)

G. Huang, L. Deng, and M. G. Payne, “Dynamics of ultraslow optical solitons in a cold three-state atomic system,” Phys. Rev. E72, 016617 (2005).
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Phys. Rev. Lett. (5)

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic of the unit cell. The plasmonic system consists of a bright element (CW) and two dark elements (SRRs). The geometrical parameters are L = 85, w = 5, a = 29, b = 5, d1 = 10, d2 = 14, h = 495, Px = 80 and Py = 120μm, respectively. The right hand of panel (a) is microscopic image of the fabricated metamaterial. (b) Possible experimental arrangement of the optical pump-terahertz probe measurement. (c) Equivalent atomic model. Energy level structure and excitation scheme of the lifetime-broadened four-level N-type atomic system with upper energy level |4〉, |3〉 and lower energy levels |1〉, |2〉. Δ2, Δ3 and Δ4 are detunings. Ωp, Ωc, and Ωd are half Rabi frequencies of the probe, control, and assisted fields, respectively.

Fig. 2
Fig. 2

The real part Re(χ/χ0) (blue dashed line) and imaginary part (red solid line) of the normalized susceptibility χ/χ0 as a function of frequency and the pump-field intensity. The power of the infrared pump field is taken as 0 (a), 75 mW (b), 320 mW (c), and 1350 mW (d), respectively.

Fig. 3
Fig. 3

The real part Re(χ/χ0) (blue dashed line) and imaginary part Im(χ/χ0) (red solid line) of the normalized susceptibility χ/χ0 as a function of frequency and the coupling coefficient κ2. Coupling coefficient κ2 is taken as 0 (a), 0.015 THz2 (b), 0.035 THz2 (c), and 0.045 THz2 (d), respectively.

Fig. 4
Fig. 4

(a) The group index ng as a function of the pump power. (b) The absorption coefficient α as a function of the pump power. (c) The superluminal propagation (Vg = −3.3 c) of the terahertz radiation with pump power 300 mW. (d) The subluminal propagation (Vg = 0.02 c) of the terahertz radiation with pump power 1350 mW. The initial condition is E = E0e−0.25(t/τ)2 with τ = 10−12 s.

Equations (11)

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i t ( a 1 a 2 a 3 a 4 ) = ( 0 0 Ω p * 0 0 d 2 Ω c * Ω d * Ω p Ω c d 3 0 0 Ω d 0 d 4 ) ( a 1 a 2 a 3 a 4 )
λ ( a ˜ 1 a ˜ 2 a ˜ 3 a ˜ 4 ) = ( 0 0 Ω p * 0 0 Δ 2 Ω c * Ω d * Ω p Ω c d 3 0 0 Ω d 0 Δ 4 ) ( a ˜ 1 a ˜ 2 a ˜ 3 a ˜ 4 ) ,
| ψ dark = 1 1 + | Ω p | 2 | Ω c | 2 + | Ω p | 2 | Ω d | 2 Δ 4 2 | Ω c | 2 ( | 1 Ω p Ω c | 2 + Ω p Ω d Δ 4 Ω c | 4 ) ,
ω ± = ( δ 2 + δ 4 ) ± ( δ 2 + δ 4 ) 2 + 4 | Ω d | 2 2 ,
x ¨ 1 ( t ) + γ 1 x ˙ 1 ( t ) + ω 0 2 x 1 ( t ) κ 1 x 2 ( t ) = g E ,
x ¨ 2 ( t ) + γ 2 x ˙ 2 ( t ) + ω 0 2 x 2 ( t ) κ 1 x 1 ( t ) κ 2 x 3 ( t ) = 0 ,
x ¨ 3 ( t ) + γ 3 x ˙ 3 ( t ) + ω 0 2 x 3 ( t ) κ 2 x 2 ( t ) = 0 ,
x ˜ 1 = g E 0 ( D 2 D 3 κ 2 2 ) D 1 ( D 2 D 3 κ 2 2 ) κ 1 2 D 3
ω r ± = ω 0 2 ± κ 2 .
i ( z + 1 c t ) E 0 + ω 2 c χ E 0 = 0 ,
n g = 1 + Re χ ( ω ) + ω 2 Re χ ( ω ) ω .

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