## Plasmonic analog of electromagnetically induced transparency in nanostructure graphene |

Optics Express, Vol. 21, Issue 23, pp. 28438-28443 (2013)

http://dx.doi.org/10.1364/OE.21.028438

Acrobat PDF (1785 KB)

### Abstract

Graphene has shown intriguing optical properties as a new class of plasmonic material in the terahertz regime. In particular, plasmonic modes in graphene nanostructures can be confined to a spatial size that is hundreds of times smaller than their corresponding wavelengths in vacuum. Here, we show numerically that by designing graphene nanostructures in such deep-subwavelength scales, one can obtain plasmonic modes with the desired radiative properties such as radiative and dark modes. By placing the radiative and dark modes in the vicinity of each other, we further demonstrate electromagnetically induced transparency (EIT), analogous to the atomic EIT. At the transparent window, there exist very large group delays, one order of magnitude larger than those offered by metal structures. The EIT spectrum can be further tuned electrically by applying a gate voltage. Our results suggest that the demonstrated EIT based on graphene plasmonics may offer new possibilities for applications in photonics.

© 2013 Optical Society of America

## 1. Introduction

1. Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. **96**(12), 123901 (2006). [CrossRef] [PubMed]

6. Y. Sun, H. Jiang, Y. Yang, Y. Zhang, H. Chen, and S. Zhu, “Electromagnetically induced transparency in metamaterials: Influence of intrinsic loss and dynamic evolution,” Phys. Rev. B **83**(19), 195140 (2011). [CrossRef]

3. S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. **101**(4), 047401 (2008). [CrossRef] [PubMed]

7. T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B **80**(19), 195415 (2009). [CrossRef]

10. L. Verslegers, Z. Yu, Z. Ruan, P. B. Catrysse, and S. Fan, “From electromagnetically induced transparency to superscattering with a single structure: a coupled-mode theory for doubly resonant structures,” Phys. Rev. Lett. **108**(8), 083902 (2012). [CrossRef] [PubMed]

3. S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. **101**(4), 047401 (2008). [CrossRef] [PubMed]

8. N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. **8**(9), 758–762 (2009). [CrossRef] [PubMed]

11. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. **81**(1), 109–162 (2009). [CrossRef]

12. B. Wunsch, T. Stauber, F. Sols, and F. Guinea, “Dynamical polarization of graphene at finite doping,” New J. Phys. **8**(12), 318 (2006). [CrossRef]

14. M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B **80**(24), 245435 (2009). [CrossRef]

15. F. Bonaccorso, Z. Sun, T. Hassan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics **4**(9), 611–622 (2010). [CrossRef]

16. A. N. Grirorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics **6**(11), 749–758 (2012). [CrossRef]

12. B. Wunsch, T. Stauber, F. Sols, and F. Guinea, “Dynamical polarization of graphene at finite doping,” New J. Phys. **8**(12), 318 (2006). [CrossRef]

14. M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B **80**(24), 245435 (2009). [CrossRef]

*ω*is the angular frequency,

*k*is the wave vector,

*E*is the Fermi energy of the graphene layer,

_{F}*α*is the fine-structure constant,

*ħ*is the reduced Planck constant,

*c*is the speed of light in vacuum, and

*ε*

_{1}and

*ε*

_{2}are the dielectric constants of the two dielectrics. Such a dispersion relation shows two unique features. First, it exhibits modal profiles with a deep-subwavelength confinement. For instance, for a plasmon mode with a frequency of 20 THz (corresponding to a wavelength of 15 μm in vacuum) supported by a graphene layer in air the corresponding plasmon wavelength is smaller than 400 nm for

*E*eV. Such small modal sizes may open up new opportunities for engineering optical modes at a deep-subwavelength length scale.

_{F =0.15}17. F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science **320**(5873), 206–209 (2008). [CrossRef] [PubMed]

20. A. Yu Nikitin, F. Guinea, F. J. García-Vidal, and L. Martín-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B **84**(16), 161407 (2011). [CrossRef]

21. 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]

22. H. Ian, Y. X. Liu, and F. Nori, “Tunable electromagnetically induced transparency and absorption with dressed superconducting qubits,” Phys. Rev. A **81**(6), 063823 (2010). [CrossRef]

## 2. Design of plasmonic modes

3. S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. **101**(4), 047401 (2008). [CrossRef] [PubMed]

*x*direction. The dark element for dark modes consists of two identical parallel graphene strips with a dimension of 12 nm by 48 nm, lying along the

*y*direction. The separation between the two graphene strips is 8 nm. The basic unit of the graphene plasmonic structure for realizing EIT is a combination of the radiative and dark elements with a separation of 15 nm. This separation is a key parameter to control the coupling between the two modes. Large separations usually give rise to a weak coupling. All graphene nanostructures are situated on a supporting dielectric substrate with a dielectric constant of 2.1 and a thickness of 20 nm. Note that the resonant modes of the graphene nanostructures are also influenced by the dielectric constant of the substrate. This dependency on the substrate's dielectric constant may provide an additional degree of freedom to tailor the resonant modes.

*x‒y*plane and Floquet ports in the

*z*direction for terminating the domain. In the simulations, graphene is modeled by an ultrathin layer of electron gas whose conductivity is simply given by a Drude term [19

19. F. H. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. **11**(8), 3370–3377 (2011). [CrossRef] [PubMed]

23. T. R. Zhan, X. Shi, Y. Y. Dai, X. H. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys. Condens. Matter **25**(21), 215301 (2013). [CrossRef] [PubMed]

*τ*is the intrinsic relaxation time, taken to be 1 ps. Graphene can thus be described effectively by a dielectric function

*t*is the thickness of the ultrathin layer of electron gas, taken to be 1 nm, similar to that used in [24

24. A. Vakil and N. Engheta, “Transformation optics using graphene,” Science **332**(6035), 1291–1294 (2011). [CrossRef] [PubMed]

## 3. Results and discussions

12. B. Wunsch, T. Stauber, F. Sols, and F. Guinea, “Dynamical polarization of graphene at finite doping,” New J. Phys. **8**(12), 318 (2006). [CrossRef]

14. M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B **80**(24), 245435 (2009). [CrossRef]

19. F. H. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. **11**(8), 3370–3377 (2011). [CrossRef] [PubMed]

20. A. Yu Nikitin, F. Guinea, F. J. García-Vidal, and L. Martín-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B **84**(16), 161407 (2011). [CrossRef]

25. S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. **108**(4), 047401 (2012). [CrossRef] [PubMed]

*ω*(

*K*), where

*L*being the strip length and

*m*the order of the dipole resonances [20

20. A. Yu Nikitin, F. Guinea, F. J. García-Vidal, and L. Martín-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B **84**(16), 161407 (2011). [CrossRef]

**101**(4), 047401 (2008). [CrossRef] [PubMed]

26. Y. Lu, H. Xu, J. Y. Rhee, W. H. Jang, B. S. Ham, and Y. Lee, “Magnetic plasmon resonance: underlying route to plasmonic electromagnetically induced transparency in metamaterials,” Phys. Rev. B **82**(19), 195112 (2010). [CrossRef]

21. 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]

**E**| at these interested frequencies. For the transparent peak at 23.25 THz, incident light can directly excite the dipole mode in the radiative element while the direct excitation of the quadruple mode in the dark element is not allowed. However, the dark mode can be indirectly activated via the coupling between the radiative and dark modes. The indirectly excited dark mode will then couple back to the radiative mode. Note that there exists a phase difference of π between the channels of the direct and indirect excitations [3

**101**(4), 047401 (2008). [CrossRef] [PubMed]

26. Y. Lu, H. Xu, J. Y. Rhee, W. H. Jang, B. S. Ham, and Y. Lee, “Magnetic plasmon resonance: underlying route to plasmonic electromagnetically induced transparency in metamaterials,” Phys. Rev. B **82**(19), 195112 (2010). [CrossRef]

**8**(12), 318 (2006). [CrossRef]

**80**(24), 245435 (2009). [CrossRef]

17. F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science **320**(5873), 206–209 (2008). [CrossRef] [PubMed]

*E*. Obviously, the center frequency of the EIT transparency window can shift from 18.84 to 26.94 THz with

_{F}*E*varying from 0.2 to 0.4 eV.

_{F}27. L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature **397**(6720), 594–598 (1999). [CrossRef]

28. U. Schnorrberger, J. D. Thompson, S. Trotzky, R. Pugatch, N. Davidson, S. Kuhr, and I. Bloch, “Electromagnetically induced transparency and light storage in an atomic Mott insulator,” Phys. Rev. Lett. **103**(3), 033003 (2009). [CrossRef] [PubMed]

1. Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. **96**(12), 123901 (2006). [CrossRef] [PubMed]

29. M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency,” Phys. Rev. Lett. **93**(23), 233903 (2004). [CrossRef] [PubMed]

*E*. Positive and negative group delays correspond to slow and fast light, respectively. Obviously, in the vicinity of the EIT transparent peak it offers large positive group delays, suggesting slow light. At the transparent peak, the group delays for different

_{F}*E*are more than 0.04 ps, equivalently corresponding to a distance of 12 μm for light traveling in vacuum. Considering graphene is only one-atomic-layer thick (1 nm in our simulations) and the substrate is 20-nm thick, in the vicinity of the transparent peak the effective group refractive index of the graphene EIT structure should be more than 500, one order of magnitude larger than that offered by the plasmonic EIT in metal structures [3

_{F}**101**(4), 047401 (2008). [CrossRef] [PubMed]

## 4. Conclusion

## Acknowledgments

## References and links

1. | Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett. |

2. | N. Papasimakis, V. A. Fedotov, N. I. Zheludev, and S. L. Prosvirnin, “Metamaterial analog of electromagnetically induced transparency,” Phys. Rev. Lett. |

3. | S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett. |

4. | X. Yang, M. Yu, D.-L. Kwong, and C. W. Wong, “All-optical analog to electromagnetically induced transparency in multiple coupled photonic crystal cavities,” Phys. Rev. Lett. |

5. | P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Low-loss metamaterials based on classical electromagnetically induced transparency,” Phys. Rev. Lett. |

6. | Y. Sun, H. Jiang, Y. Yang, Y. Zhang, H. Chen, and S. Zhu, “Electromagnetically induced transparency in metamaterials: Influence of intrinsic loss and dynamic evolution,” Phys. Rev. B |

7. | T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B |

8. | N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater. |

9. | R. D. Kekatpure, E. S. Barnard, W. Cai, and M. L. Brongersma, “Phase-coupled plasmon-induced transparency,” Phys. Rev. Lett. |

10. | L. Verslegers, Z. Yu, Z. Ruan, P. B. Catrysse, and S. Fan, “From electromagnetically induced transparency to superscattering with a single structure: a coupled-mode theory for doubly resonant structures,” Phys. Rev. Lett. |

11. | A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. |

12. | B. Wunsch, T. Stauber, F. Sols, and F. Guinea, “Dynamical polarization of graphene at finite doping,” New J. Phys. |

13. | E. H. Hwang and S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B |

14. | M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B |

15. | F. Bonaccorso, Z. Sun, T. Hassan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics |

16. | A. N. Grirorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics |

17. | F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science |

18. | L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. |

19. | F. H. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. |

20. | A. Yu Nikitin, F. Guinea, F. J. García-Vidal, and L. Martín-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B |

21. | 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 |

22. | H. Ian, Y. X. Liu, and F. Nori, “Tunable electromagnetically induced transparency and absorption with dressed superconducting qubits,” Phys. Rev. A |

23. | T. R. Zhan, X. Shi, Y. Y. Dai, X. H. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys. Condens. Matter |

24. | A. Vakil and N. Engheta, “Transformation optics using graphene,” Science |

25. | S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. |

26. | Y. Lu, H. Xu, J. Y. Rhee, W. H. Jang, B. S. Ham, and Y. Lee, “Magnetic plasmon resonance: underlying route to plasmonic electromagnetically induced transparency in metamaterials,” Phys. Rev. B |

27. | L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature |

28. | U. Schnorrberger, J. D. Thompson, S. Trotzky, R. Pugatch, N. Davidson, S. Kuhr, and I. Bloch, “Electromagnetically induced transparency and light storage in an atomic Mott insulator,” Phys. Rev. Lett. |

29. | M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency,” Phys. Rev. Lett. |

**OCIS Codes**

(230.4555) Optical devices : Coupled resonators

(050.6624) Diffraction and gratings : Subwavelength structures

**ToC Category:**

Plasmonics

**History**

Original Manuscript: October 10, 2013

Revised Manuscript: November 5, 2013

Manuscript Accepted: November 5, 2013

Published: November 12, 2013

**Citation**

Xi Shi, Dezhuan Han, Yunyun Dai, Zongfu Yu, Yong Sun, Hong Chen, Xiaohan Liu, and Jian Zi, "Plasmonic analog of electromagnetically induced transparency in nanostructure graphene," Opt. Express **21**, 28438-28443 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-23-28438

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### References

- Q. Xu, S. Sandhu, M. L. Povinelli, J. Shakya, S. Fan, and M. Lipson, “Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency,” Phys. Rev. Lett.96(12), 123901 (2006). [CrossRef] [PubMed]
- N. Papasimakis, V. A. Fedotov, N. I. Zheludev, and S. L. Prosvirnin, “Metamaterial analog of electromagnetically induced transparency,” Phys. Rev. Lett.101(25), 253903 (2008). [CrossRef] [PubMed]
- S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, “Plasmon-induced transparency in metamaterials,” Phys. Rev. Lett.101(4), 047401 (2008). [CrossRef] [PubMed]
- X. Yang, M. Yu, D.-L. Kwong, and C. W. Wong, “All-optical analog to electromagnetically induced transparency in multiple coupled photonic crystal cavities,” Phys. Rev. Lett.102(17), 173902 (2009). [CrossRef] [PubMed]
- P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, “Low-loss metamaterials based on classical electromagnetically induced transparency,” Phys. Rev. Lett.102(5), 053901 (2009). [CrossRef] [PubMed]
- Y. Sun, H. Jiang, Y. Yang, Y. Zhang, H. Chen, and S. Zhu, “Electromagnetically induced transparency in metamaterials: Influence of intrinsic loss and dynamic evolution,” Phys. Rev. B83(19), 195140 (2011). [CrossRef]
- T. Zentgraf, S. Zhang, R. F. Oulton, and X. Zhang, “Ultranarrow coupling-induced transparency bands in hybrid plasmonic systems,” Phys. Rev. B80(19), 195415 (2009). [CrossRef]
- N. Liu, L. Langguth, T. Weiss, J. Kästel, M. Fleischhauer, T. Pfau, and H. Giessen, “Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit,” Nat. Mater.8(9), 758–762 (2009). [CrossRef] [PubMed]
- R. D. Kekatpure, E. S. Barnard, W. Cai, and M. L. Brongersma, “Phase-coupled plasmon-induced transparency,” Phys. Rev. Lett.104(24), 243902 (2010). [CrossRef] [PubMed]
- L. Verslegers, Z. Yu, Z. Ruan, P. B. Catrysse, and S. Fan, “From electromagnetically induced transparency to superscattering with a single structure: a coupled-mode theory for doubly resonant structures,” Phys. Rev. Lett.108(8), 083902 (2012). [CrossRef] [PubMed]
- A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys.81(1), 109–162 (2009). [CrossRef]
- B. Wunsch, T. Stauber, F. Sols, and F. Guinea, “Dynamical polarization of graphene at finite doping,” New J. Phys.8(12), 318 (2006). [CrossRef]
- E. H. Hwang and S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B75(20), 205418 (2007). [CrossRef]
- M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B80(24), 245435 (2009). [CrossRef]
- F. Bonaccorso, Z. Sun, T. Hassan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics4(9), 611–622 (2010). [CrossRef]
- A. N. Grirorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nat. Photonics6(11), 749–758 (2012). [CrossRef]
- F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science320(5873), 206–209 (2008). [CrossRef] [PubMed]
- L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol.6(10), 630–634 (2011). [CrossRef] [PubMed]
- F. H. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett.11(8), 3370–3377 (2011). [CrossRef] [PubMed]
- A. Yu Nikitin, F. Guinea, F. J. García-Vidal, and L. Martín-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B84(16), 161407 (2011). [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 Commun3, 1151 (2012). [CrossRef] [PubMed]
- H. Ian, Y. X. Liu, and F. Nori, “Tunable electromagnetically induced transparency and absorption with dressed superconducting qubits,” Phys. Rev. A81(6), 063823 (2010). [CrossRef]
- T. R. Zhan, X. Shi, Y. Y. Dai, X. H. Liu, and J. Zi, “Transfer matrix method for optics in graphene layers,” J. Phys. Condens. Matter25(21), 215301 (2013). [CrossRef] [PubMed]
- A. Vakil and N. Engheta, “Transformation optics using graphene,” Science332(6035), 1291–1294 (2011). [CrossRef] [PubMed]
- S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett.108(4), 047401 (2012). [CrossRef] [PubMed]
- Y. Lu, H. Xu, J. Y. Rhee, W. H. Jang, B. S. Ham, and Y. Lee, “Magnetic plasmon resonance: underlying route to plasmonic electromagnetically induced transparency in metamaterials,” Phys. Rev. B82(19), 195112 (2010). [CrossRef]
- L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature397(6720), 594–598 (1999). [CrossRef]
- U. Schnorrberger, J. D. Thompson, S. Trotzky, R. Pugatch, N. Davidson, S. Kuhr, and I. Bloch, “Electromagnetically induced transparency and light storage in an atomic Mott insulator,” Phys. Rev. Lett.103(3), 033003 (2009). [CrossRef] [PubMed]
- M. F. Yanik, W. Suh, Z. Wang, and S. Fan, “Stopping light in a waveguide with an all-optical analog of electromagnetically induced transparency,” Phys. Rev. Lett.93(23), 233903 (2004). [CrossRef] [PubMed]

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