Abstract

In this Letter, we construct a metamaterial with dual-mode electromagnetically induced transparency (EIT)-like behavior by introducing “bright atoms,” “quasi-dark atoms,” and “dark atoms” simultaneously. The dual-mode EIT-like behavior has been demonstrated both experimentally and theoretically in terahertz (THz) regime. At two EIT-like modes, slow light is also observed as two time-delayed wave packets, and the effective group refractive index can reach 102. Furthermore, stable dual-mode EIT-like behavior is verified in this metamaterial for a wide range of oblique incident angles. Our work provides a design approach to mimic dual-mode EIT, and such an approach may achieve potential applications on miniaturized and versatile THz devices.

© 2014 Optical Society of America

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J. Chen, C. Wang, R. Zhang, and J. Xiao, Opt. Lett. 37, 5133 (2012).
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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. Chen, A. J. Taylor, J. Han, and W. Zhang, Nat. Commun. 3, 1151 (2012).
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P. Tassin, L. Zhang, R. Zhao, A. Jain, T. Koschny, and C. M. Soukoulis, Phys. Rev. Lett. 109, 187401 (2012).
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2011 (5)

Y. Sun, H. Jiang, Y. Yang, Y. Zhang, H. Chen, and S. Zhu, Phys. Rev. B 83, 195140 (2011).
[CrossRef]

Y. M. Liu and X. Zhang, Chem. Soc. Rev. 40, 2494 (2011).
[CrossRef]

J. Chen, P. Wang, C. Chen, Y. Lu, H. Ming, and Q. Zhan, Opt. Express 19, 5970 (2011).
[CrossRef]

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[CrossRef]

C. Kurter, P. Tassin, L. Zhang, T. Koschny, A. P. Zhuravel, A. V. Ustinov, S. M. Anlage, and C. M. Soukoulis, Phys. Rev. Lett. 107, 043901 (2011).
[CrossRef]

2010 (3)

2009 (5)

C. Y. Chen, I. W. Un, N. H. Tai, and T. J. Yen, Opt. Express 17, 15372 (2009).
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S. Y. Chiam, R. Singh, C. Rockstuhl, F. Lederer, W. Zhang, and A. A. Bettiol, Phys. Rev. B 80, 153103 (2009).
[CrossRef]

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P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, Phys. Rev. Lett. 102, 053901 (2009).
[CrossRef]

2008 (2)

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, Phys. Rev. Lett. 101, 047401 (2008).
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N. Papasimakis, V. A. Fedotov, N. I. Zheludev, and S. L. Prosvirnin, Phys. Rev. Lett. 101, 253903 (2008).
[CrossRef]

2005 (1)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
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2002 (2)

C. L. G. Alzar, M. A. G. Martinez, and P. Nussenzveig, Am. J. Phys. 70, 37 (2002).
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D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
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1990 (1)

S. E. Harris, J. E. Field, and A. Imamoglu, Phys. Rev. Lett. 64, 1107 (1990).
[CrossRef]

Alzar, C. L. G.

C. L. G. Alzar, M. A. G. Martinez, and P. Nussenzveig, Am. J. Phys. 70, 37 (2002).
[CrossRef]

Anlage, S. M.

C. Kurter, P. Tassin, L. Zhang, T. Koschny, A. P. Zhuravel, A. V. Ustinov, S. M. Anlage, and C. M. Soukoulis, Phys. Rev. Lett. 107, 043901 (2011).
[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. Chen, A. J. Taylor, J. Han, and W. Zhang, Nat. Commun. 3, 1151 (2012).
[CrossRef]

Bartal, G.

Z. Ye, S. Zhang, Y. Wang, Y. Park, T. Zentgraf, G. Bartal, X. Yin, and X. Zhang, Phys. Rev. B 86, 155148 (2012).
[CrossRef]

Bettiol, A. A.

S. Y. Chiam, R. Singh, C. Rockstuhl, F. Lederer, W. Zhang, and A. A. Bettiol, Phys. Rev. B 80, 153103 (2009).
[CrossRef]

Buchwald, W. R.

Cao, W.

W. Cao, R. Singh, C. Zhang, J. Han, M. Tonouchi, and W. Zhang, Appl. Phys. Lett. 103, 101106 (2013).
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L. Verslegers, Z. Yu, Z. Ruan, P. B. Catrysse, and S. Fan, Phys. Rev. Lett. 108, 083902 (2012).
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Chen, C.

Chen, C. Y.

Chen, H.

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. Chen, A. J. Taylor, J. Han, and W. Zhang, Nat. Commun. 3, 1151 (2012).
[CrossRef]

Y. Sun, H. Jiang, Y. Yang, Y. Zhang, H. Chen, and S. Zhu, Phys. Rev. B 83, 195140 (2011).
[CrossRef]

Chen, J.

Chiam, S. Y.

S. Y. Chiam, R. Singh, C. Rockstuhl, F. Lederer, W. Zhang, and A. A. Bettiol, Phys. Rev. B 80, 153103 (2009).
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Economou, E. N.

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Fan, S.

L. Verslegers, Z. Yu, Z. Ruan, P. B. Catrysse, and S. Fan, Phys. Rev. Lett. 108, 083902 (2012).
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Fedotov, V. A.

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Field, J. E.

S. E. Harris, J. E. Field, and A. Imamoglu, Phys. Rev. Lett. 64, 1107 (1990).
[CrossRef]

Fleischhauer, M.

N. Liu, L. Langguth, T. Weiss, J. Kastel, M. Fleischhauer, T. Pfau, and H. Giessen, Nat. Mater. 8, 758 (2009).
[CrossRef]

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

Fu, J. H.

Genov, D. A.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, Phys. Rev. Lett. 101, 047401 (2008).
[CrossRef]

Giessen, H.

N. Liu, L. Langguth, T. Weiss, J. Kastel, M. Fleischhauer, T. Pfau, and H. Giessen, Nat. Mater. 8, 758 (2009).
[CrossRef]

Gu, J.

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. Chen, A. J. Taylor, J. Han, and W. Zhang, Nat. Commun. 3, 1151 (2012).
[CrossRef]

Han, J.

W. Cao, R. Singh, C. Zhang, J. Han, M. Tonouchi, and W. Zhang, Appl. Phys. Lett. 103, 101106 (2013).
[CrossRef]

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. Chen, A. J. Taylor, J. Han, and W. Zhang, Nat. Commun. 3, 1151 (2012).
[CrossRef]

Hao, F.

N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. Van Dorpe, P. Nordlander, and S. A. Maier, Nano Lett. 9, 1663 (2009).
[CrossRef]

Harris, S. E.

S. E. Harris, J. E. Field, and A. Imamoglu, Phys. Rev. Lett. 64, 1107 (1990).
[CrossRef]

Hua, J.

Huang, X. R.

L. Qin, K. Zhang, R. W. Peng, X. Xiong, W. Zhang, X. R. Huang, and M. Wang, Phys. Rev. B 87, 125136 (2013).
[CrossRef]

Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

S. E. Harris, J. E. Field, and A. Imamoglu, Phys. Rev. Lett. 64, 1107 (1990).
[CrossRef]

Jain, A.

P. Tassin, L. Zhang, R. Zhao, A. Jain, T. Koschny, and C. M. Soukoulis, Phys. Rev. Lett. 109, 187401 (2012).
[CrossRef]

Jang, W. H.

Jeppesen, C.

Jiang, H.

Y. Sun, H. Jiang, Y. Yang, Y. Zhang, H. Chen, and S. Zhu, Phys. Rev. B 83, 195140 (2011).
[CrossRef]

Kastel, J.

N. Liu, L. Langguth, T. Weiss, J. Kastel, M. Fleischhauer, T. Pfau, and H. Giessen, Nat. Mater. 8, 758 (2009).
[CrossRef]

Kim, J.

Koschny, T.

P. Tassin, L. Zhang, R. Zhao, A. Jain, T. Koschny, and C. M. Soukoulis, Phys. Rev. Lett. 109, 187401 (2012).
[CrossRef]

C. Kurter, P. Tassin, L. Zhang, T. Koschny, A. P. Zhuravel, A. V. Ustinov, S. M. Anlage, and C. M. Soukoulis, Phys. Rev. Lett. 107, 043901 (2011).
[CrossRef]

P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, Phys. Rev. Lett. 102, 053901 (2009).
[CrossRef]

Kristensen, A.

Kurter, C.

C. Kurter, P. Tassin, L. Zhang, T. Koschny, A. P. Zhuravel, A. V. Ustinov, S. M. Anlage, and C. M. Soukoulis, Phys. Rev. Lett. 107, 043901 (2011).
[CrossRef]

Langguth, L.

N. Liu, L. Langguth, T. Weiss, J. Kastel, M. Fleischhauer, T. Pfau, and H. Giessen, Nat. Mater. 8, 758 (2009).
[CrossRef]

Lederer, F.

S. Y. Chiam, R. Singh, C. Rockstuhl, F. Lederer, W. Zhang, and A. A. Bettiol, Phys. Rev. B 80, 153103 (2009).
[CrossRef]

Lee, Y. P.

Li, X. Y.

Liu, M.

S. Zhang, D. A. Genov, Y. Wang, M. Liu, and X. Zhang, Phys. Rev. Lett. 101, 047401 (2008).
[CrossRef]

Liu, N.

N. Liu, L. Langguth, T. Weiss, J. Kastel, M. Fleischhauer, T. Pfau, and H. Giessen, Nat. Mater. 8, 758 (2009).
[CrossRef]

Liu, R. P.

Liu, S. D.

Liu, X.

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. Chen, A. J. Taylor, J. Han, and W. Zhang, Nat. Commun. 3, 1151 (2012).
[CrossRef]

Liu, Y. M.

Y. M. Liu and X. Zhang, Chem. Soc. Rev. 40, 2494 (2011).
[CrossRef]

Lu, Y.

Ma, Y.

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. Chen, A. J. Taylor, J. Han, and W. Zhang, Nat. Commun. 3, 1151 (2012).
[CrossRef]

Maier, S. A.

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. Chen, A. J. Taylor, J. Han, and W. Zhang, Nat. Commun. 3, 1151 (2012).
[CrossRef]

N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. Van Dorpe, P. Nordlander, and S. A. Maier, Nano Lett. 9, 1663 (2009).
[CrossRef]

Marangos, J. P.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Rev. Mod. Phys. 77, 633 (2005).
[CrossRef]

Markos, P.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Martinez, M. A. G.

C. L. G. Alzar, M. A. G. Martinez, and P. Nussenzveig, Am. J. Phys. 70, 37 (2002).
[CrossRef]

Meng, F. Y.

Ming, H.

Mortensen, N. A.

Moshchalkov, V. V.

N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. Van Dorpe, P. Nordlander, and S. A. Maier, Nano Lett. 9, 1663 (2009).
[CrossRef]

Nordlander, P.

N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. Van Dorpe, P. Nordlander, and S. A. Maier, Nano Lett. 9, 1663 (2009).
[CrossRef]

Nussenzveig, P.

C. L. G. Alzar, M. A. G. Martinez, and P. Nussenzveig, Am. J. Phys. 70, 37 (2002).
[CrossRef]

Papasimakis, N.

N. Papasimakis, V. A. Fedotov, N. I. Zheludev, and S. L. Prosvirnin, Phys. Rev. Lett. 101, 253903 (2008).
[CrossRef]

Park, Y.

Z. Ye, S. Zhang, Y. Wang, Y. Park, T. Zentgraf, G. Bartal, X. Yin, and X. Zhang, Phys. Rev. B 86, 155148 (2012).
[CrossRef]

Peng, R. W.

L. Qin, K. Zhang, R. W. Peng, X. Xiong, W. Zhang, X. R. Huang, and M. Wang, Phys. Rev. B 87, 125136 (2013).
[CrossRef]

Pfau, T.

N. Liu, L. Langguth, T. Weiss, J. Kastel, M. Fleischhauer, T. Pfau, and H. Giessen, Nat. Mater. 8, 758 (2009).
[CrossRef]

Prosvirnin, S. L.

N. Papasimakis, V. A. Fedotov, N. I. Zheludev, and S. L. Prosvirnin, Phys. Rev. Lett. 101, 253903 (2008).
[CrossRef]

Qin, L.

L. Qin, K. Zhang, R. W. Peng, X. Xiong, W. Zhang, X. R. Huang, and M. Wang, Phys. Rev. B 87, 125136 (2013).
[CrossRef]

Rhee, J. Y.

Rockstuhl, C.

S. Y. Chiam, R. Singh, C. Rockstuhl, F. Lederer, W. Zhang, and A. A. Bettiol, Phys. Rev. B 80, 153103 (2009).
[CrossRef]

Ruan, Z.

L. Verslegers, Z. Yu, Z. Ruan, P. B. Catrysse, and S. Fan, Phys. Rev. Lett. 108, 083902 (2012).
[CrossRef]

Schultz, S.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Singh, R.

W. Cao, R. Singh, C. Zhang, J. Han, M. Tonouchi, and W. Zhang, Appl. Phys. Lett. 103, 101106 (2013).
[CrossRef]

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. Chen, A. J. Taylor, J. Han, and W. Zhang, Nat. Commun. 3, 1151 (2012).
[CrossRef]

S. Y. Chiam, R. Singh, C. Rockstuhl, F. Lederer, W. Zhang, and A. A. Bettiol, Phys. Rev. B 80, 153103 (2009).
[CrossRef]

Smith, D. R.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Sobhani, H.

N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. Van Dorpe, P. Nordlander, and S. A. Maier, Nano Lett. 9, 1663 (2009).
[CrossRef]

Sonnefraud, Y.

N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. Van Dorpe, P. Nordlander, and S. A. Maier, Nano Lett. 9, 1663 (2009).
[CrossRef]

Soref, R.

Soukoulis, C. M.

P. Tassin, L. Zhang, R. Zhao, A. Jain, T. Koschny, and C. M. Soukoulis, Phys. Rev. Lett. 109, 187401 (2012).
[CrossRef]

C. Kurter, P. Tassin, L. Zhang, T. Koschny, A. P. Zhuravel, A. V. Ustinov, S. M. Anlage, and C. M. Soukoulis, Phys. Rev. Lett. 107, 043901 (2011).
[CrossRef]

P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, Phys. Rev. Lett. 102, 053901 (2009).
[CrossRef]

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Sun, Y.

Y. Sun, H. Jiang, Y. Yang, Y. Zhang, H. Chen, and S. Zhu, Phys. Rev. B 83, 195140 (2011).
[CrossRef]

Tai, N. H.

Tassin, P.

P. Tassin, L. Zhang, R. Zhao, A. Jain, T. Koschny, and C. M. Soukoulis, Phys. Rev. Lett. 109, 187401 (2012).
[CrossRef]

C. Kurter, P. Tassin, L. Zhang, T. Koschny, A. P. Zhuravel, A. V. Ustinov, S. M. Anlage, and C. M. Soukoulis, Phys. Rev. Lett. 107, 043901 (2011).
[CrossRef]

P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, Phys. Rev. Lett. 102, 053901 (2009).
[CrossRef]

Taylor, A. J.

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. Chen, A. J. Taylor, J. Han, and W. Zhang, Nat. Commun. 3, 1151 (2012).
[CrossRef]

Tian, Z.

J. Gu, R. Singh, X. Liu, X. Zhang, Y. Ma, S. Zhang, S. A. Maier, Z. Tian, A. K. Azad, H. Chen, A. J. Taylor, J. Han, and W. Zhang, Nat. Commun. 3, 1151 (2012).
[CrossRef]

Tonouchi, M.

W. Cao, R. Singh, C. Zhang, J. Han, M. Tonouchi, and W. Zhang, Appl. Phys. Lett. 103, 101106 (2013).
[CrossRef]

Un, I. W.

Ustinov, A. V.

C. Kurter, P. Tassin, L. Zhang, T. Koschny, A. P. Zhuravel, A. V. Ustinov, S. M. Anlage, and C. M. Soukoulis, Phys. Rev. Lett. 107, 043901 (2011).
[CrossRef]

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N. Verellen, Y. Sonnefraud, H. Sobhani, F. Hao, V. V. Moshchalkov, P. Van Dorpe, P. Nordlander, and S. A. Maier, Nano Lett. 9, 1663 (2009).
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Figures (5)

Fig. 1.
Fig. 1.

(a) Schematic of the system consisting of a “bright atom” and a “dark atom,” and (d) shows its susceptibility. (b) System consisting of a “bright atom” and a “quasi-dark atom,” and (e) shows its susceptibility. (c) System consisting of a “bright atom,” a “dark atom,” and a “quasi-dark atom,” and (f) shows the susceptibility in this three-“atom” system.

Fig. 2.
Fig. 2.

Calculated transmission coefficient spectra in designed meta-atom systems: (a) the “bright atom,” with L1=76μm and W1=8μm; (b) the “dark atom,” with L2=88μm, W2=34μm, d1=14μm, and g1=8μm; and (c) the “quasi-dark atom,” with L3=44μm, W3=24μm, d2=8μm, and g2=12μm. (d) Electric field distribution of the “dark atom” at 0.66 THz, with the electric field polarized along the y axis. (e) Transmission coefficient spectrum of system consisting of a “bright atom” and a “dark atom,” with h1=11μm; (f) its electric field intensity distribution; (g) its electric field distribution (both at 0.58 THz). (h) Transmission coefficient spectrum of system consisting of a “bright atom” and a “quasi-dark atom,” with h2=10μm; and (i) shows its electric field intensity distribution at 0.61 THz.

Fig. 3.
Fig. 3.

(a) Schematic of meta-molecule with three meta-atoms, h1=11μm and h2=10μm. (b) Transmission coefficient spectrum of the metamaterial. (c), (d) Electric field intensity distributions at 0.565 and 0.685 THz, respectively.

Fig. 4.
Fig. 4.

(a) Micrograph of the three-“atom” system. (b) Diagram of the THz time-domain spectrometer. (c) Experimentally measured time-domain transmission signals of bare substrate (black curve) and sample with the three-“atom” system (red curve). The inset is an enlarged spectrum. (d) Experimental transmission spectra of the three-“atom” system (solid black curve) and the bi-“atom” system (dashed magenta curve). (e) Simulated time-domain transmission spectrum of the three-“atom” system. (f) Effective group refractive index retrieved from the simulated results in (e).

Fig. 5.
Fig. 5.

Transmission coefficient spectra under oblique incident light with different incident angles (θ) (a) simulated and (b) experimental.

Equations (3)

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{P¨1(t)+γ1P˙1(t)+ω02P1(t)Ω2P2(t)=κ1E0(t)P¨2(t)+γ2P˙2(t)+ω02P2(t)Ω2P1(t)=κ2E0(t),
χE=κ1[(γ22ω2Ω4)(ω02ω2)(γ1γ2ω2+Ω4)2+iγ2ωγ1γ2ω2+Ω4]κ2[Ω2γ1γ2ω2+Ω4+i(γ1+γ2)Ω2(ω02ω2)ω(γ1γ2ω2+Ω4)2].
(PaPbPc)=(ω02ω2iγ1ωΩ122Ω132Ω212ω02ω2iγ2ωΩ232Ω312Ω322ω02ω2iγ3ω)1(κ1E0κ2E00).

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