Abstract

The propagation of electromagnetic waves via a one-dimensional periodic array of alternating dielectric and metal layers with periodically distributed optically activated inclusions of graphene is investigated inside a THz photonic pass band for different levels of optical activation of the graphene. On a particular example of a vacuum-aluminum nanostructure, it is shown that the presence of gain insertions can lead to a considerable increase in the transparency of dielectric-metal structures for electromagnetic radiation of the THz region. In this way one can achieve not only perfect transparency, but also significant amplification of incoming electromagnetic radiation within narrow frequency bands.

© 2017 Optical Society of America

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References

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2015 (3)

2014 (2)

2013 (3)

2012 (1)

K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490, 192–200 (2012).
[Crossref] [PubMed]

2011 (1)

2010 (2)

Kian Ping Loh, Qiaoliang Bao, Goki Eda, and Manish Chhowalla, “Graphene oxide as a chemically tunable platform for optical applications,” Nature Chemistry 2, 1015–1024 (2010).
[Crossref] [PubMed]

Shumin Xiao, Vladimir P. Drachev, Alexander V. Kildishev, Xingjie Ni, Uday K. Chettiar, Hsiao-Kuan Yuan, and Vladimir M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[Crossref] [PubMed]

2009 (1)

A. Paredes-Juárez, F. Díaz-Monge, N. M. Makarov, and F. Pérez-Rodríguez, “Nonlocal effects in the electrodynamics of metallic slabs,” JETP Letters 90(9), 623–627 (2009).
[Crossref]

2008 (1)

L. A. Falkovsky, “Optical properties of doped graphene layers,” JETP 106(3), 575–580 (2008).
[Crossref]

Alù, A.

Argyropoulos, C.

Bao, Qiaoliang

Kian Ping Loh, Qiaoliang Bao, Goki Eda, and Manish Chhowalla, “Graphene oxide as a chemically tunable platform for optical applications,” Nature Chemistry 2, 1015–1024 (2010).
[Crossref] [PubMed]

Belov, P. A.

R. S. Savelev, I. V. Shadrivov, P. A. Belov, N. N. Rosanov, S. V. Fedorov, A. A. Sukhorukov, and Y. S. Kivshar, “Loss compensation in metal-dielectric layered metamaterials,” Phys. Rev. B 87, 115139 (2013).
[Crossref]

Capolino, Filippo

Chern, Ruey-Lin

Chettiar, Uday K.

Shumin Xiao, Vladimir P. Drachev, Alexander V. Kildishev, Xingjie Ni, Uday K. Chettiar, Hsiao-Kuan Yuan, and Vladimir M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[Crossref] [PubMed]

Chhowalla, Manish

Kian Ping Loh, Qiaoliang Bao, Goki Eda, and Manish Chhowalla, “Graphene oxide as a chemically tunable platform for optical applications,” Nature Chemistry 2, 1015–1024 (2010).
[Crossref] [PubMed]

Colombo, L.

K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490, 192–200 (2012).
[Crossref] [PubMed]

Diáz-Monge, F.

Díaz-Monge, F.

A. Paredes-Juárez, F. Díaz-Monge, N. M. Makarov, and F. Pérez-Rodríguez, “Nonlocal effects in the electrodynamics of metallic slabs,” JETP Letters 90(9), 623–627 (2009).
[Crossref]

Drachev, Vladimir P.

Shumin Xiao, Vladimir P. Drachev, Alexander V. Kildishev, Xingjie Ni, Uday K. Chettiar, Hsiao-Kuan Yuan, and Vladimir M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[Crossref] [PubMed]

Eda, Goki

Kian Ping Loh, Qiaoliang Bao, Goki Eda, and Manish Chhowalla, “Graphene oxide as a chemically tunable platform for optical applications,” Nature Chemistry 2, 1015–1024 (2010).
[Crossref] [PubMed]

Estakhri, N. M.

Fal’ko, V. I.

K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490, 192–200 (2012).
[Crossref] [PubMed]

Falkovsky, L. A.

L. A. Falkovsky, “Optical properties of doped graphene layers,” JETP 106(3), 575–580 (2008).
[Crossref]

Fedorov, S. V.

R. S. Savelev, I. V. Shadrivov, P. A. Belov, N. N. Rosanov, S. V. Fedorov, A. A. Sukhorukov, and Y. S. Kivshar, “Loss compensation in metal-dielectric layered metamaterials,” Phys. Rev. B 87, 115139 (2013).
[Crossref]

Ferrari, L.

L. Ferrari, C. Wu, D. Lepage, X. Zhang, and Z. Liu, “Hyperbolic metamaterials and their applications,” Progress in Quantum Electronics 40, 1–40 (2015).
[Crossref]

Flores-Desirena, B.

Gellert, P. R.

K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490, 192–200 (2012).
[Crossref] [PubMed]

Guclu, Caner

Han, Dezhuan

Han, S.

Iakushev, D. A

Ishii, S.

Kildishev, A. V.

Kildishev, Alexander V.

Shumin Xiao, Vladimir P. Drachev, Alexander V. Kildishev, Xingjie Ni, Uday K. Chettiar, Hsiao-Kuan Yuan, and Vladimir M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[Crossref] [PubMed]

Kim, K.

K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490, 192–200 (2012).
[Crossref] [PubMed]

Kivshar, Y. S.

R. S. Savelev, I. V. Shadrivov, P. A. Belov, N. N. Rosanov, S. V. Fedorov, A. A. Sukhorukov, and Y. S. Kivshar, “Loss compensation in metal-dielectric layered metamaterials,” Phys. Rev. B 87, 115139 (2013).
[Crossref]

Lee, S.

Lepage, D.

L. Ferrari, C. Wu, D. Lepage, X. Zhang, and Z. Liu, “Hyperbolic metamaterials and their applications,” Progress in Quantum Electronics 40, 1–40 (2015).
[Crossref]

Liu, Z.

L. Ferrari, C. Wu, D. Lepage, X. Zhang, and Z. Liu, “Hyperbolic metamaterials and their applications,” Progress in Quantum Electronics 40, 1–40 (2015).
[Crossref]

Loh, Kian Ping

Kian Ping Loh, Qiaoliang Bao, Goki Eda, and Manish Chhowalla, “Graphene oxide as a chemically tunable platform for optical applications,” Nature Chemistry 2, 1015–1024 (2010).
[Crossref] [PubMed]

Makarov, N. M.

Markoš, P.

P. Markoš and C. M. Soukoulis, Wave Propagation. From Electrons to Photonic Crystals and Left-Handed Materials (Princeton University Press, 2008).

Monticone, F.

Ni, X.

Ni, Xingjie

Shumin Xiao, Vladimir P. Drachev, Alexander V. Kildishev, Xingjie Ni, Uday K. Chettiar, Hsiao-Kuan Yuan, and Vladimir M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[Crossref] [PubMed]

Novoselov, K. S.

K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490, 192–200 (2012).
[Crossref] [PubMed]

Othman, Mohamed A. K.

Paredes-Juárez, A.

Pérez-Rodríguez, F.

Rosanov, N. N.

R. S. Savelev, I. V. Shadrivov, P. A. Belov, N. N. Rosanov, S. V. Fedorov, A. A. Sukhorukov, and Y. S. Kivshar, “Loss compensation in metal-dielectric layered metamaterials,” Phys. Rev. B 87, 115139 (2013).
[Crossref]

Savelev, R. S.

R. S. Savelev, I. V. Shadrivov, P. A. Belov, N. N. Rosanov, S. V. Fedorov, A. A. Sukhorukov, and Y. S. Kivshar, “Loss compensation in metal-dielectric layered metamaterials,” Phys. Rev. B 87, 115139 (2013).
[Crossref]

Schwab, M. G.

K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490, 192–200 (2012).
[Crossref] [PubMed]

Shadrivov, I. V.

R. S. Savelev, I. V. Shadrivov, P. A. Belov, N. N. Rosanov, S. V. Fedorov, A. A. Sukhorukov, and Y. S. Kivshar, “Loss compensation in metal-dielectric layered metamaterials,” Phys. Rev. B 87, 115139 (2013).
[Crossref]

Shalaev, V. M.

Shalaev, Vladimir M.

Shumin Xiao, Vladimir P. Drachev, Alexander V. Kildishev, Xingjie Ni, Uday K. Chettiar, Hsiao-Kuan Yuan, and Vladimir M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[Crossref] [PubMed]

Soukoulis, C. M.

P. Markoš and C. M. Soukoulis, Wave Propagation. From Electrons to Photonic Crystals and Left-Handed Materials (Princeton University Press, 2008).

Sukhorukov, A. A.

R. S. Savelev, I. V. Shadrivov, P. A. Belov, N. N. Rosanov, S. V. Fedorov, A. A. Sukhorukov, and Y. S. Kivshar, “Loss compensation in metal-dielectric layered metamaterials,” Phys. Rev. B 87, 115139 (2013).
[Crossref]

Thoreson, M. D.

Wu, C.

L. Ferrari, C. Wu, D. Lepage, X. Zhang, and Z. Liu, “Hyperbolic metamaterials and their applications,” Progress in Quantum Electronics 40, 1–40 (2015).
[Crossref]

Xiao, Shumin

Shumin Xiao, Vladimir P. Drachev, Alexander V. Kildishev, Xingjie Ni, Uday K. Chettiar, Hsiao-Kuan Yuan, and Vladimir M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[Crossref] [PubMed]

Yuan, Hsiao-Kuan

Shumin Xiao, Vladimir P. Drachev, Alexander V. Kildishev, Xingjie Ni, Uday K. Chettiar, Hsiao-Kuan Yuan, and Vladimir M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[Crossref] [PubMed]

Zhang, X.

L. Ferrari, C. Wu, D. Lepage, X. Zhang, and Z. Liu, “Hyperbolic metamaterials and their applications,” Progress in Quantum Electronics 40, 1–40 (2015).
[Crossref]

JETP (1)

L. A. Falkovsky, “Optical properties of doped graphene layers,” JETP 106(3), 575–580 (2008).
[Crossref]

JETP Letters (1)

A. Paredes-Juárez, F. Díaz-Monge, N. M. Makarov, and F. Pérez-Rodríguez, “Nonlocal effects in the electrodynamics of metallic slabs,” JETP Letters 90(9), 623–627 (2009).
[Crossref]

Nature (2)

K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490, 192–200 (2012).
[Crossref] [PubMed]

Shumin Xiao, Vladimir P. Drachev, Alexander V. Kildishev, Xingjie Ni, Uday K. Chettiar, Hsiao-Kuan Yuan, and Vladimir M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature 466, 735–738 (2010).
[Crossref] [PubMed]

Nature Chemistry (1)

Kian Ping Loh, Qiaoliang Bao, Goki Eda, and Manish Chhowalla, “Graphene oxide as a chemically tunable platform for optical applications,” Nature Chemistry 2, 1015–1024 (2010).
[Crossref] [PubMed]

Opt. Express (5)

Opt. Lett. (1)

Opt. Mater. Express (1)

Phys. Rev. B (1)

R. S. Savelev, I. V. Shadrivov, P. A. Belov, N. N. Rosanov, S. V. Fedorov, A. A. Sukhorukov, and Y. S. Kivshar, “Loss compensation in metal-dielectric layered metamaterials,” Phys. Rev. B 87, 115139 (2013).
[Crossref]

Progress in Quantum Electronics (1)

L. Ferrari, C. Wu, D. Lepage, X. Zhang, and Z. Liu, “Hyperbolic metamaterials and their applications,” Progress in Quantum Electronics 40, 1–40 (2015).
[Crossref]

Other (1)

P. Markoš and C. M. Soukoulis, Wave Propagation. From Electrons to Photonic Crystals and Left-Handed Materials (Princeton University Press, 2008).

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Figures (6)

Fig. 1
Fig. 1 Schematic of the dielectric-metal superlattice with inclusions of graphene.
Fig. 2
Fig. 2 The real and imaginary parts of quantity D = 4πσ/c as a function of the wave frequency, for a graphene sheet with temperature T = 300 K and chemical potential μc = 1.2577 eV.
Fig. 3
Fig. 3 (Color Online) The real and imaginary parts of the surface impedances ζ0 and ζd for an aluminum layer of the thickness db = 25 nm.
Fig. 4
Fig. 4 (Color Online) Transmission coefficient T7 within the second pass band for vacuum-aluminum superlattice of N = 7 unit cells with α = 0.
Fig. 5
Fig. 5 (Color Online) Transmission coefficient T7 within the second pass band for vacuum-aluminum superlattice of N = 7 unit cells with α = 1.
Fig. 6
Fig. 6 (Color Online) Transmission spectra in the intermediate case α = 1 2. Panel (a): Transmission coefficient within the frequency range shown in Fig. 5. Panel (b): Transmission coefficient within the second pass band for optical activation 4πReσ/c = −0.63.

Equations (50)

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d = d a + d b .
E ( x , t ) = { 0 , E ( x , 0 ) } exp ( i ω t ) , H ( x , t ) = { 0 , 0 , H ( x ) } exp ( i ω t ) ,
n a = ε a μ a , Z a = μ a / n a , k a = n a k , φ a = k a d a , k = ω / c .
j a ( x ) = σ E a ( x ) δ ( x x n ( i ) ) ,
E a ( x ) + k a 2 E a ( x ) + 4 π i μ a ω c 2 j a ( x ) = 0 ,
H a ( x ) = 1 i k μ a E a ( x ) .
ε = ε a + 4 π i σ ω δ ( x x n ( i ) ) .
E a n ( 1 ) ( x ) = A n + ( 1 ) exp [ i k a ( x x a n ) ] + A n ( 1 ) exp [ i k a ( x x a n ) ] ,
H a n ( 1 ) ( x ) = Z a 1 { A n + ( 1 ) exp [ i k a ( x x a n ) ] A n ( 1 ) exp [ i k a ( x x a n ) ] } , inside the left sublayer , where x a n x < x n ( i ) ,
E a n ( 2 ) ( x ) = A n + ( 2 ) exp [ i k a ( x x n ( i ) ) ] + A n ( 2 ) exp [ i k a ( x x n ( i ) ) ] ,
H a n ( 2 ) ( x ) = Z a 1 { A n + ( 2 ) exp [ i k a ( x x n ( i ) ) ] A n ( 2 ) exp [ i k a ( x x n ( i ) ) ] } , inside the right sublayer , where x n ( i ) < x x b n .
E a n ( 1 ) ( x n ( i ) ) = E a n ( 2 ) ( x n ( i ) ) ,
H a n ( 2 ) ( x n ( i ) ) H a n ( 1 ) ( x n ( i ) ) = 4 π σ c E a n ( 1 ) ( x n ( i ) ) .
( A n + ( 2 ) A n ( 2 ) ) = Q ^ ( i ) ( A n + ( 1 ) A n ( 1 ) ) ,
( Q ( i ) ) 11 = ( 1 D Z a 2 ) exp ( i φ a ( 1 ) ) ,
( Q ( i ) ) 12 = D Z a 2 exp ( i φ a ( 1 ) ) ,
( Q ( i ) ) 21 = D Z a 2 exp ( i φ a ( 1 ) ) ,
( Q ( i ) ) 22 = ( 1 + D Z a 2 ) exp ( i φ a ( 1 ) ) ,
D = 4 π σ / c .
E b n ( x b n ) = H b n ( x b n ) ζ 0 H b n ( x a n + 1 ) ζ d ,
( H b n ( x a n + 1 ) H b n ( x b n ) ) = Q ^ ( a ) ( A n + ( 2 ) A n ( 2 ) ) ,
Q 11 ( a ) = ζ 0 Z a Z a ζ d exp ( i φ a ( 2 ) ) ,
Q 12 ( a ) = ζ 0 + Z a Z a ζ d exp ( i φ a ( 2 ) ) ,
Q 21 ( a ) = exp ( i φ a ( 2 ) ) Z a ,
Q 22 ( a ) = exp ( i φ a ( 2 ) ) Z a .
E b n ( x a n + 1 ) = H b n ( x b n ) ζ d H b n ( x a n + 1 ) ζ 0 ,
( A ( n + 1 ) + ( 1 ) A ( n + 1 ) ( 1 ) ) = Q ^ ( b ) ( H b n ( x a n + 1 ) H b n ( x b n ) ) ,
Q 11 ( b ) = ( Z a ζ 0 ) / 2 ,
Q 12 ( b ) = ζ d / 2 ,
Q 21 ( b ) = ( Z a + ζ 0 ) / 2 ,
Q 22 ( b ) = ζ d / 2 .
( A ( n + 1 ) + ( 1 ) A ( n + 1 ) ( 1 ) ) = Q ^ ( A n + ( 1 ) A n ( 1 ) ) ,
Q ^ = Q ^ ( b ) Q ^ ( a ) Q ^ ( i ) .
cos ( κ d ) = ( Q 11 + Q 22 ) / 2 .
cos ( κ d ) = ζ 0 ζ d cos φ a i Z a 2 + ζ 0 2 ζ d 2 2 Z a ζ d sin φ a + D 4 ζ d [ ( Z a 2 + ζ 0 2 ζ d 2 ) cos φ a 2 i Z a ζ 0 sin φ a ( Z a 2 ζ 0 2 + ζ d 2 ) cos ( α φ a ) ] .
α = ( l 1 l 2 ) / d a
cos ( κ d ) = ζ 0 ζ d cos φ a i Z a 2 + ζ 0 2 ζ d 2 2 Z a ζ d sin φ a .
T N = | ( Q N ) 22 | 2 .
| ζ 0 | , | ζ d | Z a ,
cos ( κ d ) = D ( ζ 0 2 ζ d 2 Z a 2 ) 4 ζ d + [ D ( ζ 0 2 ζ d 2 + Z a 2 ) 4 ζ d + ζ 0 ζ d ] cos φ a + Z a 2 ( D ζ 0 + 1 ) + ζ 0 2 ζ d 2 2 i Z a ζ d sin φ a .
σ ( intra ) = 2 i e 2 k B T π 2 ω ln [ 2 cosh ( μ c 2 k B T ) ] ,
σ ( inter ) = e 2 4 { 1 2 + 1 π arctan ω 2 μ c 2 k B T i 2 π ln ( ω + 2 μ c ) 2 ( ω 2 μ c ) 2 + ( 2 k B T ) 2 } ,
φ a j a π = 1 2 [ 1 cos ( j a π ) ] Z a Im D + 2 Z a [ Im ζ 0 Im ζ d cos ( j a π ) cos ( Re κ d ) ] .
Δ ω j a = 2 π [ 1 cos ( j a π ) ] Z a n a Im σ d a .
cos ( κ d ) = [ ζ 0 ζ d + D ( ζ 0 2 ζ d 2 ) 2 ζ d ] cos φ a i ( Z a 2 + ζ 0 2 ζ d 2 2 Z a ζ d + D Z a ζ 0 2 ζ d ) sin φ a .
φ a j a π = 4 Z a Im ζ 0 cos ( j a π ) Im ζ d cos ( Re κ d ) 2 cos ( j a π ) Z a Im D α sin ( j a π α ) + 1 cos ( j a π ) cos ( j a π α ) 2 ( Z a Im D ) 1 cos ( j a π ) α sin ( j a π α ) .
Δ ω j a = 1 cos ( j a π ) cos ( j a π α ) 2 ( Z a Im D ) 1 cos ( j a π ) α sin ( j a π α ) c n a d a .
ζ 0 = i k d b s = 1 k s 2 k 2 ε ( k s ) , ζ d = i k d b s = cos ( k s d b ) k s 2 k 2 ε ( k s ) .
ε ( k s ) = 1 ω p 2 ω ( ω + i ν ) 𝒦 ( k s l ω ) ,
𝒦 ( k s l ω ) = 3 2 { [ 1 k s l ω + 1 ( k s l ω ) 3 ] arctan ( k s l ω ) 1 ( k s l ω ) 2 } .

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