Abstract

In this paper we present the efficient design of functional thin-film metamaterial devices with the effective surface conductivity approach. As an example, we demonstrate a graphene based perfect absorber. After formulating the requirements to the perfect absorber in terms of surface conductivity we investigate the properties of graphene wire medium and graphene fishnet metamaterials and demonstrate both narrowband and broadband tunable absorbers.

© 2013 OSA

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2012 (21)

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

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons.” Nature (London)487, 77–81 (2012).

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging.” Nature (London)487, 82–85 (2012).

A. N. Grigorenko, M. Polini, and K. S. Novoselov, “Graphene plasmonics,” Nature Photonics487, 749–758 (2012).
[CrossRef]

B. Sensale-Rodriguez, R. Yan, and M. Kelly, “Broadband graphene terahertz modulators enabled by intraband transitions,” Nature Comm.3, 780–787 (2012).
[CrossRef]

S. H. Lee, M. Choi, T.-T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C.-G. Choi, S.-Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials.” Nature Mat.11, 936–941 (2012).
[CrossRef]

A. Andryieuski, A. Lavrinenko, and D. Chigrin, “Graphene hyperlens for terahertz radiation,” Phys. Rev. B86, 121108(R) (2012).
[CrossRef]

R. Alaee, M. Farhat, C. Rockstuhl, and F. Lederer, “A perfect absorber made of a graphene micro-ribbon meta-material,” Opt. Express20, 28017–28024 (2012).
[CrossRef] [PubMed]

A. Fallahi and J. Perruisseau-Carrier, “Design of tunable biperiodic graphene metasurfaces,” Phys. Rev. B86, 195408 (2012).
[CrossRef]

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks.” Nature Nanotech.7, 330–334 (2012).
[CrossRef]

B. Sensale-Rodriguez, R. Yan, S. Rafique, M. Zhu, W. Li, X. Liang, D. Gundlach, V. Protasenko, M. M. Kelly, D. Jena, L. Liu, and H. G. Xing, “Extraordinary control of terahertz beam reflectance in graphene electro-absorption modulators,” Nano Lett.12, 4518–4522 (2012).
[CrossRef] [PubMed]

A. Nikitin, F. Guinea, F. Garcia-Vidal, and L. Martin-Moreno, “Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons,” Phys. Rev. B85, 081405 (2012).
[CrossRef]

A. Y. Nikitin, F. Guinea, and L. Martin-Moreno, “Resonant plasmonic effects in periodic graphene antidot arrays,” Appl. Phys. Lett.101, 151119 (2012).
[CrossRef]

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

J. D. Buron, D. H. Petersen, P. Bøggild, D. G. Cooke, M. Hilke, J. Sun, E. Whiteway, P. F. Nielsen, O. Hansen, A. Yurgens, and P. U. Jepsen, “Graphene conductance uniformity mapping.” Nano Lett.12, 5074–5081 (2012).
[CrossRef] [PubMed]

K. F. Mak, L. Ju, F. Wang, and T. F. Heinz, “Optical spectroscopy of graphene: from the far infrared to the ultraviolet,” Solid State Comm.152, 1341–1349 (2012).
[CrossRef]

L. Ren, Q. Zhang, J. Yao, Z. Sun, R. Kaneko, Z. Yan, S. Nanot, Z. Jin, I. Kawayama, M. Tonouchi, J. M. Tour, and J. Kono, “Terahertz and infrared spectroscopy of gated large-area graphene,” Nano Lett.12, 3711–3715 (2012).
[CrossRef] [PubMed]

Q. Bao and K. P. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices.” ACS Nano6, 3677–3694 (2012).
[CrossRef] [PubMed]

T. Otsuji, S. A. Boubanga Tombet, A. Satou, H. Fukidome, M. Suemitsu, E. Sano, V. Popov, M. Ryzhii, and V. Ryzhii, “Graphene-based devices in terahertz science and technology,” J. Phys. D45, 303001 (2012).
[CrossRef]

I. Llatser, C. Kremers, A. Cabellos-Aparicio, J. M. Jornet, E. Alarcón, and D. N. Chigrin, “Graphene-based nano-patch antenna for terahertz radiation,” Photon. Nanostr. Fundam. Appl.10, 353–358 (2012).
[CrossRef]

P. Tassin, T. Koschny, and C. M. Soukoulis, “Effective material parameter retrieval for thin sheets: theory and application to graphene, thin silver films, and single-layer metamaterials,” Physica B: Condensed Matter407, 4062–4065 (2012).
[CrossRef]

2011 (5)

P. D. Cunningham, N. N. Valdes, F. a. Vallejo, L. M. Hayden, B. Polishak, X.-H. Zhou, J. Luo, A. K.-Y. Jen, J. C. Williams, and R. J. Twieg, “Broadband terahertz characterization of the refractive index and absorption of some important polymeric and organic electro-optic materials,” Journal of Applied Physics109, 043505 (2011).
[CrossRef]

B. Sensale-Rodriguez, T. Fang, R. Yan, M. M. Kelly, D. Jena, L. Liu, and H. (Grace) Xing, “Unique prospects for graphene-based terahertz modulators,” Appl. Phys. Lett.99, 113104 (2011).
[CrossRef]

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

A. Vakil and N. Engheta, “Transformation optics using graphene.” Science332, 1291–1294 (2011).
[CrossRef] [PubMed]

P. Jepsen, D. Cooke, and M. Koch, “Terahertz spectroscopy and imaging - modern techniques and applications,” Laser & Photonics Rev.5, 124–166 (2011).
[CrossRef]

2010 (1)

J. Federici and L. Moeller, “Review of terahertz and subterahertz wireless communications,” J. Appl. Phys.107, 111101 (2010).
[CrossRef]

2009 (3)

A. Hill, S. A. Mikhailov, and K. Ziegler, “Dielectric function and plasmons in graphene,” Europhysics Lett.87, 27005 (2009).
[CrossRef]

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B80, 245435 (2009).
[CrossRef]

A. Geim, “Graphene: status and prospects.” Science324, 1530–1534 (2009).
[CrossRef] [PubMed]

2008 (2)

K. Bolotin, K. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun.146, 351–355 (2008).
[CrossRef]

G. Hanson, “Dyadic Green’s functions for an anisotropic, non-local model of biased graphene,” IEEE Trans. Antennas and Propagation, 56, 747–757 (2008).
[CrossRef]

2007 (2)

M. Tonouchi, “Cutting-edge terahertz technology,” Nature (London)1, 97–105 (2007).

S. Mikhailov and K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett.99, 016803 (2007).
[CrossRef] [PubMed]

(Grace) Xing, H.

B. Sensale-Rodriguez, T. Fang, R. Yan, M. M. Kelly, D. Jena, L. Liu, and H. (Grace) Xing, “Unique prospects for graphene-based terahertz modulators,” Appl. Phys. Lett.99, 113104 (2011).
[CrossRef]

Alaee, R.

Alarcón, E.

I. Llatser, C. Kremers, A. Cabellos-Aparicio, J. M. Jornet, E. Alarcón, and D. N. Chigrin, “Graphene-based nano-patch antenna for terahertz radiation,” Photon. Nanostr. Fundam. Appl.10, 353–358 (2012).
[CrossRef]

Alonso-González, P.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons.” Nature (London)487, 77–81 (2012).

Andreev, G. O.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging.” Nature (London)487, 82–85 (2012).

Andryieuski, A.

A. Andryieuski, A. Lavrinenko, and D. Chigrin, “Graphene hyperlens for terahertz radiation,” Phys. Rev. B86, 121108(R) (2012).
[CrossRef]

Avouris, P.

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks.” Nature Nanotech.7, 330–334 (2012).
[CrossRef]

Badioli, M.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons.” Nature (London)487, 77–81 (2012).

Bao, Q.

Q. Bao and K. P. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices.” ACS Nano6, 3677–3694 (2012).
[CrossRef] [PubMed]

Bao, W.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging.” Nature (London)487, 82–85 (2012).

Basov, D. N.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging.” Nature (London)487, 82–85 (2012).

Bøggild, P.

J. D. Buron, D. H. Petersen, P. Bøggild, D. G. Cooke, M. Hilke, J. Sun, E. Whiteway, P. F. Nielsen, O. Hansen, A. Yurgens, and P. U. Jepsen, “Graphene conductance uniformity mapping.” Nano Lett.12, 5074–5081 (2012).
[CrossRef] [PubMed]

Bolotin, K.

K. Bolotin, K. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun.146, 351–355 (2008).
[CrossRef]

Boubanga Tombet, S. A.

T. Otsuji, S. A. Boubanga Tombet, A. Satou, H. Fukidome, M. Suemitsu, E. Sano, V. Popov, M. Ryzhii, and V. Ryzhii, “Graphene-based devices in terahertz science and technology,” J. Phys. D45, 303001 (2012).
[CrossRef]

Buljan, H.

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B80, 245435 (2009).
[CrossRef]

Buron, J. D.

J. D. Buron, D. H. Petersen, P. Bøggild, D. G. Cooke, M. Hilke, J. Sun, E. Whiteway, P. F. Nielsen, O. Hansen, A. Yurgens, and P. U. Jepsen, “Graphene conductance uniformity mapping.” Nano Lett.12, 5074–5081 (2012).
[CrossRef] [PubMed]

Cabellos-Aparicio, A.

I. Llatser, C. Kremers, A. Cabellos-Aparicio, J. M. Jornet, E. Alarcón, and D. N. Chigrin, “Graphene-based nano-patch antenna for terahertz radiation,” Photon. Nanostr. Fundam. Appl.10, 353–358 (2012).
[CrossRef]

Camara, N.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons.” Nature (London)487, 77–81 (2012).

Castro Neto, A. H.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging.” Nature (London)487, 82–85 (2012).

Centeno, A.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons.” Nature (London)487, 77–81 (2012).

Chandra, B.

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks.” Nature Nanotech.7, 330–334 (2012).
[CrossRef]

Chang, D. E.

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

Chen, J.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons.” Nature (London)487, 77–81 (2012).

Chigrin, D.

A. Andryieuski, A. Lavrinenko, and D. Chigrin, “Graphene hyperlens for terahertz radiation,” Phys. Rev. B86, 121108(R) (2012).
[CrossRef]

Chigrin, D. N.

I. Llatser, C. Kremers, A. Cabellos-Aparicio, J. M. Jornet, E. Alarcón, and D. N. Chigrin, “Graphene-based nano-patch antenna for terahertz radiation,” Photon. Nanostr. Fundam. Appl.10, 353–358 (2012).
[CrossRef]

Choi, C.-G.

S. H. Lee, M. Choi, T.-T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C.-G. Choi, S.-Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials.” Nature Mat.11, 936–941 (2012).
[CrossRef]

Choi, H. K.

S. H. Lee, M. Choi, T.-T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C.-G. Choi, S.-Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials.” Nature Mat.11, 936–941 (2012).
[CrossRef]

Choi, M.

S. H. Lee, M. Choi, T.-T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C.-G. Choi, S.-Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials.” Nature Mat.11, 936–941 (2012).
[CrossRef]

Choi, S.-Y.

S. H. Lee, M. Choi, T.-T. Kim, S. Lee, M. Liu, X. Yin, H. K. Choi, S. S. Lee, C.-G. Choi, S.-Y. Choi, X. Zhang, and B. Min, “Switching terahertz waves with gate-controlled active graphene metamaterials.” Nature Mat.11, 936–941 (2012).
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P. D. Cunningham, N. N. Valdes, F. a. Vallejo, L. M. Hayden, B. Polishak, X.-H. Zhou, J. Luo, A. K.-Y. Jen, J. C. Williams, and R. J. Twieg, “Broadband terahertz characterization of the refractive index and absorption of some important polymeric and organic electro-optic materials,” Journal of Applied Physics109, 043505 (2011).
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Figures (6)

Fig. 1
Fig. 1

The conductive interface (for example, graphene layer) between two dielectrics is equivalent to a load attached to the junction between two transmission lines.

Fig. 2
Fig. 2

Total absorbance can be achieved in the graphene metamaterial film above a ground plane. (a) Equivalent transmission line. Graphene metamaterial is equivalent to a load, metallic mirror is equivalent to short circuit. (b) Graphene metamaterial and mirror (ground plane) are separated with a thick dielectric layer of thickness h. The metamaterial itself consists of two layers of structured graphene separated with a very thin dielectric.

Fig. 3
Fig. 3

Absorbance shows a global maximum at ξ = 1, ζ + γcot(Φ) = 0. The working range A ≥ 0.9 lies within a circle of the radius ≈ 0.7 centered at ξ = 1, ζ + γcotΦ = 0.

Fig. 4
Fig. 4

Real and imaginary part of normalized effective surface conductivity σSZ0 of continuous graphene (a), graphene wire medium (b) and graphene fishnet metamaterial (c). In all cases there are two layers of graphene separated with a thin dielectric. Graphene wire medium shows reduced Drude-like conductivity as compared with continuous graphene, whereas graphene fishnet exhibits a plasmonic resonance that gives large values of real part and negative imaginary part of conductivity.

Fig. 5
Fig. 5

(a) Real part of normalized surface conductivity of two graphene layers ξ = 1 at 2.3 THz. (b) Imaginary part ζ (green line) defines the value of dielectric thickness h, so that quickly changing γcotΦ(orange line with triangles) compensate ζ and give ζ + γcotΦ = 0 (red line with circles) at the same frequency 2.3 THz. (c) Absorbance of the device is tuned by Fermi energy [0 (black), 0.1 (orange), 0.2 (green), 0.5 (red) eV]. The analytical predictions (lines) are in a perfect correspondence with full-wave simulation results (symbols). The working bandwidth at A ≥ 0.9 is 0.4 THz.

Fig. 6
Fig. 6

(a) Real part of normalized surface conductivity of two graphene fishnet layers ξ = 1 at 2.7 THz. (b) Imaginary part ζ (green line) defines the value of dielectric thickness h, so that quickly changing γcotΦ(red line with circles) compensate ζ and give ζ + γcotΦ = 0 (orange line with triangles) at the same frequency 2.7 THz. (c) Absorbance of the device is tuned by Fermi energy [0 (black), 0.1 (orange), 0.2 (green), 0.5 (red) eV]. The analytical predictions (lines) are in a perfect correspondence with full-wave simulation results (symbols). The working bandwidth at A ≥ 0.9 is 1.9 THz.

Equations (28)

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t = 2 n 1 n 1 + n 2 + σ S Z 0 ,
r = n 1 n 2 σ S Z 0 n 1 + n 2 + σ S Z 0 ,
t T E = 2 q 1 q 1 + q 2 + Z 0 σ S ,
r T E = q 1 q 2 Z 0 σ S q 1 + q 2 + Z 0 σ S ,
t T M = 2 ε 1 q 1 ε 1 q 1 + ε 2 q 2 + Z 0 σ S ,
r T M = ε 1 q 1 ε 2 q 2 Z 0 σ S ε 1 q 1 + ε 2 q 2 + Z 0 σ S ,
t = 2 1 + γ + ξ + i ζ ,
r = 1 γ ξ i ζ 1 + γ + ξ + i ζ ,
T = γ | t | 2 = 4 γ ( 1 + γ + ξ ) 2 + ζ 2 ,
R = ( 1 γ ξ ) 2 + ζ 2 ( 1 + γ + ξ ) 2 + ζ 2 ,
A = 1 T R = 4 ξ ( 1 + γ + ξ ) 2 + ζ 2 .
A max = 1 1 + γ .
r = r 1 t 1 t 2 exp ( i 2 Φ ) + r 2 ,
t 1 = 2 1 + γ + ξ + i ζ ,
t 2 = 2 γ 1 + γ + ξ + i ζ ,
r 1 = 1 γ ξ i ζ 1 + γ + ξ + i ζ ,
r 2 = γ 1 ξ i ζ 1 + γ + ξ + i ζ .
A = 4 ξ ( 1 + ξ ) 2 + [ ζ + γ cot ( Φ ) ] 2 .
ξ = 1 ,
ζ + γ cot ( Φ ) = 0 .
σ S = σ S intra + σ S inter ,
σ S intra = 2 k B T e 2 π h ¯ 2 ln ( 2 cosh E F 2 k B T ) i ω + i τ 1 ,
σ S inter = e 2 4 h ¯ [ H ( ω 2 ) + i 4 ω π 0 H ( Ω ) H ( ω 2 ) ω 2 4 Ω 2 d Ω ] ,
σ S e 2 E F π h ¯ 2 i ω + i τ 1 .
ε eff , t = 1 + i σ S ε 0 ω Δ .
ω P = [ 2 e 2 k B T π h ¯ 2 ε 0 Δ ln ( 2 cosh E F 2 k B T ) ] 1 / 2 .
ξ + i ζ = 2 t ( 1 + γ ) .
σ S eff Z 0 = 2 S 21 n 1 n 2 ( n 1 + n 2 ) .

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