Abstract

We demonstrate tunable mid-infrared (MIR) beam steering devices based on multilayer graphene-dielectric metamaterials. The effective refractive index of such metamaterials can be manipulated by changing the chemical potential of each graphene layer. This can arbitrarily tailor the spatial distribution of the phase of the transmitted beam, providing mechanisms for active beam steering. Three different beam steerer (BS) designs are discussed: a graded-index (GRIN) graphene-based metamaterial block, an array of metallic waveguides filled with graphene-dielectric metamaterial and an array of planar waveguides created in a graphene-dielectric metamaterial block with a specific spatial profile of graphene sheets doping. The performances of the BSs are numerically analyzed, showing the tunability of the proposed designs for a wide range of output angles (up to approximately 70°). The proposed graphene-based tunable beam steering can be used in tunable transmitter/receiver modules for infrared imaging and sensing.

© 2016 Optical Society of America

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2015 (9)

B. Orazbayev, N. Mohammadi Estakhri, M. Beruete, and A. Alù, “Terahertz carpet cloak based on a ring resonator metasurface,” Phys. Rev. B 91(19), 195444 (2015).
[Crossref]

Y. Dai, X. Zhu, N. A. Mortensen, J. Zi, and S. Xiao, “Nanofocusing in a tapered graphene plasmonic waveguide,” J. Opt. 17(6), 065002 (2015).
[Crossref]

R. Z. Zhang and Z. M. Zhang, “Tunable positive and negative refraction of infrared radiation in graphene-dielectric multilayers,” Appl. Phys. Lett. 107(19), 191112 (2015).
[Crossref]

J. S. Gomez-Diaz, C. Moldovan, S. Capdevila, J. Romeu, L. S. Bernard, A. Magrez, A. M. Ionescu, and J. Perruisseau-Carrier, “Self-biased reconfigurable graphene stacks for terahertz plasmonics,” Nat. Commun. 6, 6334 (2015).
[Crossref] [PubMed]

X. Liu, N. Wen, X. Wang, and Y. Zheng, “Layer-by-layer self-assembled graphene multilayer films via covalent bonds for supercapacitor electrodes,” Nanomater. Nanotechnol. 5, 1–7 (2015).

D. Qiu and E. K. Kim, “Electrically tunable and negative Schottky barriers in multi-layered graphene/MoS2 heterostructured transistors,” Sci. Rep. 5, 13743 (2015).
[Crossref] [PubMed]

D. A. Boyd, W.-H. Lin, C.-C. Hsu, M. L. Teague, C.-C. Chen, Y.-Y. Lo, W.-Y. Chan, W.-B. Su, T.-C. Cheng, C.-S. Chang, C.-I. Wu, and N.-C. Yeh, “Single-step deposition of high-mobility graphene at reduced temperatures,” Nat. Commun. 6, 6620 (2015).
[Crossref] [PubMed]

L. Banszerus, M. Schmitz, S. Engels, J. Dauber, M. Oellers, F. Haupt, K. Watanabe, T. Taniguchi, B. Beschoten, and C. Stampfer, “Ultrahigh-mobility graphene devices from chemical vapor deposition on reusable copper,” Sci. Adv. 1(6), e1500222 (2015).
[Crossref] [PubMed]

L. Yang, C. Pei, A. Shen, C. Zhao, Y. Li, X. Li, H. Yu, Y. Li, X. Jiang, and J. Yang, “An all-optical modulation method in sub-micron scale,” Sci. Rep. 5, 9206 (2015).
[Crossref] [PubMed]

2014 (10)

P.-Y. Chen, M. Farhat, A. N. Askarpour, M. Tymchenko, and A. Alù, “Infrared beam-steering using acoustically modulated surface plasmons over a graphene monolayer,” J. Opt. 16(9), 094008 (2014).
[Crossref]

M. Esquius-Morote, J. S. Gomez-Diaz, and J. Perruisseau-Carrier, “Sinusoidally modulated graphene leaky-wave antenna for electronic beamscanning at THz,” IEEE Trans. Terahertz Sci. Technol. 4(1), 116–122 (2014).
[Crossref]

V. Pacheco-Peña, V. Torres, B. Orazbayev, M. Beruete, M. Navarro-Cía, M. Sorolla Ayza, and N. Engheta, “Mechanical 144 GHz beam steering with all-metallic epsilon-near-zero lens antenna,” Appl. Phys. Lett. 105(24), 243503 (2014).
[Crossref]

V. Pacheco-Peña, V. Torres, M. Beruete, M. Navarro-Cía, and N. Engheta, “ϵ -near-zero (ENZ) graded index quasi-optical devices: steering and splitting millimeter waves,” J. Opt. 16(9), 094009 (2014).
[Crossref]

J. Cong, Y. Chen, J. Luo, and X. Liu, “Fabrication of graphene/polyaniline composite multilayer films by electrostatic layer-by-layer assembly,” J. Solid State Chem. 218, 171–177 (2014).
[Crossref]

I. Khromova, A. Andryieuski, and A. Lavrinenko, “Ultrasensitive terahertz/infrared waveguide modulators based on multilayer graphene metamaterials,” Laser Photonics Rev. 8(6), 916–923 (2014).
[Crossref]

J. Lao, J. Tao, Q. J. Wang, and X. G. Huang, “Tunable graphene-based plasmonic waveguides: nano modulators and nano attenuators,” Laser Photonics Rev. 8(4), 569–574 (2014).
[Crossref]

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref] [PubMed]

T. Chen and S. He, “Frequency-tunable circular polarization beam splitter using a graphene-dielectric sub-wavelength film,” Opt. Express 22(16), 19748–19757 (2014).
[Crossref] [PubMed]

T. P. Steinbusch, H. K. Tyagi, M. C. Schaafsma, G. Georgiou, and J. Gómez Rivas, “Active terahertz beam steering by photo-generated graded index gratings in thin semiconductor films,” Opt. Express 22(22), 26559–26571 (2014).
[Crossref] [PubMed]

2013 (10)

X. Zhu, W. Yan, N. A. Mortensen, and S. Xiao, “Bends and splitters in graphene nanoribbon waveguides,” Opt. Express 21(3), 3486–3491 (2013).
[Crossref] [PubMed]

C. T. DeRose, R. D. Kekatpure, D. C. Trotter, A. Starbuck, J. R. Wendt, A. Yaacobi, M. R. Watts, U. Chettiar, N. Engheta, and P. S. Davids, “Electronically controlled optical beam-steering by an active phased array of metallic nanoantennas,” Opt. Express 21(4), 5198–5208 (2013).
[Crossref] [PubMed]

M. A. K. Othman, C. Guclu, and F. Capolino, “Graphene-based tunable hyperbolic metamaterials and enhanced near-field absorption,” Opt. Express 21(6), 7614–7632 (2013).
[Crossref] [PubMed]

B. Zhu, G. Ren, S. Zheng, Z. Lin, and S. Jian, “Nanoscale dielectric-graphene-dielectric tunable infrared waveguide with ultrahigh refractive indices,” Opt. Express 21(14), 17089–17096 (2013).
[Crossref] [PubMed]

J. S. Gómez-Díaz, M. Esquius-Morote, and J. Perruisseau-Carrier, “Plane wave excitation-detection of non-resonant plasmons along finite-width graphene strips,” Opt. Express 21(21), 24856–24872 (2013).
[Crossref] [PubMed]

S. He, X. Zhang, and Y. He, “Graphene nano-ribbon waveguides of record-small mode area and ultra-high effective refractive indices for future VLSI,” Opt. Express 21(25), 30664–30673 (2013).
[Crossref] [PubMed]

I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. Belov, and Y. S. Kivshar, “Hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B 87(7), 075416 (2013).
[Crossref]

S. H. Lee, J. Choi, H.-D. Kim, H. Choi, and B. Min, “Ultrafast refractive index control of a terahertz graphene metamaterial,” Sci. Rep. 3, 2135 (2013).
[Crossref] [PubMed]

M. A. K. Othman, C. Guclu, and F. Capolino, “Graphene–dielectric composite metamaterials: evolution from elliptic to hyperbolic wavevector dispersion and the transverse epsilon-near-zero condition,” J. Nanophotonics 7(1), 073089 (2013).
[Crossref]

J. Neu, R. Beigang, and M. Rahm, “Metamaterial-based gradient index beam steerers for terahertz radiation,” Appl. Phys. Lett. 103(4), 041109 (2013).
[Crossref]

2012 (6)

M. Tamagnone, J. S. Gómez-Díaz, J. R. Mosig, and J. Perruisseau-Carrier, “Reconfigurable terahertz plasmonic antenna concept using a graphene stack,” Appl. Phys. Lett. 101(21), 214102 (2012).
[Crossref]

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 487(7405), 82–85 (2012).
[PubMed]

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 487(7405), 77–81 (2012).
[PubMed]

D. Rainwater, A. Kerkhoff, K. Melin, J. C. Soric, G. Moreno, and A. Alù, “Experimental verification of three-dimensional plasmonic cloaking in free-space,” New J. Phys. 14(1), 013054 (2012).
[Crossref]

A. Andryieuski, A. V. Lavrinenko, and D. N. Chigrin, “Graphene hyperlens for terahertz radiation,” Phys. Rev. B 86(12), 121108 (2012).
[Crossref]

A. Fallahi and J. Perruisseau-Carrier, “Design of tunable biperiodic graphene metasurfaces,” Phys. Rev. B. 86(19), 195408 (2012).
[Crossref]

2011 (5)

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]

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

D. Kwong, A. Hosseini, Y. Zhang, and R. T. Chen, “1×12 Unequally spaced waveguide array for actively tuned optical phased array on a silicon nanomembrane,” Appl. Phys. Lett. 99(5), 051104 (2011).
[Crossref]

C. García-Meca, M. M. Tung, J. V. Galán, R. Ortuño, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Squeezing and expanding light without reflections via transformation optics,” Opt. Express 19(4), 3562–3575 (2011).
[Crossref] [PubMed]

J. T. Kim and S.-Y. Choi, “Graphene-based plasmonic waveguides for photonic integrated circuits,” Opt. Express 19(24), 24557–24562 (2011).
[Crossref] [PubMed]

2010 (1)

2009 (1)

O. Sydoruk, E. Tatartschuk, E. Shamonina, and L. Solymar, “Analytical formulation for the resonant frequency of split rings,” J. Appl. Phys. 105(1), 014903 (2009).
[Crossref]

2008 (1)

K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. L. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146(9-10), 351–355 (2008).
[Crossref]

2006 (2)

Q. Sun, Y. Rostovtsev, and M. Zubairy, “Optical beam steering based on electromagnetically induced transparency,” Phys. Rev. A 74(3), 033819 (2006).
[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]

2004 (1)

X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[Crossref] [PubMed]

1960 (1)

S. Roberts, “Optical properties of copper,” Phys. Rev. 118(6), 1509–1518 (1960).
[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 487(7405), 77–81 (2012).
[PubMed]

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Figures (5)

Fig. 1
Fig. 1

(a) Graphene complex conductivity normalized to σ0 = e2/4ħ = 0.061 mS for T = 300 K, γ = 10−12 s−1 at f = 20 THz. (Inset) Geometry of the graphene-dielectric metamaterial. (b) Complex effective permittivity, εeff, for εm = 3, T = 300 K, f = 20 THz and different values of spacer thickness d. Solid and dashed lines stand for real and imaginary parts, respectively.

Fig. 2
Fig. 2

Schemes for the BS1 (a), BS2 (c) and BS3 (e). (b), (d), (f) Real part of the effective refractive index vs the x coordinate for the BS1, BS2, and BS3, respectively. (g) Spatial distribution of the widths hq in BS3.

Fig. 3
Fig. 3

Numerically calculated magnitude of the Ey-field for the first (a-c), second (e-g) and third design (i-k) for output angles: θ = 30° (first column, a,e,i), θ = 45° (second column, b,f,j), θ = 60° (third column, c,g,k). Black dashed lines in (a-c) represent the analytical solutions for the ray propagation inside the GRIN medium. (d), (h) and (l) show the radiation patterns of the BS1, BS2, and BS3, respectively, analytically (dashed) and numerically (solid) calculated for the output angles of 30° (red), 45° (blue), and 60° (green).

Fig. 4
Fig. 4

Analytically (dashed lines) and numerically (solid lines) calculated output angles of the BSs vs the inclination of the graphene’s chemical potential Δµx in the metamaterial for the BS1 (red), BS2 (blue) and BS3 (green). Horizontal solid lines represent the maximum output angles for the three BS designs.

Fig. 5
Fig. 5

Analytically (solid lines) and numerically calculated effective refractive index for a TEM mode of a parallel-plate waveguide filled with a dielectric medium (dotted lines) and with graphene-dielectric metamaterial (dashed lines). This shows the validity of tensorial effective medium approach for BS2 for faster calculations.

Tables (1)

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Table 1 Numerical Analysis of the Three Proposed BSs

Equations (10)

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ε=( ε m 0 0 0 ε eff 0 0 0 ε eff )
ε eff ( ω,μ,d )= ε m + i σ s ( ω,μ ) dω ε 0
n( x )= sin( θ ) L z (x L x )+ n max
L z(min) = L x sin( θ max ) ε max ε min
d 2 x d z 2 = 1 n(x) dn(x) dx
β q = k 0 n eff q
ϕ q = β 0 L z mod( k 0 x q sin( θ ),2π )
L z = 2π β max β min
n eff q = ϕ q k 0 L z
h q k 0 ε c ( n eff q ) 2 =2 tan 1 ( ( n eff q ) 2 ε cl ε c ( n eff q ) 2 )+π( m1 )

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