Abstract

Considering the dielectric permittivity of graphene can be tuned to be negative by external electric field, we propose to construct alternating graphene/dielectric multilayer based optical hyperlens for far-field subdiffraction imaging at mid-infrared frequencies. For such a scheme, hyperbolic dispersion curve can be achieved under the condition that the thickness of dielectric layer is made comparable to that of graphene layer, which is capable of supporting the propagation of evanescent wave with large wave vector. Simulation results by finite-element method demonstrate that two point sources with separation far below the diffraction limit can be magnified by the systems to the extent that conventional far-field optical microscopy can further manipulate. Such a hyperlens has the advantage of operating in a wideband region due to the tunability of graphene’s dielectric permittivity as opposed to previous metal based hyperlens, enabling the potential applications in real-time super-resolution imaging, nanolithography, and sensing.

© 2013 OSA

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2013 (4)

L. Chen, X. Li, and G. P. Wang, “A hybrid long-range plasmonic waveguide with sub-wavelength confinement,” Opt. Commun.291, 400–404 (2013).
[CrossRef]

H. Hu, D. Ji, X. Zeng, K. Liu, and Q. Gan, “Rainbow trapping in hyperbolic metamaterial waveguide,” Sci. Rep.3, 1249 (2013).
[CrossRef] [PubMed]

I. V. Iorsh, I. S. Mukhin, I. V. Shadrivov, P. A. Belov, and Y. S. Kivshar, “Hyperbolic metamaterials based on multilayer graphene structures,” Phys. Rev. B87(7), 075416 (2013).
[CrossRef]

M. A. Othman, C. Guclu, and F. Capolino, “Graphene-based tunable hyperbolic metamaterials and enhanced near-field absorption,” Opt. Express21(6), 7614–7632 (2013).
[CrossRef] [PubMed]

2012 (12)

M. Z. Alam, J. S. Aitchison, and M. Mojahedi, “Compact and silicon-on-insulator-compatible hybrid plasmonic TE-pass polarizer,” Opt. Lett.37(1), 55–57 (2012).
[CrossRef] [PubMed]

L. Chen, X. Li, G. P. Wang, W. Li, S. H. Chen, L. Xiao, and D. S. Gao, “A silicon-based 3-D hybrid long-range plasmonic waveguide for nanophotonic integration,” J. Lightwave Technol.30(1), 163–168 (2012).
[CrossRef]

L. Chen, T. Zhang, X. Li, and W. P. Huang, “Novel hybrid plasmonic waveguide consisting of two identical dielectric nanowires symmetrically placed on each side of a thin metal film,” Opt. Express20(18), 20535–20544 (2012).
[CrossRef] [PubMed]

B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett.109(7), 073901 (2012).
[CrossRef] [PubMed]

A. Grigorenko, M. Polini, and K. Novoselov, “Graphene plasmonics,” Nat. Photonics6(11), 749–758 (2012).
[CrossRef]

R. Quhe, J. Zheng, G. Luo, Q. Liu, R. Qin, J. Zhou, D. Yu, S. Nagase, W.-N. Mei, Z. Gao, and J. Lu, “Tunable and sizable band gap of single-layer graphene sandwiched between hexagonal boron nitride,” NPG Asia Mater.4(2), e6 (2012).
[CrossRef]

A. Andryieuski, A. V. Lavrinenko, and D. N. Chigrin, “Graphene hyperlens for terahertz radiation,” Phys. Rev. B86(12), 121108 (2012).
[CrossRef]

J. Wang, Y. Xu, H. Chen, and B. Zhang, “Ultraviolet dielectric hyperlens with layered graphene and boron nitride,” J. Mater. Chem.22(31), 15863–15868 (2012).
[CrossRef]

B. Wang, X. Zhang, X. Yuan, and J. Teng, “Optical coupling of surface plasmons between graphene sheets,” Appl. Phys. Lett.100(13), 131111 (2012).
[CrossRef]

N. Petrone, C. R. Dean, I. Meric, A. M. van der Zande, P. Y. Huang, L. Wang, D. Muller, K. L. Shepard, and J. Hone, “Chemical vapor deposition-derived graphene with electrical performance of exfoliated graphene,” Nano Lett.12(6), 2751–2756 (2012).
[CrossRef] [PubMed]

L. Ji, H. Zheng, A. Ismach, Z. Tan, S. Xun, E. Lin, V. Battaglia, V. Srinivasan, and Y. Zhang, “Graphene/Si multilayer structure anodes for advanced half and full lithium-ion cells,” Nano Energy1(1), 164–171 (2012).
[CrossRef]

D. Lu and Z. Liu, “Hyperlenses and metalenses for far-field super-resolution imaging,” Nat Commun3, 1205 (2012).
[CrossRef] [PubMed]

2011 (5)

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science332(6035), 1291–1294 (2011).
[CrossRef] [PubMed]

K.-J. Lee, A. P. Chandrakasan, and J. Kong, “Breakdown current density of CVD-grown multilayer graphene interconnects,” IEEE Electron Device Lett.32(4), 557–559 (2011).
[CrossRef]

P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano5(7), 5855–5863 (2011).
[CrossRef] [PubMed]

L. Chen, G. P. Wang, X. Li, W. Li, Y. Shen, J. Lai, and S. Chen, “Broadband slow-light in graded-grating-loaded plasmonic waveguides at telecom frequencies,” Appl. Phys. B104(3), 653–657 (2011).
[CrossRef]

A. Ramasubramaniam, D. Naveh, and E. Towe, “Tunable band gaps in bilayer graphene-BN heterostructures,” Nano Lett.11(3), 1070–1075 (2011).
[CrossRef] [PubMed]

2010 (3)

J. A. Robinson, M. Labella, K. A. Trumbull, X. Weng, R. Cavelero, T. Daniels, Z. Hughes, M. Hollander, M. Fanton, and D. Snyder, “Epitaxial graphene materials integration: effects of dielectric overlayers on structural and electronic properties,” ACS Nano4(5), 2667–2672 (2010).
[CrossRef] [PubMed]

E. Moreau, S. Godey, F. Ferrer, D. Vignaud, X. Wallart, J. Avila, M. Asensio, F. Bournel, and J.-J. Gallet, “Graphene growth by molecular beam epitaxy on the carbon-face of SiC,” Appl. Phys. Lett.97(24), 241907 (2010).
[CrossRef]

J. Zhang, J. Xiao, X. Meng, C. Monroe, Y. Huang, and J.-M. Zuo, “Free folding of suspended graphene sheets by random mechanical stimulation,” Phys. Rev. Lett.104(16), 166805 (2010).
[CrossRef] [PubMed]

2009 (4)

A. H. Castro Neto, 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]

J. Li, L. Fok, X. Yin, G. Bartal, and X. Zhang, “Experimental demonstration of an acoustic magnifying hyperlens,” Nat. Mater.8(12), 931–934 (2009).
[CrossRef] [PubMed]

T. Mohiuddin, A. Lombardo, R. Nair, A. Bonetti, G. Savini, R. Jalil, N. Bonini, D. Basko, C. Galiotis, N. Marzari, K. S. Novoselov, A. Geim, and A. Ferrari, “Uniaxial strain in graphene by Raman spectroscopy: G peak splitting, Grüneisen parameters, and sample orientation,” Phys. Rev. B79(20), 205433 (2009).
[CrossRef]

L. Chen and G. P. Wang, “Pyramid-shaped hyperlenses for three-dimensional subdiffraction optical imaging,” Opt. Express17(5), 3903–3912 (2009).
[CrossRef] [PubMed]

2008 (5)

L. Chen, X. Zhou, and G. Wang, “V-shaped metal–dielectric multilayers for far-field subdiffraction imaging,” Appl. Phys. B92(2), 127–131 (2008).
[CrossRef]

X. Zhang and Z. Liu, “Superlenses to overcome the diffraction limit,” Nat. Mater.7(6), 435–441 (2008).
[CrossRef] [PubMed]

Q. Gan, Z. Fu, Y. J. Ding, and F. J. Bartoli, “Ultrawide-bandwidth slow-light system based on THz plasmonic graded metallic grating structures,” Phys. Rev. Lett.100(25), 256803 (2008).
[CrossRef] [PubMed]

S. Kawata, A. Ono, and P. Verma, “Subwavelength colour imaging with a metallic nanolens,” Nat. Photonics2(7), 438–442 (2008).
[CrossRef]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics2(8), 496–500 (2008).
[CrossRef]

2007 (9)

L. Chen and G. Wang, “Nanofocusing of light energy by ridged metal heterostructures,” Appl. Phys. B89(4), 573–577 (2007).
[CrossRef]

E. H. Hwang and S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B75(20), 205418 (2007).
[CrossRef]

E. H. Hwang, S. Adam, and S. D. Sarma, “Carrier transport in two-dimensional graphene layers,” Phys. Rev. Lett.98(18), 186806 (2007).
[CrossRef] [PubMed]

E. V. Castro, K. S. Novoselov, S. V. Morozov, N. M. Peres, J. M. dos Santos, J. Nilsson, F. Guinea, A. K. Geim, and A. H. Neto, “Biased bilayer graphene: semiconductor with a gap tunable by the electric field effect,” Phys. Rev. Lett.99(21), 216802 (2007).
[CrossRef] [PubMed]

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature450(7168), 397–401 (2007).
[CrossRef] [PubMed]

Y. Xiong, Z. Liu, C. Sun, and X. Zhang, “Two-dimensional imaging by far-field superlens at visible wavelengths,” Nano Lett.7(11), 3360–3365 (2007).
[CrossRef] [PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science315(5819), 1686 (2007).
[CrossRef] [PubMed]

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Semiclassical theory of the hyperlens,” J. Opt. Soc. Am. A24(10), A52–A59 (2007).
[CrossRef] [PubMed]

H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Development of optical hyperlens for imaging below the diffraction limit,” Opt. Express15(24), 15886–15891 (2007).
[CrossRef] [PubMed]

2006 (2)

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express14(18), 8247–8256 (2006).
[CrossRef] [PubMed]

A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations,” Phys. Rev. B74(7), 075103 (2006).
[CrossRef]

2005 (2)

K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. Geim, “Two-dimensional atomic crystals,” Proc. Natl. Acad. Sci. U.S.A.102(30), 10451–10453 (2005).
[CrossRef] [PubMed]

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science308(5721), 534–537 (2005).
[CrossRef] [PubMed]

2004 (1)

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett.93(13), 137404 (2004).
[CrossRef] [PubMed]

2003 (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett.85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

1986 (1)

U. Dürig, D. Pohl, and F. Rohner, “Near-field optical-scanning microscopy,” J. Appl. Phys.59(10), 3318–3327 (1986).
[CrossRef]

1873 (1)

E. Abbe, “Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Arch. Mikrosk. Anat.9(1), 413–418 (1873).
[CrossRef]

Abbe, E.

E. Abbe, “Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Arch. Mikrosk. Anat.9(1), 413–418 (1873).
[CrossRef]

Adam, S.

E. H. Hwang, S. Adam, and S. D. Sarma, “Carrier transport in two-dimensional graphene layers,” Phys. Rev. Lett.98(18), 186806 (2007).
[CrossRef] [PubMed]

Aitchison, J. S.

Alam, M. Z.

Alekseyev, L. V.

Alù, A.

P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano5(7), 5855–5863 (2011).
[CrossRef] [PubMed]

Andryieuski, A.

A. Andryieuski, A. V. Lavrinenko, and D. N. Chigrin, “Graphene hyperlens for terahertz radiation,” Phys. Rev. B86(12), 121108 (2012).
[CrossRef]

Asensio, M.

E. Moreau, S. Godey, F. Ferrer, D. Vignaud, X. Wallart, J. Avila, M. Asensio, F. Bournel, and J.-J. Gallet, “Graphene growth by molecular beam epitaxy on the carbon-face of SiC,” Appl. Phys. Lett.97(24), 241907 (2010).
[CrossRef]

Avila, J.

E. Moreau, S. Godey, F. Ferrer, D. Vignaud, X. Wallart, J. Avila, M. Asensio, F. Bournel, and J.-J. Gallet, “Graphene growth by molecular beam epitaxy on the carbon-face of SiC,” Appl. Phys. Lett.97(24), 241907 (2010).
[CrossRef]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003).
[CrossRef] [PubMed]

Bartal, G.

J. Li, L. Fok, X. Yin, G. Bartal, and X. Zhang, “Experimental demonstration of an acoustic magnifying hyperlens,” Nat. Mater.8(12), 931–934 (2009).
[CrossRef] [PubMed]

Bartoli, F. J.

Q. Gan, Z. Fu, Y. J. Ding, and F. J. Bartoli, “Ultrawide-bandwidth slow-light system based on THz plasmonic graded metallic grating structures,” Phys. Rev. Lett.100(25), 256803 (2008).
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Basko, D.

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Figures (7)

Fig. 1
Fig. 1

(a) Dependence of the real parts of effective permittivity of graphene layer (blue line), tangential (green line) and radial (red line) permittivities for alternating graphene/dielectric multilayer as a function of wavelength ranging from 8 to 11 μm with μc = 0.087 eV. The thicknesses of graphene and dielectric layers are both assumed to be 1 nm. (b) Dispersion relation of hyperlens. Blue line: λ = 8.5 μm, green line: λ = 9.5 μm, and red line: λ = 10 μm.

Fig. 2
Fig. 2

(a) Cross-section of triangle-shaped hyperlens based on alternating graphene/silicon multilayer, which is covered with a silver layer (100 nm thick) with two slits (10 nm wide) separated by d = 3.3 μm in the bottom, where the two slits serve as two light scatters. The top of the structure is obliquely cut to form a base angle θ. (b-d) Magnetic field distributions of |(H)|2 in the x-y plane: (b) θ = 50°, (c) θ = 60°, and (d) θ = 70°. (e) Magnetic field profile of |(H)|2 at the input plane as the amplitude ratio of the incident light sources is set at 1:7.16. (f-h) Magnetic field profiles of |(H)|2 along the slope surface: (f) θ = 50°, (g) θ = 60°, and (h) θ = 70°.

Fig. 3
Fig. 3

Cross-section of a cylindrical alternating graphene/dielectric multilayer with the thickness t along the radial direction, where the inner surface is coated with a thin silver layer (100 nm thick) with two slits (50 nm wide) separated by d = 1 μm. The radius of the inner surface is denoted as r ( = 1 μm).

Fig. 4
Fig. 4

(a) Magnetic field distribution of |(H)|2 with t = 6 μm as the hyperlens is illuminated by a plane wave along y axis, while all the other parameters are the same as those of Fig. 3. (b) Magnetic field profile of |(H)|2 as a function of angle at the input surface with r = 1 μm. (c) Magnetic field profiles of |(H)|2 as a function of angle at the output surface with t = 6 μm (blue solid line), and t = 7 μm (red dashed line), respectively.

Fig. 5
Fig. 5

(a-c) Magnetic field distributions of |(H)|2 for different incident wavelengths: (a) λ = 9.5 μm (εg = −7.434 + 0.684i, ε// = 2.137 + 0.342i, ε = −39.128 + 10.017i), (b) λ = 9.7 μm (εg = −9.032 + 0.6923i, ε// = 1.337 + 0.3461i, ε = −72.63 + 24.86i), and (c) λ = 9.9 μm (εg = −10.62 + 0.7032i, ε// = 0.5431 + 0.3516i, ε = −154.4 + 115.1i). (d) Optical modulation and Re(ε//)/Re(-ε) versus the incident wavelength ranging from 9.4 μm to 10 μm. For all the simulations, t and μc are held constant at 6 μm and 0.087 eV, respectively.

Fig. 6
Fig. 6

(a) Dependence of Re(ε//) and Re(ε) on μc for λ = 9.5 μm. (b-d) Magnetic field distributions of |(H)|2 with t = 6 μm and λ = 9.5 μm for different μc: (b) μc = 0.07 eV (ε// = 12.507 + 0.927i, ε = 12.515 + 0.808i), (c) μc = 0.087 eV (ε// = 2.140 + 0.342i, ε = −39.023 + 9.984i), and (d) μc = 0.093 eV (ε// = 0.057 + 0.315i, ε = −52.365 + 422.06i).

Fig. 7
Fig. 7

Broadband far-field subdiffraction imaging by tuning μc to satisfy ε//>0, ε<0 and ε//→0: (a) λ = 9.2 μm (μc = 0.0965 eV, ε// = 0.1419 + 0.2933i, ε = −159.8 + 378.6i), (b) λ = 10.2 μm (μc = 0.085 eV, ε// = 0.1058 + 0.3709i, ε = −74.07 + 341.7i), (c) λ = 11.2 μm (μc = 0.075 eV, ε// = 0.4481 + 0.4678i, ε = −122.9 + 152.8i) and (d) λ = 12.2 μm (μc = 0.067 eV, ε// = 0.761 + 0.5831i, ε = −90.05 + 86.94i), respectively.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

ε // =( a 1 ε 1 + a 2 ε 2 )/( a 1 + a 2 ), ε =( a 1 + a 2 ) ε 1 ε 2 /( a 2 ε 1 + a 1 ε 2 )
σ g =i e 2 k B T π 2 ( ω+i τ 1 ) [ μ c k B T +2ln( exp( μ c k B T )+1 ) ] +i e 2 4π 2 ln[ 2| μ c |( ω+i τ 1 ) 2| μ c |+( ω+i τ 1 ) ]
ε g =1+ i σ g η 0 k 0 Δ

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