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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 18 — Sep. 9, 2013
  • pp: 20888–20899
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Graphene-based tunable broadband hyperlens for far-field subdiffraction imaging at mid-infrared frequencies

Tian Zhang, Lin Chen, and Xun Li  »View Author Affiliations


Optics Express, Vol. 21, Issue 18, pp. 20888-20899 (2013)
http://dx.doi.org/10.1364/OE.21.020888


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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

1. Introduction

The diffraction limit of light, caused by the exponential decay of evanescent waves which carry high spatial frequency information, prevents the conventional microscopy imaging below half of light wavelength [1

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

]. To overcome the diffraction limit, near-field scanning optical microscopy has been invented to reach a much finer resolution below the diffraction limit and has led to the possibility of resolving details on the orders of the 10-100 nm scale [2

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

]. However, the major constraint of this invention might be the need for scanning the sample surface point by point, making the entire scanning procedure extremely slow, hence whole imaging cannot be formed in real time.

Emerging within the last decade, the fields of plasmonics and metamaterials have offered exciting solutions for exhibiting many exotic optical phenomena and material properties, such as subwavelength waveguiding [3

3. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]

8

8. 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]

], nanofocusing [9

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

, 10

10. L. Chen and G. Wang, “Nanofocusing of light energy by ridged metal heterostructures,” Appl. Phys. B 89(4), 573–577 (2007). [CrossRef]

], negative-index of refraction [11

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

, 12

12. N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005). [CrossRef] [PubMed]

], strongly anisotropic materials [13

13. Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006). [CrossRef] [PubMed]

17

17. L. Chen and G. P. Wang, “Pyramid-shaped hyperlenses for three-dimensional subdiffraction optical imaging,” Opt. Express 17(5), 3903–3912 (2009). [CrossRef] [PubMed]

], and “trapped rainbow” effect [18

18. K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007). [CrossRef] [PubMed]

21

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

]. A new super-resolution imaging concept so-called “superlens” has attracted tremendous research interest for its capability of amplifying evanescent waves by use of negative-index material and projecting subdiffraction images without scanning [11

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

, 12

12. N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005). [CrossRef] [PubMed]

]. However, the amplified imaging is within the limit of the near field because the evanescent waves will disappear within a short distance after the negative-index material, hence is undetectable by conventional optics. It is highly desirable for many applications to produce a direct far-field optical image with subwavelength features that can be further processed by conventional optical microscopy. Far-field superlens, consisting of a silver superlens coated with additional nanoscale corrugations on its top surface, was proposed to achieve this goal by projecting a sub-diffraction imaging into the far-field [22

22. 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]

]. The evanescent waves can be amplified by the silver superlens, and subsequently, converted into propagation waves via a designed surface corrugation. The far-field images are obtained by retrieving the field angular spectrum, hence it should not be regarded as a direct imaging. Metallic nanowires based subwavelength imaging systems have also attracted intensive research interests for their abilities to achieve far-field sub-diffraction imaging within a wideband frequencies and low-loss [23

23. S. Kawata, A. Ono, and P. Verma, “Subwavelength colour imaging with a metallic nanolens,” Nat. Photonics 2(7), 438–442 (2008). [CrossRef]

]. However, it remains a great challenge in creating uniform metallic nanowire arrays as well as introducing of nanoscale gaps between the arrays.

In contrast to metal, graphene, whose optical response is characterized by surface conductivity, has attracted special attention in optical field since free standing graphene was found [29

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

39

39. 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]

]. Recent study has demonstrated that two-dimensional electrons and holes in graphene respond to an external electric field by screening the external field, i.e., modifying or changing the external field in a complex manner [36

36. E. H. Hwang and S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B 75(20), 205418 (2007). [CrossRef]

39

39. 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]

]. At low frequencies such as mid-infrared range, graphene behaves like a thin metal layer with negative permittivity as the imaginary part of conductivity can be tuned to be positive via external tunability such as electric field, magnetic field, and gate voltage [29

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

, 30

30. 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]

]. This unique feature has made graphene a promising candidate for constructing various nanophotonic devices, such as superlens, Luneburg lens and SPP waveguides. Optical hyperlenses for THz and ultraviolet frequency have been theoretically demonstrated by use of graphene wire medium, graphene or boron-nitride layered structures, respectively [40

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

, 41

41. 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]

]. Recently, alternating graphene/dielectric multilayer has been demonstrated to be capable of supporting hyperbolic dispersion curve, where the effective dielectric permittivity along radial (εr) and tangential direction (εθ) are positive and negative, respectively [34

34. 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. B 87(7), 075416 (2013). [CrossRef]

]. However, for hyperlens implementation εr<0 and εθ>0 is highly desirable.

In this article, considering that the dielectric permittivity of graphene can be tuned to be negative via external tunability, we give a proposal for optical hyperlens for far-field subdiffraction imaging based on alternating graphene/dielectric multilayer in the mid-infrared domain. The thickness of dielectric layer is made comparable to that of graphene layer, leading to hyperbolic dispersion curve with εr<0 and εθ>0, which is capable of supporting the propagation of evanescent waves. Numerical simulation results by finite-element method confirm 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 resolve. We also demonstrate such a hyperlens can be made to work in a broadband region due to the flexible tunability of graphene’s dielectric permittivity.

In Section 2, we will briefly introduce the working principle for far-field subdiffraction imaging based on alternating graphene/dielectric multilayer. In Section 3, triangle-shaped hyperlens is proposed, and the effect of far-field subwavelength imaging is validated by numerical simulations. In Section 4, we will propose cylindrical hyperlens, and reveal that such a hyperlens can work in a wideband frequency by tuning graphene’s relative permittivity via external tunability. In Section 5, we will draw a brief conclusion.

2. Principle of hyperlens based on alternating graphene/dielectric multilayer

In a cylindrical coordinate system the dispersion relationship of electromagnetic wave can be simply described as kθ2/εr + kr2/εθ = k02, where kθ and kr are wave vectors, εθ and εr are relative permittivities along tangential and radial directions, respectively [14

14. A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations,” Phys. Rev. B 74(7), 075103 (2006). [CrossRef]

]. In the k space, this equation represents an ellipse or hyperbola depending on the sign of εθ and εr. When the sign(εθ) is unequal to sign(εr), the dispersion curve represents a hyperbola with the asymptotes denoted as kr = ± |εθ/εr|1/2kθ. As compared to ellipse-shaped dispersion curve, the hyperbolic one has the advantage of supporting the propagation of high frequency components carried by evanescent waves, leading to a subdiffraction imaging in the far-field. To retrieve an undistorted imaging, the hyperbolic dispersion curve should be designed to be very flat to ensure all the light waves propagate along the radial direction, i.e., εθ is close to zero. In other words, the field distribution in an arbitrary plane can be transferred to any other plane point by point without imaging distortion [14

14. A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations,” Phys. Rev. B 74(7), 075103 (2006). [CrossRef]

]. Generally, such kind of anisotropic material at optical frequencies can be simply realized by use of alternating metal/dielectric multilayer, where the dielectric permittivities of metal and dielectric layer are negative and positive, respectively [13

13. Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006). [CrossRef] [PubMed]

, 14

14. A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations,” Phys. Rev. B 74(7), 075103 (2006). [CrossRef]

]. If the thicknesses of both layers d1 and d2 are much smaller than the operating wavelength, this layered structure can be represented as a uniform anisotropic material with a permittivity tensor given by [14

14. A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations,” Phys. Rev. B 74(7), 075103 (2006). [CrossRef]

]
ε//=(a1ε1+a2ε2)/(a1+a2),ε=(a1+a2)ε1ε2/(a2ε1+a1ε2)
(1)
Where ε// and ε denote the permittivities along the tangential and radial directions, respectively. a1 and a2 are filling ratios, respectively, and satisfying a1 + a2 = 1, ε1 and ε2 are the permittivities of metal and dielectric layers, respectively.

To realize a hyperlens without distorted imaging, it is highly required that ε//>0, ε<0 and ε//→0, hence ε1<0, ε2 >0, and a1ε1 + a2ε2→0 is highly desirable for a hyperlens. In the ultraviolet and visible range, silver could be chosen as the negative-index material [17

17. L. Chen and G. P. Wang, “Pyramid-shaped hyperlenses for three-dimensional subdiffraction optical imaging,” Opt. Express 17(5), 3903–3912 (2009). [CrossRef] [PubMed]

, 22

22. 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]

]. Nevertheless, in the infrared domain, it is a significant challenge in constructing a hyperlens based on metal owing to its large permittivity and high transmission loss. For example, silver layer has the real part of relative permittivity of −5132.3, and can only support the propagation of electromagnetic wave for a distance of approximately 11 nm at the wavelength of 10 μm.

From Eq. (1) we can simply obtain the real parts of ε// [Re(ε//)] and ε [Re(ε)] for alternating graphene/dielectric multilayer. The dependence of Re(ε//) and Re(ε) on the incident wavelength is depicted in Fig. 1(a). For λ = 8.5 μm, such a metamaterial supports an elliptical dispersion curve with Re(ε//) = 2.028 and Re(ε) = 6.388 [Fig. 1(b)]. Increasing the working wavelength can make the metamaterial support hyperbolic dispersion curve with Re(ε//) = −39.13, Re(ε) = 2.136 [λ = 9.5 μm in Fig. 1(b)], and Re(ε//) = −113.1, Re(ε) = 0.1468 [λ = 10 μm in Fig. 1(b)], respectively, which is capable of supporting the propagation of evanescent wave. It should be noted here, although this layered structure can work for far-field subdiffraction imaging for both wavelengths, it is more appropriate for imaging without distortion at λ = 10 μm due to a much flatter dispersion curve.

3. Triangle-shaped hyperlens

We first investigate the feasibility of using triangle-shaped alternating graphene/dielectric multilayer for far-field subdiffraction imaging. Figure 2(a)
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°.
schematically shows the proposed layered structure with an oblique cut on the top, which is covered with a silver layer with two slits in the bottom. To test the effect of far-field subdiffraction imaging, we consider two slits (10nm width) served as two point sources with separation below the diffraction limit, d = 3.3 μm. It should be noted here, other materials that do not change graphene's unique properties, such as hafnium oxide, need to be adopted as the light scatters in actual cases [45

45. J. A. Robinson, M. Labella III, 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 Nano 4(5), 2667–2672 (2010). [CrossRef] [PubMed]

, 46

46. H. Alles, J. Aarik, J. Kozlova, A. Niilisk, R. Rammula, and V. Sammelselg, “Atomic layer deposition of high-k oxides on graphene,” in Graphene–Synthesis, Characterization, Properties and Applications, J. R. Gong, ed. (InTech, 2011), pp. 99–114.

]. Figures 2(b)-2(d) shows the magnetic field distributions of |H|2 in the x-y plane as the amplitude ratio of the incident light sources is set at 1:7.16 [see the magnetic field profile at the input plane in Fig. 2(e)] for different base angles: θ = 50°, 60°, and 70°. In the calculations, μc is equal to 0.087 eV, which is the same as that is used in Fig. 1(b). The present results show that the light wave propagates straightly along the normal direction of the multilayer, which confirms our prediction in the above analysis. Additionally, the unequal amplitude of the incident light sources in the two slits ensures equal light intensity of two imaging spots at the slope surface with θ = 50° [Figs. 2(b) and 2(f)]. Through the transfer by the oblique output plane, the image separation, D, will appear to be d/cosθ. Apparently, one can modulate the base angle to get a proper magnification. The calculated separations between the two output beams at the slope surfaces are λ/1.95 (θ = 50°), λ/1.52 (θ = 60°), and λ/1.04 (θ = 70°), respectively, which are much larger than the diffraction limit [Figs. 2(f)-2(h)]. A larger θ will lead to a greater magnification. The intensity distribution in the far-field zone can then be detected by a conventional optical microscopy. However, the optical paths from different point sources to the imaging plane are different, hence attenuations experienced by different beams are different, which might lead to the variation of imaging intensity and forming a distorted image. This problem can be avoided by use of other shapes of hyperlens, such as cylindrical alternating graphene/dielectric multilayer.

4. Cylindrical hyperlens

Recently, lots of work has been focused on cylinder-shaped hyperlenses, which have been theoretically and experimentally demonstrated to be capable of achieving far-field super-resolution imaging [13

13. Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006). [CrossRef] [PubMed]

, 15

15. Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007). [CrossRef] [PubMed]

]. Apart from being capable of imaging without distortion due to the equal traveling distance for different beams, cylindrical geometry has the advantage of enlarging imaging magnification by enhancing the ratio of the radii of output and input surface, which offers the possibility of resolving details far below the diffraction limit. Figure 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).
schematically shows the cross-section of the cylinder-shaped hyperlens, where the inner surface is coated with a thin silver layer with two slits separated by d = 1 μm. We can see from Fig. 4(a)
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.
that, upon light illumination, light wave from two slits will propagate along the normal direction of the layered structure, and form two imaging spots at the output surface. The distance between the two spots at the output surface is D = d(r + t)/r, where r and t, denote the radius of the inner surface and thickness of multilayer, respectively. The image turns out to be enlarged by a factor (r + t)/r. Under the plane wave illumination, the field intensities at two imaging points will be equal, hence making an undistorted magnified image in the far-field zone that can be further processed by conventional optical microscopy [Figs. 4(b) and 4(c)]. We have noted in a theoretical study on optical phonons of graphene, bending of graphene would change graphene's phonon structure, which will change scattering process and modify graphene's conductivity [47

47. 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. B 79(20), 205433 (2009). [CrossRef]

]. To effectively minish the influence of phonon scattering process on the surface conductivity of graphene due to curvature, sufficiently large r could be chosen for a cylindrical hyperlens. Meanwhile, we can increase t to maintain a proper imaging magnification factor (1 + t/r). Consequently, we believe that the influence of phonon scattering process due to the curvature on graphene's conductivity can be significantly eliminated for the present hyperlens.

If ε//→0 is not strictly satisfied, light wave after the two slits still propagates along the radial direction but with a much larger beam divergence. In this situation, far-field subdiffraction imaging can still be achievable, but the image quality may become worse owing to the mutual interference of the propagation beam. Figures 5(a)
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.
-5(c) show the magnetic field distributions of |H|2 with t = 6 μm for different incident wavelengths. We can see that the beam divergence become interferential if the wavelength is assumed to make Re(ε//) much larger than zero [Fig. 5(a)]. Reducing Re(ε//) can significantly decrease the mutual interference at the imaging plane [Fig. 5(b)]. The best image quality can be achievable under the condition Re(ε//) is close to zero [Fig. 5(c)]. In order to quantitatively estimate the effect of mutual interference of beam divergence on the image quality, optical modulation is introduced to represent the image contrast. Generally, optical modulation is defined as the saddle to peak field intensity M = I2/I1, where I2 and I1 denote the saddle and peak field intensity at the output surface, respectively [48

48. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (CUP Archive, 1999).

]. It can be seen from Fig. 5(d), the modulation M firstly decreases with the reduced slope of asymptote represented by Re(ε//)/ Re(-ε), and approaches zero as the dispersion curve is nearly flat [Re(ε//)/Re(-ε)→zero] at λ = 9.85 μm, where an optimum image quality occurs. We have noted in a recent report on hyperlens based on layered graphene or hexagonal Boron Nitride for far-field imaging in the ultraviolet range, the traveling beams from two point sources mutually interfere significantly because the dispersion curve is not made flat for rectilinear propagation [41

41. 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]

].

It should be noted that it is feasible to perform far-field subdiffraction imaging within a broadband frequencies by tuning μc to satisfy ε//>0, ε<0 and ε//→0 that is required for a hyperlens without distorted image. For a fixed operating wavelength, one can always choose an appropriate μc to meet the above-mentioned requirements that far-field subdiffraction image can be realizable. Simulation results from 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.
show that we are able to achieve far-field super-resolution ranging from 9.2 μm [Fig. 7(a)], 10.2 μm [Fig. 7(b)], 11.2 μm [Fig. 7(c)], 12.2 μm [Fig. 7(d)] with μc varied from 0.0965 eV, 0.085 eV, 0.075 eV, 0.067 eV, respectively.

Finally, it is technologically achievable to fabricate layered structure consisting of alternating graphene/dielectric layers, where the dielectric layer is made infinitesimally thin. We can employ cleavage technique [49

49. 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]

], chemical vapor deposition (CVD) [50

50. 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]

], as well as molecular beam epitaxy [51

51. 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]

] methods to implement fabrication of single graphene layer. Recently, fabrication of graphene layered structures, such as the folding of graphene sheets by mechanical deformation and 10-20nm graphene films by CVD growth, has been reported [51

51. 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]

53

53. 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]

]. Three-dimensional composites of graphene not only present excellent flexibility that can be bent, stretched, and twisted without breaking, but also preserve the optical properties of two-dimensional graphene. For future experimental implementation of such graphene/silicon multilayer based hyperlenses, deposition techniques (e.g., sputtering and/or E-bean evaporation) can be employed to form the silver layer. The graphene/silicon multilayer structures above the silver layer can be fabricated through a repeated process of filtering liquid-phase exfoliated graphene film and the subsequent coating of silicon film via plasma-enhanced chemical vapor deposition (PECVD) method [54

54. 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 Energy 1(1), 164–171 (2012). [CrossRef]

]. In a series of studies, heterostructures composed of alternating graphene/hexagonal Boron Nitride have been already experimentally fabricated [32

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

, 33

33. 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]

]. Hexagonal Boron Nitride, which has thickness that is comparable to graphene layer and relative permittivity around 4, can be employed to serve as the dielectric layer. Consequently, we believe that such a graphene/dielectric layered structure might be “designed” freely based on the current nanofabrication technologies in the near future.

5 Conclusions

In conclusion, we have proposed a novel hyperlens based on alternating graphene/dielectric layers for far-field sub-resolution imaging at mid-infrared frequencies. The dispersion curve for such a scheme can be tuned to be hyperbolic by modulating graphene’s permittivity to be negative via external electric field. Due to the hyperbolic dispersion curve, such a structure is capable of supporting the propagation of evanescent wave with very large wave vector, hence projecting an amplified far-field image in the far-field region that can be further manipulated by conventional optics systems. Triangular and cylindrical geometries have been employed to validate the imaging effect and were numerically demonstrated to be capable of resolving two point sources that is separated far below the diffraction limit. We have also demonstrated the possibility of achieving broadband far-field subdiffraction imaging without distortion by varying graphene’s dielectric permittivity to get a nearly flat dispersion curve for different wavelengths. The present results enable the potential applications in real-time super-resolution imaging, nanolithography, and sensing.

Acknowledgment

This work is supported by NSFC (Grant No. 11104093), and ‘the Fundamental Research Funds for the Central Universities’, HUST: 2013TS046”.

References and links

1.

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

2.

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

3.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]

4.

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. Photonics 2(8), 496–500 (2008). [CrossRef]

5.

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]

6.

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]

7.

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. Express 20(18), 20535–20544 (2012). [CrossRef] [PubMed]

8.

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]

9.

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

10.

L. Chen and G. Wang, “Nanofocusing of light energy by ridged metal heterostructures,” Appl. Phys. B 89(4), 573–577 (2007). [CrossRef]

11.

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

12.

N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub-diffraction-limited optical imaging with a silver superlens,” Science 308(5721), 534–537 (2005). [CrossRef] [PubMed]

13.

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14(18), 8247–8256 (2006). [CrossRef] [PubMed]

14.

A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations,” Phys. Rev. B 74(7), 075103 (2006). [CrossRef]

15.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007). [CrossRef] [PubMed]

16.

L. Chen, X. Zhou, and G. Wang, “V-shaped metal–dielectric multilayers for far-field subdiffraction imaging,” Appl. Phys. B 92(2), 127–131 (2008). [CrossRef]

17.

L. Chen and G. P. Wang, “Pyramid-shaped hyperlenses for three-dimensional subdiffraction optical imaging,” Opt. Express 17(5), 3903–3912 (2009). [CrossRef] [PubMed]

18.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007). [CrossRef] [PubMed]

19.

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]

20.

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. B 104(3), 653–657 (2011). [CrossRef]

21.

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

22.

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]

23.

S. Kawata, A. Ono, and P. Verma, “Subwavelength colour imaging with a metallic nanolens,” Nat. Photonics 2(7), 438–442 (2008). [CrossRef]

24.

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Semiclassical theory of the hyperlens,” J. Opt. Soc. Am. A 24(10), A52–A59 (2007). [CrossRef] [PubMed]

25.

H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Development of optical hyperlens for imaging below the diffraction limit,” Opt. Express 15(24), 15886–15891 (2007). [CrossRef] [PubMed]

26.

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]

27.

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

28.

D. Lu and Z. Liu, “Hyperlenses and metalenses for far-field super-resolution imaging,” Nat Commun 3, 1205 (2012). [CrossRef] [PubMed]

29.

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

30.

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]

31.

A. Grigorenko, M. Polini, and K. Novoselov, “Graphene plasmonics,” Nat. Photonics 6(11), 749–758 (2012). [CrossRef]

32.

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

33.

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]

34.

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. B 87(7), 075416 (2013). [CrossRef]

35.

M. A. 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]

36.

E. H. Hwang and S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B 75(20), 205418 (2007). [CrossRef]

37.

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]

38.

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]

39.

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]

40.

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

41.

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]

42.

P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011). [CrossRef] [PubMed]

43.

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]

44.

E. Palik, Handbook of Optical Constants of Solids (Academic, 1991).

45.

J. A. Robinson, M. Labella III, 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 Nano 4(5), 2667–2672 (2010). [CrossRef] [PubMed]

46.

H. Alles, J. Aarik, J. Kozlova, A. Niilisk, R. Rammula, and V. Sammelselg, “Atomic layer deposition of high-k oxides on graphene,” in Graphene–Synthesis, Characterization, Properties and Applications, J. R. Gong, ed. (InTech, 2011), pp. 99–114.

47.

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. B 79(20), 205433 (2009). [CrossRef]

48.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (CUP Archive, 1999).

49.

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]

50.

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]

51.

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]

52.

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]

53.

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]

54.

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 Energy 1(1), 164–171 (2012). [CrossRef]

OCIS Codes
(110.0180) Imaging systems : Microscopy
(160.1190) Materials : Anisotropic optical materials
(220.0220) Optical design and fabrication : Optical design and fabrication

ToC Category:
Imaging Systems

History
Original Manuscript: July 2, 2013
Revised Manuscript: August 11, 2013
Manuscript Accepted: August 22, 2013
Published: August 29, 2013

Citation
Tian Zhang, Lin Chen, and Xun Li, "Graphene-based tunable broadband hyperlens for far-field subdiffraction imaging at mid-infrared frequencies," Opt. Express 21, 20888-20899 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-18-20888


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References

  1. E. Abbe, “Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Arch. Mikrosk. Anat.9(1), 413–418 (1873). [CrossRef]
  2. U. Dürig, D. Pohl, and F. Rohner, “Near-field optical-scanning microscopy,” J. Appl. Phys.59(10), 3318–3327 (1986). [CrossRef]
  3. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003). [CrossRef] [PubMed]
  4. 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]
  5. 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]
  6. 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]
  7. 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]
  8. 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]
  9. M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett.93(13), 137404 (2004). [CrossRef] [PubMed]
  10. L. Chen and G. Wang, “Nanofocusing of light energy by ridged metal heterostructures,” Appl. Phys. B89(4), 573–577 (2007). [CrossRef]
  11. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett.85(18), 3966–3969 (2000). [CrossRef] [PubMed]
  12. 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]
  13. 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]
  14. A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations,” Phys. Rev. B74(7), 075103 (2006). [CrossRef]
  15. 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]
  16. 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]
  17. L. Chen and G. P. Wang, “Pyramid-shaped hyperlenses for three-dimensional subdiffraction optical imaging,” Opt. Express17(5), 3903–3912 (2009). [CrossRef] [PubMed]
  18. K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature450(7168), 397–401 (2007). [CrossRef] [PubMed]
  19. 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]
  20. 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]
  21. H. Hu, D. Ji, X. Zeng, K. Liu, and Q. Gan, “Rainbow trapping in hyperbolic metamaterial waveguide,” Sci. Rep.3, 1249 (2013). [CrossRef] [PubMed]
  22. 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]
  23. S. Kawata, A. Ono, and P. Verma, “Subwavelength colour imaging with a metallic nanolens,” Nat. Photonics2(7), 438–442 (2008). [CrossRef]
  24. Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Semiclassical theory of the hyperlens,” J. Opt. Soc. Am. A24(10), A52–A59 (2007). [CrossRef] [PubMed]
  25. 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]
  26. 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]
  27. X. Zhang and Z. Liu, “Superlenses to overcome the diffraction limit,” Nat. Mater.7(6), 435–441 (2008). [CrossRef] [PubMed]
  28. D. Lu and Z. Liu, “Hyperlenses and metalenses for far-field super-resolution imaging,” Nat Commun3, 1205 (2012). [CrossRef] [PubMed]
  29. A. Vakil and N. Engheta, “Transformation optics using graphene,” Science332(6035), 1291–1294 (2011). [CrossRef] [PubMed]
  30. 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]
  31. A. Grigorenko, M. Polini, and K. Novoselov, “Graphene plasmonics,” Nat. Photonics6(11), 749–758 (2012). [CrossRef]
  32. A. Ramasubramaniam, D. Naveh, and E. Towe, “Tunable band gaps in bilayer graphene-BN heterostructures,” Nano Lett.11(3), 1070–1075 (2011). [CrossRef] [PubMed]
  33. 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]
  34. 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]
  35. 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]
  36. E. H. Hwang and S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B75(20), 205418 (2007). [CrossRef]
  37. 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]
  38. 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]
  39. 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]
  40. A. Andryieuski, A. V. Lavrinenko, and D. N. Chigrin, “Graphene hyperlens for terahertz radiation,” Phys. Rev. B86(12), 121108 (2012). [CrossRef]
  41. 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]
  42. P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano5(7), 5855–5863 (2011). [CrossRef] [PubMed]
  43. 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]
  44. E. Palik, Handbook of Optical Constants of Solids (Academic, 1991).
  45. 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]
  46. H. Alles, J. Aarik, J. Kozlova, A. Niilisk, R. Rammula, and V. Sammelselg, “Atomic layer deposition of high-k oxides on graphene,” in Graphene–Synthesis, Characterization, Properties and Applications, J. R. Gong, ed. (InTech, 2011), pp. 99–114.
  47. 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]
  48. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (CUP Archive, 1999).
  49. 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]
  50. 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]
  51. 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]
  52. 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]
  53. 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]
  54. 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]

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