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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 10 — May. 20, 2013
  • pp: 12592–12603
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A 3D tunable and multi-frequency graphene plasmonic cloak

Mohamed Farhat, Carsten Rockstuhl, and Hakan Bağcı  »View Author Affiliations


Optics Express, Vol. 21, Issue 10, pp. 12592-12603 (2013)
http://dx.doi.org/10.1364/OE.21.012592


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Abstract

We demonstrate the possibility of cloaking three-dimensional objects at multi-frequencies in the far-infrared part of the spectrum. The proposed cloaking mechanism exploits graphene layers wrapped around the object to be concealed. Graphene layers are doped via a variable external voltage difference permitting continuous tuning of the cloaking frequencies. Particularly, two configurations are investigated: (i) Only one graphene layer is used to suppress the scattering from a dielectric sphere. (ii) Several of these layers biased at different gate voltages are used to achieve a multi-frequency cloak. These frequencies can be set independently. The proposed cloak’s functionality is verified by near- and far-field computations. By considering geometry and material parameters that are realizable by practical experiments, we contribute to the development of graphene based plasmonic applications that may find use in disruptive photonic technologies.

© 2013 OSA

1. Introduction

Cloaking is undoubtedly among the most intriguing applications of metamaterials [1

1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006). [CrossRef] [PubMed]

,2

2. U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006). [CrossRef] [PubMed]

]. Recent technological advancements in manufacturing and characterizing materials at the milli-, micro-, and nano-meter scales suggest that practical cloaking will be possible in the near future [3

3. T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010). [CrossRef] [PubMed]

]. The idea of cloaking exploiting transformation optics was introduced by Pendry [1

1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006). [CrossRef] [PubMed]

]. This type of cloaking makes use of a singular transformation to predict material properties that make the cloaking region look like a point to external observers [1

1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006). [CrossRef] [PubMed]

]. At the same time and independently, Leonhardt proposed a similar concept termed conformal invisibility, which is valid in the geometric optics limit [2

2. U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006). [CrossRef] [PubMed]

]. It is now well known that this class of cloaks suffers from highly anisotropic and singular material properties required by the transformation. Particularly, the (approximate) practical numerical and experimental realizations of these singular material properties alter the ideal cloaking efficiency [4

4. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007). [CrossRef]

6

6. I. I. Smolyaninov, V. N. Smolyaninova, A. V. Kildishev, and V. M. Shalaev, “Anisotropic metamaterials emulated by tapered waveguides: Application to optical cloaking,” Phys. Rev. Lett. 102(21), 213901 (2009). [CrossRef] [PubMed]

]. Additionally, the size of the cloaking shell is usually in the order of the object being concealed [7

7. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006). [CrossRef] [PubMed]

]. This limits the number of possible applications since compactness is typically required for several practical uses of invisibility cloaks, such as concealing probes and sensors.

In the same vein, Alù and Engheta proposed a transparency device that exploits the scattering cancellation technique (SCT) [8

8. A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016623 (2005). [CrossRef] [PubMed]

]. SCT makes use of a negative local polarizability cover with low or negative permittivity to suppress the total electric dipole moment of the object being concealed. This class of cloaks has been shown to be quite robust to changes in the geometry of objects and the frequency of operation [9

9. A. Alù and N. Engheta, “Plasmonic materials in transparency and cloaking problems: Mechanism, robustness, and physical insights,” Opt. Express 15(6), 3318–3332 (2007). [CrossRef] [PubMed]

11

11. M. Farhat, S. Mühlig, C. Rockstuhl, and F. Lederer, “Scattering cancellation of the magnetic dipole field from macroscopic spheres,” Opt. Express 20(13), 13896–13906 (2012). [CrossRef] [PubMed]

]. A recent experimental validation of SCT has been realized at microwave frequencies [12

12. 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]

]. Like its transformation optics-based counterpart, this class of cloaks suffers from several practical physical limitations: Plasmonic cloaks have narrow band of operation since they rely on the plasmonic properties of their building blocks, which are generally noble metals with negative or close-to-zero permittivity. Once the geometry of the shell is designed and constructed, the scattering reduction is only operational at a single frequency. Practical applications would often necessitate more flexibility of the design and frequency band of operation.

In this work, to alleviate the severity of these practical implementation issues, we propose to use graphene to construct plasmonic SCT-based invisibility shells. Graphene sheets comprising honeycomb crystal of carbon atoms [sketched in Fig. 1(a)
Fig. 1 (a) Sketch of a graphene sheet on top of dielectric substrate. (b) SPP dispersion relation with chemical potential set to 1000 meV. (c) Real and (d) imaginary parts of the bulk permittivity of graphene layer given by Eqs. (1)-(4) for various values of chemical potential ranging from 100 to 1000 meV and frequency ranging from 100 to 750 THz. The inset shows the energy bands of the graphene. (c) Effect of damping frequency (Γc) on graphene permittivity εV,G: solid lines represent the real part whereas dotted-dashed lines represent imaginary part.
] were first isolated by Geim and Novoselov [13

13. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004). [CrossRef] [PubMed]

]. Further experimental investigations have demonstrated graphene’s unusual characteristics [14

14. A. H. Castro Neto, F. Guinea, 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]

18

18. M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011). [CrossRef] [PubMed]

]. Among those, the one that is most relevant to plasmonics is its ability to support the propagation of guided surface electromagnetic waves at its interface with an insulator, the so-called surface plasmon polaritons (SPPs) [19

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

20

20. M. Jablan, H. Buljan, and M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009). [CrossRef]

]. These SPPs are highly tunable through chemical doping or an external voltage difference applied to the graphene layer. Additionally, when compared to their metallic counterparts, graphene SPPs have longer propagation lengths [21

21. 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]

]. These properties open the way for tunable plasmonics [21

21. 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]

23

23. L. Wang, W. Cai, X. Zhang, and J. Xu, “Surface plasmons at the interface between graphene and Kerr-type nonlinear media,” Opt. Lett. 37(13), 2730–2732 (2012). [CrossRef] [PubMed]

] that could have many real world applications [24

24. K. Y. Shin, J.-Y. Hong, and J. Jang, “Micropatterning of graphene sheets by inkjet printing and its wideband dipole-antenna application,” Adv. Mater. 23(18), 2113–2118 (2011). [CrossRef] [PubMed]

30

30. R. Alaee, M. Farhat, C. Rockstuhl, and F. Lederer, “A perfect absorber made of a graphene micro-ribbon metamaterial,” Opt. Express 20(27), 28017–28024 (2012). [CrossRef] [PubMed]

].

In this work, the dynamically tunable SPPs induced on graphene layer(s) are exploited to circumvent some of the limitations associated with plasmonic SCT-based cloaks. The proposed cloak makes use of graphene layers wrapped around dielectric core objects to suppress their scattering response. The tunability of the scattering cancellation is achieved by biasing the graphene layers with a variable external voltage difference. Particularly, two configurations are investigated: (i) Only one graphene layer is used to conceal the scattering from a dielectric sphere. (ii) Several of these layers biased at different voltages are used to generate plasmonic cloaking at tunable multi-frequencies.

The remainder of the paper is organized as follows. First, plasmonic properties of graphene layers on top of dielectrics are analyzed to demonstrate the potential of tuning the plasmon resonance at will by sweeping the chemical potential via applying gate voltage. Then, it is demonstrated that a single layer of graphene covering a dielectric sphere can drastically reduce its scattering cross section. The dependence of the cloaking dip on the chemical potential of graphene is clearly shown. This permits the design of a tunable plasmonic cloak. This design is further developed by cascading graphene layers with gate voltages set at different levels on top of the very same obstacle. This improved cloak has multi-frequency bands of operation, i.e., many dips in the scattering cross section are observed. The number of these dips is equal to the number of layers constituting the cloak.

It should be noted here that even though only numerical experiments are provided, the proposed cloaks can actually be constructed thanks to the recent experimental progress in wrapping graphene sheets around various shapes (cylindrical or spherical) [31

31. J. W. Ko, S.-W. Kim, J. Hong, K. Kang, and C. B. Park, “Synthesis of graphene-wrapped CuO hybrid materials by CO2 mineralization,” Green Chem. 14(9), 2391–2394 (2012). [CrossRef]

,32

32. J. S. Lee, K. H. You, and C. B. Park, “Highly photoactive, low bandgap TiO2 nanoparticles wrapped by graphene,” Adv. Mater. 24(8), 1084–1088 (2012). [CrossRef] [PubMed]

]. Additionally, it should be mentioned here that the approach to cancel the scattered fields at various frequencies proposed here may also represent a viable way for non-invasive sensing and probing with improved bandwidth [33

33. A. Alù and N. Engheta, “Cloaked near-field scanning optical microscope tip for noninvasive near-field imaging,” Phys. Rev. Lett. 105(26), 263906 (2010). [CrossRef] [PubMed]

].

2. Tunable plasmonics induced by graphene

As shown by both theoretical and experimental studies, non-doped graphene exhibits a very high absorption [15

15. R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308–1308 (2008). [CrossRef] [PubMed]

,16

16. K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490(7419), 192–200 (2012). [CrossRef] [PubMed]

] at optical frequencies at zero temperatures. This is especially remarkable given the fact that thickness of a graphene layer is only sub nanometer. It should be noted here that the graphene layer’s conductivity is independent of any material parameters and is only function of the fine structure constant [15

15. R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308–1308 (2008). [CrossRef] [PubMed]

]. This is mainly due to the linear dispersion relation of its quasi-particles close to the Fermi energy [inset of Fig. 1(c)]. Another important feature of graphene is its anomalous band structure: the valence band has a negative energy whereas the conduction band has a positive energy, and both bands have an intersection point at zero energy, without any bandgap (in contrast to metals and dielectrics) [inset of Fig. 1(c)]. Graphene could thus be considered as a semiconductor with zero-gap. In contrast, doped graphene (non-zero Fermi energy or chemical potential) layers exhibit a completely different behavior: The complex surface conductivity σS,G for a graphene layer can be calculated from Kubo’s formula having contributions from intraband and interband absorption [34

34. G. W. Hanson, “Dyadic Green’s functions and guided surface waves on graphene,” J. Appl. Phys. 103, 064302 (2006). [CrossRef]

]:
σS,G(ω)=σS,G(ω)jσS,G(ω)=σintra(ω)+σinter(ω).
(1)
In Eq. (1), σintra and σinter represent absorption due to intraband electron-photon scattering and interband electron transition processes, respectively. They are evaluated using
σintra(ω)=jq2π(ω+jΓc)[μc+2kBTln(eμc/kBT+1)],
(2)
σinter(ω)=jq24πln[2|μc|(ω+jΓc)2|μc|+(ω+jΓc)],
(3)
respectively. It should be noted here that the second expression is simplified and valid in the regime where |μc|,ωkBT. Here, ω is the angular frequency, q is the charge of electron, is the reduced planck constant, kB is the Boltzman constant, T is the temperature, μc is the chemical potential of doped graphene layer, and Γc is the damping constant. The temperature is assigned the default value of T=300K. The damping constant of graphene reads as Γc=qvf2/μμc, where vf=c/300m/s is the Fermi velocity, μ=10,000cm2/Vs is the electron mobility. Note that this choice of μ is a rather conservative upon considering latest experimental results provided in [16

16. K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490(7419), 192–200 (2012). [CrossRef] [PubMed]

]. As could be seen from Eqs. (2) and (3) both the interband and intraband absorption are dependent upon the chemical potential μc, damping Γc and operating frequency ω.

The dependence of the complex permittivity of graphene, εV,G given by Eq. (4), on the chemical potential μc and the damping coefficient Γc parameters is characterized between 100 and 800 THz. Figures 1(c) and 1(d) plot real and imaginary parts of εV,G as a function of chemical potential μc and frequency. They clearly show the resulting blue-shift as μc is increased at a given frequency. Figure 1(e) characterizes the effect of damping Γc for a fixed value of μc and clearly demonstrates the decreasing and broadening of εV,G around the metal-dielectric transition frequency when Γc is increased. As demonstrated in Fig. 1, the optical properties of graphene could be largely controlled by its chemical potential μc and damping coefficient Γc. Note that Γc depends on the purity of graphene sheets and the experimental method used to produce it, whereas μc can be easily tuned via doping or applying a gate voltage Vg. The latter is preferred here since it makes it possible to dynamically tune the variation in the far-infrared response of the graphene SPPs. This is not possible with conventional noble metals (e.g. gold and silver). This key characteristic of graphene is exploited in the plasmonic SCT-based cloak designs to achieve a tunable frequency response and multi-frequency band of operation as detailed in the following two sections.

It should be noted here that in the simulations carried out for this work, the thickness of the graphene layer δ=1nm. This choice was mainly motivated by the seminal work of Vakil and Engheta [26

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

] and several others studying graphene plasmonics [22

22. F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: A platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011). [CrossRef] [PubMed]

]. As expected, the actual value of δ, provided that it is much smaller than the wavelength of excitation, has a negligible impact on the optical response of the designs under study.

3. Dynamically tunable plasmonic SCT-based cloak

3.1 Tunable single layered cloak

To better illustrate the efficiency of the proposed invisibility cloak, we have computed the electric fields scattered from the cloaked and bare dielectric spheres illuminated by a plane wave with unit amplitude (1V/m) electric field in the x-direction and propagating in the y-direction. The frequency of the excitation is 58 THz. Figure 3
Fig. 3 Norm of the total electric field in V/m in linear scale in the presence of (a) the bare dielectric sphere and (b) cloaked sphere, both illuminated by a plane wave with unit amplitude (1 V/m) electric field in the x-direction and propagating in the y-direction. The excitation frequency is 58THz. Scattering cross section σS normalized by the geometrical cross section πa2 in linear scale for (c) the bare dielectric sphere and (d) the cloaked sphere on the xy-plane. The scattering form the cloaked sphere is approximately 40 times smaller than the scattering from the bare sphere. Note that the polar axis scales in (c) and (d) are different.
shows the amplitude of the total electric field on the xy plane in the case of (a) the bare dielectric sphere (represented in gray color) and (b) the cloaked sphere (cloaking shell is represented in black color). One can clearly see that the total field is less disturbed when the sphere is concealed using the proposed cloak. Uniform amplitude of the total field is restored all around the cloak as if it would propagate in a medium without the scatterer. This confirms the effectiveness of the proposed cloak. In Figs. 3(c) and 3(d) the far-field scattering patterns on the xy plane are provided: It is clearly shown that the cloaked sphere is almost undetectable in the far-field at all angles. The amplitudes of the far-fields scattered from the cloaked sphere are orders of magnitude lower than those of the fields scattered from the bare sphere. Note that the polar axis scales in Figs. 3(c) and 3(d) are different.

3.2 Multi-frequency multi-layered cloak

4. Summary

We describe realistic graphene-based cloaks to conceal three-dimensional objects by suppressing their dipolar scattering at different tunable frequencies (band of frequencies). The proposed cloaking mechanism exploits the fact that graphene layers behave like metals at THz regime with a tunable optical response. It is demonstrated that a cloak, which achieves transparency at a tunable frequency, can be designed with only one graphene shell whose chemical potential can be varied by applying a gate voltage. Based on the same idea, utilizing multiple number of graphene shells biased at different gate voltages results in a cloak that operates at a tunable band of frequencies. We can thus solve one of the most challenging problems of metamaterial cloaks: The limitation on the operation band. One may envision that designs proposed in this work, which exploit tunable electrical properties of graphene, may further render the cloaking theory closer to its practical and feasible realization at optical and THz frequencies. We believe that our results can be easily implemented within an experimental setup. This metamaterial cloak may therefore also represent a viable way for non-invasive sensing and probing with improved bandwidth.

Acknowledgments

Carsten Rockstuhl would like to acknowledge support by the Federal Ministry of Education and Research (Phona) as well as from the State of Thuringia within the Pro-Excellence program (MeMa).

References and links

1.

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006). [CrossRef] [PubMed]

2.

U. Leonhardt, “Optical conformal mapping,” Science 312(5781), 1777–1780 (2006). [CrossRef] [PubMed]

3.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010). [CrossRef] [PubMed]

4.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007). [CrossRef]

5.

M. Farhat, S. Guenneau, A. B. Movchan, and S. Enoch, “Achieving invisibility over a finite range of frequencies,” Opt. Express 16(8), 5656–5661 (2008). [CrossRef] [PubMed]

6.

I. I. Smolyaninov, V. N. Smolyaninova, A. V. Kildishev, and V. M. Shalaev, “Anisotropic metamaterials emulated by tapered waveguides: Application to optical cloaking,” Phys. Rev. Lett. 102(21), 213901 (2009). [CrossRef] [PubMed]

7.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006). [CrossRef] [PubMed]

8.

A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016623 (2005). [CrossRef] [PubMed]

9.

A. Alù and N. Engheta, “Plasmonic materials in transparency and cloaking problems: Mechanism, robustness, and physical insights,” Opt. Express 15(6), 3318–3332 (2007). [CrossRef] [PubMed]

10.

S. Mühlig, M. Farhat, C. Rockstuhl, and F. Lederer, “Cloaking dielectric spherical objects by a shell of metallic nanoparticles,” Phys. Rev. B 83(19), 195116 (2011). [CrossRef]

11.

M. Farhat, S. Mühlig, C. Rockstuhl, and F. Lederer, “Scattering cancellation of the magnetic dipole field from macroscopic spheres,” Opt. Express 20(13), 13896–13906 (2012). [CrossRef] [PubMed]

12.

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]

13.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004). [CrossRef] [PubMed]

14.

A. H. Castro Neto, F. Guinea, 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]

15.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308–1308 (2008). [CrossRef] [PubMed]

16.

K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490(7419), 192–200 (2012). [CrossRef] [PubMed]

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T. Mueller, F. N. Xia, and P. Avouris, “Graphene photodetectors for high-speed optical communications,” Nat. Photonics 4(5), 297–301 (2010). [CrossRef]

18.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011). [CrossRef] [PubMed]

19.

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

20.

M. Jablan, H. Buljan, and M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80(24), 245435 (2009). [CrossRef]

21.

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]

22.

F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: A platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011). [CrossRef] [PubMed]

23.

L. Wang, W. Cai, X. Zhang, and J. Xu, “Surface plasmons at the interface between graphene and Kerr-type nonlinear media,” Opt. Lett. 37(13), 2730–2732 (2012). [CrossRef] [PubMed]

24.

K. Y. Shin, J.-Y. Hong, and J. Jang, “Micropatterning of graphene sheets by inkjet printing and its wideband dipole-antenna application,” Adv. Mater. 23(18), 2113–2118 (2011). [CrossRef] [PubMed]

25.

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26.

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

27.

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

28.

S. Thongrattanasiri, F. H. L. Koppens, and F. J. García de Abajo, “Complete optical absorption in periodically patterned graphene,” Phys. Rev. Lett. 108(4), 047401 (2012). [CrossRef] [PubMed]

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30.

R. Alaee, M. Farhat, C. Rockstuhl, and F. Lederer, “A perfect absorber made of a graphene micro-ribbon metamaterial,” Opt. Express 20(27), 28017–28024 (2012). [CrossRef] [PubMed]

31.

J. W. Ko, S.-W. Kim, J. Hong, K. Kang, and C. B. Park, “Synthesis of graphene-wrapped CuO hybrid materials by CO2 mineralization,” Green Chem. 14(9), 2391–2394 (2012). [CrossRef]

32.

J. S. Lee, K. H. You, and C. B. Park, “Highly photoactive, low bandgap TiO2 nanoparticles wrapped by graphene,” Adv. Mater. 24(8), 1084–1088 (2012). [CrossRef] [PubMed]

33.

A. Alù and N. Engheta, “Cloaked near-field scanning optical microscope tip for noninvasive near-field imaging,” Phys. Rev. Lett. 105(26), 263906 (2010). [CrossRef] [PubMed]

34.

G. W. Hanson, “Dyadic Green’s functions and guided surface waves on graphene,” J. Appl. Phys. 103, 064302 (2006). [CrossRef]

35.

P. Y. Chen, J. Soric, and A. Alù, “Invisibility and cloaking based on scattering cancellation,” Adv. Mater. 24(44), OP281–OP304 (2012). [CrossRef] [PubMed]

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P. Y. Chen and A. Alù, “Mantle cloaking using thin patterned metasurfaces,” Phys. Rev. B 84(20), 205110 (2011). [CrossRef]

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A. Alù, “Mantle cloak: Invisibility induced by a surface,” Phys. Rev. B 80(24), 245115 (2009). [CrossRef]

38.

F. Monticone, C. Argyropoulos, and A. Alù, “Layered plasmonic cloaks to tailor the optical scattering at the nanoscale,” Sci Rep 2, 912–918 (2012). [CrossRef] [PubMed]

OCIS Codes
(160.3918) Materials : Metamaterials
(050.6624) Diffraction and gratings : Subwavelength structures
(230.3205) Optical devices : Invisibility cloaks

ToC Category:
Metamaterials

History
Original Manuscript: March 4, 2013
Revised Manuscript: May 11, 2013
Manuscript Accepted: May 12, 2013
Published: May 15, 2013

Citation
Mohamed Farhat, Carsten Rockstuhl, and Hakan Bağcı, "A 3D tunable and multi-frequency graphene plasmonic cloak," Opt. Express 21, 12592-12603 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-10-12592


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