OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 9 — May. 6, 2013
  • pp: 10475–10482
« Show journal navigation

Flexible transformation plasmonics using graphene

Wei Bing Lu, Wei Zhu, Hong Ju Xu, Zhen Hua Ni, Zheng Gao Dong, and Tie Jun Cui  »View Author Affiliations


Optics Express, Vol. 21, Issue 9, pp. 10475-10482 (2013)
http://dx.doi.org/10.1364/OE.21.010475


View Full Text Article

Acrobat PDF (3059 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The flexible control of surface plasmon polaritons (SPPs) is important and intriguing due to its wide application in novel plasmonic devices. Transformation optics (TO) offers the capability either to confine the SPP propagation on rigid curved/uneven surfaces, or to control the flow of SPPs on planar surfaces. However, TO has not permitted us to confine, manipulate, and control SPP waves on flexible curved surfaces. Here, we propose to confine and freely control flexible SPPs using TO and graphene. We show that SPP waves can be naturally confined and propagate on curved or uneven graphene surfaces with little bending and radiation losses, and the confined SPPs are further manipulated and controlled using TO. Flexible plasmonic devices are presented, including the bending waveguides, wave splitter, and Luneburg lens on curved surfaces. Together with the intrinsic flexibility, graphene can be served as a good platform for flexible transformation plasmonics.

© 2013 OSA

1. Introduction

Flexible plasmonics has received great attention by industry and scientific community due to its various and promising applications on nonplanar surfaces [1

1. A. D. Falco, M. Ploschner, and T. F. Krauss, “Flexible metamaterials at visible wavelengths,” New J. Phys. 12(11), 113006 (2010). [CrossRef]

5

5. O. Vazquez-Mena, T. Sannomiya, M. Tosun, L. G. Villanueva, V. Savu, J. Voros, and J. Brugger, “High-resolution resistless nanopatterning on polymer and flexible substrates for plasmonic biosensing using stencil masks,” ACS Nano 6(6), 5474–5481 (2012). [CrossRef] [PubMed]

]. However, the current applications of flexible plasmonics only make use of the electromagnetic response of plasmonic structures on flexible substrate (e.g. plasmonic antennas [1

1. A. D. Falco, M. Ploschner, and T. F. Krauss, “Flexible metamaterials at visible wavelengths,” New J. Phys. 12(11), 113006 (2010). [CrossRef]

,2

2. S. Aksu, M. Huang, A. Artar, A. A. Yanik, S. Selvarasah, M. R. Dokmeci, and H. Altug, “Flexible plasmonics on unconventional and nonplanar substrates,” Adv. Mater. 23(38), 4422–4430 (2011). [CrossRef] [PubMed]

], absorbers [3

3. I. M. Pryce, K. Aydin, Y. A. Kelaita, R. M. Briggs, and H. A. Atwater, “Highly strained compliant optical metamaterials with large frequency tunability,” Nano Lett. 10(10), 4222–4227 (2010). [CrossRef] [PubMed]

,4

4. G. X. Li, S. M. Chen, W. H. Wong, E. Y. B. Pun, and K. W. Cheah, “Highly flexible near-infrared metamaterials,” Opt. Express 20(1), 397–402 (2012). [CrossRef] [PubMed]

], and sensors [5

5. O. Vazquez-Mena, T. Sannomiya, M. Tosun, L. G. Villanueva, V. Savu, J. Voros, and J. Brugger, “High-resolution resistless nanopatterning on polymer and flexible substrates for plasmonic biosensing using stencil masks,” ACS Nano 6(6), 5474–5481 (2012). [CrossRef] [PubMed]

]). To the best of our knowledge, no flexible plasmonic devices have been realized by controlling the flow of surface plasmon polaritons (SPPs). This is mainly because the surface topological variation can modify the SPP propagation characteristics [6

6. Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett. 10(6), 1991–1997 (2010). [CrossRef] [PubMed]

]. Hence the confinement of flexible SPP waves is still a big challenge.

Recently, transformation optics (TO) has been proposed as a general technique to control the light flow in any desirable ways [7

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

10

10. J. B. Pendry, A. Aubry, D. R. Smith, and S. A. Maier, “Transformation optics and subwavelength control of light,” Science 337(6094), 549–552 (2012). [CrossRef] [PubMed]

], which plays significant role in the design of novel devices with unprecedented properties (e.g. invisibility cloaks [11

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

13

13. 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]

], lenses [14

14. Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater. 8(8), 639–642 (2009). [CrossRef] [PubMed]

16

16. H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat Commun 1(8), 124 (2010). [CrossRef] [PubMed]

], and optical black holes [17

17. D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009). [CrossRef]

,18

18. Q. Cheng, T. J. Cui, W. X. Jiang, and B. G. Cai, “An omnidirectional electromagnetic absorber made of metamaterials,” New J. Phys. 12(6), 063006 (2010). [CrossRef]

]). More recently, TO has been used to precisely and efficiently control the propagation of SPP waves [6

6. Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett. 10(6), 1991–1997 (2010). [CrossRef] [PubMed]

,19

19. P. A. Huidobro, M. L. Nesterov, L. Martín-Moreno, and F. J. García-Vidal, “Transformation optics for plasmonics,” Nano Lett. 10(6), 1985–1990 (2010). [CrossRef] [PubMed]

23

23. M. Kadic, S. Guenneau, S. Enoch, P. A. Huidobro, L. Martín-Moreno, F. García-Vidal, J. Renger, and R. Quidant, “Transformation plasmonics,” Nanophotonic 1, 51–64 (2012).

], achieving a series of new plasmonic devices such as the invisibility carpet cloaks [19

19. P. A. Huidobro, M. L. Nesterov, L. Martín-Moreno, and F. J. García-Vidal, “Transformation optics for plasmonics,” Nano Lett. 10(6), 1985–1990 (2010). [CrossRef] [PubMed]

,20

20. M. Kadic, S. Guenneau, and S. Enoch, “Transformational plasmonics: cloak, concentrator and rotator for SPPs,” Opt. Express 18(11), 12027–12032 (2010). [CrossRef] [PubMed]

], bending waveguides [6

6. Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett. 10(6), 1991–1997 (2010). [CrossRef] [PubMed]

,21

21. P. A. Huidobro, M. L. Nesterov, L. Martín-Moreno, and F. J. García-Vidal, “Moulding the flow of surface plasmons using conformal and quasiconformal mappings,” New J. Phys. 13(3), 033011 (2011). [CrossRef]

], cylindrical cloaks [19

19. P. A. Huidobro, M. L. Nesterov, L. Martín-Moreno, and F. J. García-Vidal, “Transformation optics for plasmonics,” Nano Lett. 10(6), 1985–1990 (2010). [CrossRef] [PubMed]

,20

20. M. Kadic, S. Guenneau, and S. Enoch, “Transformational plasmonics: cloak, concentrator and rotator for SPPs,” Opt. Express 18(11), 12027–12032 (2010). [CrossRef] [PubMed]

], and Luneburg lenses [6

6. Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett. 10(6), 1991–1997 (2010). [CrossRef] [PubMed]

,22

22. T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and eaton lenses,” Nat. Nanotechnol. 6(3), 151–155 (2011). [CrossRef] [PubMed]

]. Although TO has the ability to mould the flow of SPP waves on two-dimensional (2D) planar surfaces or confine the SPP propagation on rigid curved or uneven surfaces, it cannot do both simultaneously. This is because the procedures to confine and precisely control SPPs require two different TO strategies. In addition, TO cannot be used to control the flexible SPP propagation on curved surfaces of traditional noble metals, since the framework of TO used to confine SPPs should be redesigned once the curved surface topology is changed. However, graphene provides a possibility to solve the problem.

Graphene has shown its intriguing characteristics as a good platform for plamonics. The propagation of SPPs on planar graphene has been demonstrated experimentally by two groups almost simultaneously [24

24. Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012). [PubMed]

,25

25. J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012). [PubMed]

]. Since 2011, TO has been used to control the propagation of SPPs and design novel plasmonic elements with the aid of graphene [26

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

28

28. H. J. Xu, W. B. Lu, W. Zhu, Z. G. Dong, and T. J. Cui, “Efficient manipulation of surface plasmon polariton waves in graphene,” Appl. Phys. Lett. 100(24), 243110 (2012). [CrossRef]

], due to its tunability of the conductivity via electrostatic gating and/or chemical doping [29

29. D. K. Efetov and P. Kim, “Controlling electron-phonon interactions in graphene at ultrahigh carrier densities,” Phys. Rev. Lett. 105(25), 256805 (2010). [CrossRef] [PubMed]

31

31. W. Chen, S. Chen, D. C. Qi, X. Y. Gao, and A. T. S. Wee, “Surface transfer p-type doping of epitaxial graphene,” J. Am. Chem. Soc. 129(34), 10418–10422 (2007). [CrossRef] [PubMed]

]. Nevertheless, all the transformation plasmonic devices based on graphene are implemented on 2D planar surfaces. Here, we make strong confinements and desirable controls of flexible SPP waves on curved surfaces, taking advantages of both TO and graphene. We show that SPP waves on graphene surfaces have very strong lateral confinements, and SPPs can naturally be restricted on curved graphene surfaces with little bending and radiation losses. Such a priority of graphene can be easily used to design special plasmonic devices such as bending waveguides. We further show that the propagation of SPPs confined on curved graphene surfaces can be freely controlled by using TO. As a result, a Y-shaped beam splitter and a Luneburg lens have been demonstrated on curved graphene surfaces. These findings reveal the remarkable properties of graphene to manipulate SPP waves. Integrated with plasmonic nanofeatures and flexible substrates, graphene is a good alternative platform for transformation flexible plasmonics.

2. Strong confinement of SPP waves on graphene

The propagation of SPPs on graphene is strongly dependent on the chemical potential. It has been shown that, for a sufficiently high Fermi level which can be achieved by increasing the chemical potential, the plasmon losses in graphene are very small [32

32. D. R. Andersen, “Graphene-based long-wave infrared TM surface plasmon modulator,” J. Opt. Soc. Am. B 27(4), 818–822 (2010). [CrossRef]

]. In order to investigate the effect of chemical potential on characteristics of SPP waves on graphene, we choose a lower chemical potential μc=0.246 eV, which corresponds to carrier density of ns=5.10×1012 cm−2, and a higher chemical potential μc=0.8 eV, which corresponds to carrier density of ns=5.23×1013 cm−2, for comparison [33

33. P. Tassin, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “A comparison of graphene, superconductors and metals as conductors for metamaterials and plasmonics,” Nat. Photonics 6(4), 259–264 (2012). [CrossRef]

,34

34. G. W. Hanson, “Dyadic green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103(6), 064302 (2008). [CrossRef]

]. The chemical potential of μc=0.8 eV in graphene has been realized experimentally by chemical doping or ion-get gating [29

29. D. K. Efetov and P. Kim, “Controlling electron-phonon interactions in graphene at ultrahigh carrier densities,” Phys. Rev. Lett. 105(25), 256805 (2010). [CrossRef] [PubMed]

31

31. W. Chen, S. Chen, D. C. Qi, X. Y. Gao, and A. T. S. Wee, “Surface transfer p-type doping of epitaxial graphene,” J. Am. Chem. Soc. 129(34), 10418–10422 (2007). [CrossRef] [PubMed]

]. The phenomenological scattering rate Γ is chosen as 3.3 meV, corresponding to the momentum relaxation time of τ=0.1 ps, which coincides with the experiment [35

35. H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7(5), 330–334 (2012). [CrossRef] [PubMed]

]. According to the Kubo formula [34

34. G. W. Hanson, “Dyadic green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103(6), 064302 (2008). [CrossRef]

], the conductivity of graphene can be achieved in these two potentials. Then, combined with Re(εr,eq)=σg,iωΔε0 [26

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

] (Δ is the thickness of graphene, here we set Δ=1 nm), the real part of the equivalent permittivity, Re(εr,eq), of the graphene layer is given in Fig. 1
Fig. 1 The real parts of equivalent permittivity for graphene at T=300 K and Γ=3.3 meV. (a) μc=0.246 eV. (b) μc=0.8 eV.
. For μc=0.246 eV, the working frequency of SPP wave ranges from 20 to 80 THz; for μc=0.8 eV, the frequency ranges from 20 to 250 THz. Within such frequencies, the propagation of SPP waves satisfies the condition Re(εr,eq)<1 [36

36. H. Raether, Surface Plasmons: On Smooth and Rough Surfaces and on Gratings; Springer: Berlin, 1998.

]. From Fig. 1 we notice that the SPP frequency range can be dramatically enlarged by increasing the chemical potential in graphene.

The characteristics of SPP waves supported by a flat free-standing graphene layer and a flat thin-silver (with thickness of 30 nm) are compared. For SPPs on graphene, the dispersion relation is [26

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

]
βg=k01(2σgη0)2,
(1)
whereσg, k0 and η0 are the conductivity of graphene, the free space wavenumber, and the intrinsic impedance of free space, respectively. The effective mode index is ng_spp=1(2σgη0)2, and the SPP wavelength is calculated by λg_spp=λ0/ng_spp, in which λ0 is the free space wavelength. The propagation length is calculated by Lg=1/Im(β), and the lateral decay length is g_spp=1/Re(β2(ω/c)2) [33

33. P. Tassin, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “A comparison of graphene, superconductors and metals as conductors for metamaterials and plasmonics,” Nat. Photonics 6(4), 259–264 (2012). [CrossRef]

]. As comparison, the propagation length LAg_sppand lateral decay length Ag_spp of silver can be calculated according to [36

36. H. Raether, Surface Plasmons: On Smooth and Rough Surfaces and on Gratings; Springer: Berlin, 1998.

].

Figure 2
Fig. 2 Comparison of the SPP properties on graphene (μc=0.246 eV and μc=0.8 eV) and silver film (with 30 nm thickness). (a) The ratio of propagation length to the SPP wavelength. (b) The lateral decay length.
illustrates the ratios of propagation length to SPP wavelength (Fig. 2(a)) and lateral decay lengths (Fig. 2(b)) for silver and graphene with chemical potentials μc=0.246 eV and μc=0.8 eV. From Fig. 2(b), we observe that the SPP waves on graphene have very strong confinements, with lateral decay length one or two orders better than that on the silver surface. Although the SPP wave on graphene with lower chemical potential (μc=0.246 eV) has the best confinement, the propagation length is only several SPP wavelengths, which can hardly be used for real applications. However, the propagation length of SPP wave on graphene with higher chemical potential (μc=0.8 eV) can reach dozens of wavelength, which is comparable to that of silver at high frequency. Hence, considering the strong SPP confinement and sufficient propagation length, we predict that graphene with higher chemical potential has great advantages over silver, especially on curved surfaces. The conclusion we obtained here can be a good complement to that achieved in [33

33. P. Tassin, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “A comparison of graphene, superconductors and metals as conductors for metamaterials and plasmonics,” Nat. Photonics 6(4), 259–264 (2012). [CrossRef]

], in which the chemical potential was assumed to be 0.246 eV by using back-gate [37

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

].

3. The propagation of SPP waves on curved graphene surfaces

The critical curvature radius can be calculated by
rck0βck0=k0Re(βc2(ω/c)2)(βck0),
(2)
where nspp, c and βc are the effective mode index, the lateral decay length of SPP, and the SPP wavenumber propagating on the curved surface, respectively. Since the dispersion relation of fundamental mode on the curved slab closely follows the flat film [38

38. K. Hasegawa, J. U. Nockel, and M. Deutsch, “Curvature-induced radiation of surface plasmon polaritons propagating around bends,” Phys. Rev. A 75(6), 063816 (2007). [CrossRef]

,39

39. M. Faddaoui, A. Folacci, and P. Gabrielli, “Surface polaritons of a left-handed curved slab,” http://arxiv.org/abs/1007.1337.

], we assume that βc=β (β is the SPP wavenumber on flat film). For a free-standing graphene, the wavelength to support SPP waves is λg_spp = 27 nm under the conditions of T = 300 K, Γ=3.3 meV, f = 160 THz, and μc=0.8 eV. For a 30-nm-thick silver under the conditions of T = 300 K and f = 500 THz, the SPP wavelength is λAg_spp=0.55μm. Then we calculate the critical curvature radii (r) for graphene and silver are rg=0.02λg_spp and rAg=3.4λAg_spp, respectively. Only when the radius of curvature is larger than r, the SPP wave could be supported. Hence we conclude that the range of curved graphene surfaces to support SPP waves is much broader than that of silver, which is in accordance with the strong-confinement ability of graphene.

We have simulated the propagations of SPP waves on 30-nm-thick silver films (Fig. 3(a)
Fig. 3 SPP waves on curved surfaces. (a), (b), The tangent magnetic fields Hy of the SPP waves at different curvatures for 30-nm-thick silver film (a) and graphene (b). From top to bottom, the curvature radii are 1.65 µm (equal to 3λAg_spp), 4.125 µm, , respectively in (a); and 81 nm (equal to 3λg_spp), 202.5 nm, , respectively in (b). The inset shows the geometry of the curved slab.
) and on graphene (Fig. 3(b)) along arc surfaces with different radii but the same electrical length larc=5λAg(g)_spp. Three curvature radii are selected for both silver and graphene surfaces: 3λAg(g)_spp, 7.5λAg(g)_spp, and , from the top to bottom. From Fig. 3, we clearly observe that the SPP waves propagate efficiently on the air-graphene-air interfaces with different radii. However, on the air-silver-air interfaces, when the radius is 7.5λAg_spp (which is larger than rAg), the confinement of SPP waves is not as good as on air-graphene-air interfaces, and when the radius of 3λAg_spp(which is less than rAg), it can no longer support SPP waves.

According to the above analysis, the priority of graphene can be easily used to design special plasmonic devices, including 180° bending waveguides, S-shaped waveguides, spiral waveguides, and curved waveguide. As noted earlier [6

6. Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett. 10(6), 1991–1997 (2010). [CrossRef] [PubMed]

], in the bending dielectric-metal surface, almost all energy leaks to free space and metal cannot be directly used for the 180° bending, as shown in Fig. 4(a)
Fig. 4 Bending waveguides. (a), (b), The simulation results of the 180°-bending waveguide for 30-nm-thick silver film at f = 500 THz, R1 = 1.2 µm (a) and graphene at f = 160 THz, Γ=3.3 meV, T = 300 K, and μc=0.8 eV, R2 = 60 nm (b). (c), (d), The distributions of tangent magnetic fields Hy on the 180°-bending area in silver (c) and graphene (d). (e), (f), (g), The simulation results of the tangent magnetic fields Hy for the SPP waves of flexible SPP devices on curved graphene surfaces at f = 160 THz, Γ=3.3 meV, T = 300 K, μc=0.8 eV, R3 = 55 nm, R4 = 21 nm, R5 = 33 nm, R6 = 55 nm, and R7 = 30 nm: the S-shaped waveguide (e), the spiral waveguide (f), and the curved waveguide (g).
. However, in Fig. 4(b), one clearly observes that the SPP wave on graphene can propagate through the 180° bend excellently well. In order to estimate the scattering loss or the propagation efficiency, the distribution of tangent magnetic fields Hy along the bending area are illustrated in Figs. 4(c) and 4(d). For the 180° graphene bending interface, almost all energies of SPP waves are transported through the bending area; while for silver interface, almost all SPP energies are leaked to free space. We further realize very complicated S-shaped waveguide and spiral waveguide using graphene. The geometry and simulation results are demonstrated in Figs. 4(e) and 4(f), which reveal that the SPP waves can be manipulated along arbitrarily curved trajectories using graphene. The S-shaped waveguide and spiral waveguide could be applied to photonic integrated circuits which can directionally route the SPP energies and reduce the sizes of the devices.

4. Flexible transformation plasmonics using graphene

The propagation of SPPs confined on curved graphene surfaces can be further controlled using TO. Hence we can realize flexible transformation SPP devices based on curved graphene layers. We first consider a Y-shaped waveguide variant, which consists of two distinct regions on graphene under the conditions of f = 160 THz, Γ=3.3 meV, and T = 300 K. The Y-shaped region possesses the chemical potential of 0.8eV, which corresponds to the carrier density of ns=5.23×1013 cm−2, resulting in the equivalent permittivity of εr,eq1=8.6+i0.13 (which can support SPP waves). The remaining region possesses the chemical potential of 0.4 eV, which corresponds to the carrier density of ns=1.32×1013 cm−2, resulting in the equivalent permittivity of εr,eq2=0.15+i0.71 (which cannot support SPP waves). The side view of the Y-shaped waveguide variant is a sinusoidal curve with the function z(x)=12sin(πx/60) nm in the region 0x300nm, where x is the propagation direction and z is normal to the surface. Although the graphene layer has been bent to a curved surface, due to the strong confinement, the SPP waves still propagate well along the graphene and are split into two paths, as shown in Fig. 5(a)
Fig. 5 (a) The Y-shaped flexible waveguide. Simulation results of the tangent magnetic fields Hy of SPP waves for a Y-shaped waveguide using grapheme at f = 160 THz, Γ=3.3 meV, and T = 300 K. The graphene layer in section I is doped by μc=0.8 eV, which can support SPP waves; while the section II is doped by μc=0.4 eV, which cannot support SPP waves. L1 = 120 nm, b = 140 nm, a = 30 nm, L2 = 100 nm, L3 = 80 nm, L4 = 30 nm, and θ=22.5. In the side view, the half cycle of the sinusoidal function is 60 nm. (b) The Flexible Luneburg lens. The simulation results of tangent magnetic fields Hy of SPP waves along the Luneburg lens based on curved graphene, where R = 130 nm and r = 40 nm.
. Such a Y-shaped waveguide variant can realize the function of power dividers in curved surfaces.

In summary, compared to noble metal, graphene has much stronger confinement for SPPs on curved surfaces. We have shown that flexible SPP waves can be strongly confined and efficiently manipulated by combining graphene with TO. Novel flexible plasmonic devices with intriguing functions have been realized on curved graphene surfaces, including the bending waveguides, 180°-bending waveguide, S-shaped waveguide, spiral waveguide, curved waveguide, Y-shaped waveguide variant, and curved Luneburg lens. Together with the intrinsic flexibility, graphene is promised as a good platform for transformation flexible plasmonics.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant Nos. 61271057, 61071045, 11104026, and 11174051), Doctoral Fund of Ministry of Education of China (No. 20110092110009). TJC acknowledges supports by the National Science Foundation of China (60990324, 61138001, and 60921063) and the 111 Project (111-2-05).

References and links

1.

A. D. Falco, M. Ploschner, and T. F. Krauss, “Flexible metamaterials at visible wavelengths,” New J. Phys. 12(11), 113006 (2010). [CrossRef]

2.

S. Aksu, M. Huang, A. Artar, A. A. Yanik, S. Selvarasah, M. R. Dokmeci, and H. Altug, “Flexible plasmonics on unconventional and nonplanar substrates,” Adv. Mater. 23(38), 4422–4430 (2011). [CrossRef] [PubMed]

3.

I. M. Pryce, K. Aydin, Y. A. Kelaita, R. M. Briggs, and H. A. Atwater, “Highly strained compliant optical metamaterials with large frequency tunability,” Nano Lett. 10(10), 4222–4227 (2010). [CrossRef] [PubMed]

4.

G. X. Li, S. M. Chen, W. H. Wong, E. Y. B. Pun, and K. W. Cheah, “Highly flexible near-infrared metamaterials,” Opt. Express 20(1), 397–402 (2012). [CrossRef] [PubMed]

5.

O. Vazquez-Mena, T. Sannomiya, M. Tosun, L. G. Villanueva, V. Savu, J. Voros, and J. Brugger, “High-resolution resistless nanopatterning on polymer and flexible substrates for plasmonic biosensing using stencil masks,” ACS Nano 6(6), 5474–5481 (2012). [CrossRef] [PubMed]

6.

Y. Liu, T. Zentgraf, G. Bartal, and X. Zhang, “Transformational plasmon optics,” Nano Lett. 10(6), 1991–1997 (2010). [CrossRef] [PubMed]

7.

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

8.

D. Kwon and D. H. Werner, “Transformation electromagnetic: an overview of the theory and applications,” IEEE Trans. Antennas Propag. 52(1), 24–46 (2010). [CrossRef]

9.

N. B. Kundtz, D. R. Smith, and J. B. Pendry, “Electromagnetic design with transformation optics,” Proc. IEEE 99(10), 1622–1633 (2011). [CrossRef]

10.

J. B. Pendry, A. Aubry, D. R. Smith, and S. A. Maier, “Transformation optics and subwavelength control of light,” Science 337(6094), 549–552 (2012). [CrossRef] [PubMed]

11.

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

12.

W. X. Jiang, J. Y. Chin, and T. J. Cui, “Anisotropic metamaterial devices,” Mater. Today 12(12), 26–33 (2009). [CrossRef]

13.

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]

14.

Y. G. Ma, C. K. Ong, T. Tyc, and U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater. 8(8), 639–642 (2009). [CrossRef] [PubMed]

15.

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010). [CrossRef] [PubMed]

16.

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat Commun 1(8), 124 (2010). [CrossRef] [PubMed]

17.

D. A. Genov, S. Zhang, and X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009). [CrossRef]

18.

Q. Cheng, T. J. Cui, W. X. Jiang, and B. G. Cai, “An omnidirectional electromagnetic absorber made of metamaterials,” New J. Phys. 12(6), 063006 (2010). [CrossRef]

19.

P. A. Huidobro, M. L. Nesterov, L. Martín-Moreno, and F. J. García-Vidal, “Transformation optics for plasmonics,” Nano Lett. 10(6), 1985–1990 (2010). [CrossRef] [PubMed]

20.

M. Kadic, S. Guenneau, and S. Enoch, “Transformational plasmonics: cloak, concentrator and rotator for SPPs,” Opt. Express 18(11), 12027–12032 (2010). [CrossRef] [PubMed]

21.

P. A. Huidobro, M. L. Nesterov, L. Martín-Moreno, and F. J. García-Vidal, “Moulding the flow of surface plasmons using conformal and quasiconformal mappings,” New J. Phys. 13(3), 033011 (2011). [CrossRef]

22.

T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and eaton lenses,” Nat. Nanotechnol. 6(3), 151–155 (2011). [CrossRef] [PubMed]

23.

M. Kadic, S. Guenneau, S. Enoch, P. A. Huidobro, L. Martín-Moreno, F. García-Vidal, J. Renger, and R. Quidant, “Transformation plasmonics,” Nanophotonic 1, 51–64 (2012).

24.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012). [PubMed]

25.

J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012). [PubMed]

26.

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

27.

H. J. Xu, W. B. Lu, Y. Jiang, and Z. G. Dong, “Beam-scanning planar lens based on graphene,” Appl. Phys. Lett. 100(5), 051903 (2012). [CrossRef]

28.

H. J. Xu, W. B. Lu, W. Zhu, Z. G. Dong, and T. J. Cui, “Efficient manipulation of surface plasmon polariton waves in graphene,” Appl. Phys. Lett. 100(24), 243110 (2012). [CrossRef]

29.

D. K. Efetov and P. Kim, “Controlling electron-phonon interactions in graphene at ultrahigh carrier densities,” Phys. Rev. Lett. 105(25), 256805 (2010). [CrossRef] [PubMed]

30.

C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, and F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471(7340), 617–620 (2011). [CrossRef] [PubMed]

31.

W. Chen, S. Chen, D. C. Qi, X. Y. Gao, and A. T. S. Wee, “Surface transfer p-type doping of epitaxial graphene,” J. Am. Chem. Soc. 129(34), 10418–10422 (2007). [CrossRef] [PubMed]

32.

D. R. Andersen, “Graphene-based long-wave infrared TM surface plasmon modulator,” J. Opt. Soc. Am. B 27(4), 818–822 (2010). [CrossRef]

33.

P. Tassin, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “A comparison of graphene, superconductors and metals as conductors for metamaterials and plasmonics,” Nat. Photonics 6(4), 259–264 (2012). [CrossRef]

34.

G. W. Hanson, “Dyadic green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103(6), 064302 (2008). [CrossRef]

35.

H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, and F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7(5), 330–334 (2012). [CrossRef] [PubMed]

36.

H. Raether, Surface Plasmons: On Smooth and Rough Surfaces and on Gratings; Springer: Berlin, 1998.

37.

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

38.

K. Hasegawa, J. U. Nockel, and M. Deutsch, “Curvature-induced radiation of surface plasmon polaritons propagating around bends,” Phys. Rev. A 75(6), 063816 (2007). [CrossRef]

39.

M. Faddaoui, A. Folacci, and P. Gabrielli, “Surface polaritons of a left-handed curved slab,” http://arxiv.org/abs/1007.1337.

OCIS Codes
(230.7370) Optical devices : Waveguides
(240.6680) Optics at surfaces : Surface plasmons
(160.4236) Materials : Nanomaterials

ToC Category:
Optics at Surfaces

History
Original Manuscript: March 12, 2013
Revised Manuscript: April 10, 2013
Manuscript Accepted: April 15, 2013
Published: April 22, 2013

Citation
Wei Bing Lu, Wei Zhu, Hong Ju Xu, Zhen Hua Ni, Zheng Gao Dong, and Tie Jun Cui, "Flexible transformation plasmonics using graphene," Opt. Express 21, 10475-10482 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-9-10475


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. A. D. Falco, M. Ploschner, T. F. Krauss, “Flexible metamaterials at visible wavelengths,” New J. Phys. 12(11), 113006 (2010). [CrossRef]
  2. S. Aksu, M. Huang, A. Artar, A. A. Yanik, S. Selvarasah, M. R. Dokmeci, H. Altug, “Flexible plasmonics on unconventional and nonplanar substrates,” Adv. Mater. 23(38), 4422–4430 (2011). [CrossRef] [PubMed]
  3. I. M. Pryce, K. Aydin, Y. A. Kelaita, R. M. Briggs, H. A. Atwater, “Highly strained compliant optical metamaterials with large frequency tunability,” Nano Lett. 10(10), 4222–4227 (2010). [CrossRef] [PubMed]
  4. G. X. Li, S. M. Chen, W. H. Wong, E. Y. B. Pun, K. W. Cheah, “Highly flexible near-infrared metamaterials,” Opt. Express 20(1), 397–402 (2012). [CrossRef] [PubMed]
  5. O. Vazquez-Mena, T. Sannomiya, M. Tosun, L. G. Villanueva, V. Savu, J. Voros, J. Brugger, “High-resolution resistless nanopatterning on polymer and flexible substrates for plasmonic biosensing using stencil masks,” ACS Nano 6(6), 5474–5481 (2012). [CrossRef] [PubMed]
  6. Y. Liu, T. Zentgraf, G. Bartal, X. Zhang, “Transformational plasmon optics,” Nano Lett. 10(6), 1991–1997 (2010). [CrossRef] [PubMed]
  7. J. B. Pendry, D. Schurig, D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006). [CrossRef] [PubMed]
  8. D. Kwon, D. H. Werner, “Transformation electromagnetic: an overview of the theory and applications,” IEEE Trans. Antennas Propag. 52(1), 24–46 (2010). [CrossRef]
  9. N. B. Kundtz, D. R. Smith, J. B. Pendry, “Electromagnetic design with transformation optics,” Proc. IEEE 99(10), 1622–1633 (2011). [CrossRef]
  10. J. B. Pendry, A. Aubry, D. R. Smith, S. A. Maier, “Transformation optics and subwavelength control of light,” Science 337(6094), 549–552 (2012). [CrossRef] [PubMed]
  11. W. Cai, U. K. Chettiar, A. V. Kildishev, V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1(4), 224–227 (2007). [CrossRef]
  12. W. X. Jiang, J. Y. Chin, T. J. Cui, “Anisotropic metamaterial devices,” Mater. Today 12(12), 26–33 (2009). [CrossRef]
  13. T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science 328(5976), 337–339 (2010). [CrossRef] [PubMed]
  14. Y. G. Ma, C. K. Ong, T. Tyc, U. Leonhardt, “An omnidirectional retroreflector based on the transmutation of dielectric singularities,” Nat. Mater. 8(8), 639–642 (2009). [CrossRef] [PubMed]
  15. N. Kundtz, D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9(2), 129–132 (2010). [CrossRef] [PubMed]
  16. H. F. Ma, T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat Commun 1(8), 124 (2010). [CrossRef] [PubMed]
  17. D. A. Genov, S. Zhang, X. Zhang, “Mimicking celestial mechanics in metamaterials,” Nat. Phys. 5(9), 687–692 (2009). [CrossRef]
  18. Q. Cheng, T. J. Cui, W. X. Jiang, B. G. Cai, “An omnidirectional electromagnetic absorber made of metamaterials,” New J. Phys. 12(6), 063006 (2010). [CrossRef]
  19. P. A. Huidobro, M. L. Nesterov, L. Martín-Moreno, F. J. García-Vidal, “Transformation optics for plasmonics,” Nano Lett. 10(6), 1985–1990 (2010). [CrossRef] [PubMed]
  20. M. Kadic, S. Guenneau, S. Enoch, “Transformational plasmonics: cloak, concentrator and rotator for SPPs,” Opt. Express 18(11), 12027–12032 (2010). [CrossRef] [PubMed]
  21. P. A. Huidobro, M. L. Nesterov, L. Martín-Moreno, F. J. García-Vidal, “Moulding the flow of surface plasmons using conformal and quasiconformal mappings,” New J. Phys. 13(3), 033011 (2011). [CrossRef]
  22. T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, X. Zhang, “Plasmonic Luneburg and eaton lenses,” Nat. Nanotechnol. 6(3), 151–155 (2011). [CrossRef] [PubMed]
  23. M. Kadic, S. Guenneau, S. Enoch, P. A. Huidobro, L. Martín-Moreno, F. García-Vidal, J. Renger, R. Quidant, “Transformation plasmonics,” Nanophotonic 1, 51–64 (2012).
  24. Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012). [PubMed]
  25. J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012). [PubMed]
  26. A. Vakil, N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011). [CrossRef] [PubMed]
  27. H. J. Xu, W. B. Lu, Y. Jiang, Z. G. Dong, “Beam-scanning planar lens based on graphene,” Appl. Phys. Lett. 100(5), 051903 (2012). [CrossRef]
  28. H. J. Xu, W. B. Lu, W. Zhu, Z. G. Dong, T. J. Cui, “Efficient manipulation of surface plasmon polariton waves in graphene,” Appl. Phys. Lett. 100(24), 243110 (2012). [CrossRef]
  29. D. K. Efetov, P. Kim, “Controlling electron-phonon interactions in graphene at ultrahigh carrier densities,” Phys. Rev. Lett. 105(25), 256805 (2010). [CrossRef] [PubMed]
  30. C. F. Chen, C. H. Park, B. W. Boudouris, J. Horng, B. Geng, C. Girit, A. Zettl, M. F. Crommie, R. A. Segalman, S. G. Louie, F. Wang, “Controlling inelastic light scattering quantum pathways in graphene,” Nature 471(7340), 617–620 (2011). [CrossRef] [PubMed]
  31. W. Chen, S. Chen, D. C. Qi, X. Y. Gao, A. T. S. Wee, “Surface transfer p-type doping of epitaxial graphene,” J. Am. Chem. Soc. 129(34), 10418–10422 (2007). [CrossRef] [PubMed]
  32. D. R. Andersen, “Graphene-based long-wave infrared TM surface plasmon modulator,” J. Opt. Soc. Am. B 27(4), 818–822 (2010). [CrossRef]
  33. P. Tassin, T. Koschny, M. Kafesaki, C. M. Soukoulis, “A comparison of graphene, superconductors and metals as conductors for metamaterials and plasmonics,” Nat. Photonics 6(4), 259–264 (2012). [CrossRef]
  34. G. W. Hanson, “Dyadic green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103(6), 064302 (2008). [CrossRef]
  35. H. Yan, X. Li, B. Chandra, G. Tulevski, Y. Wu, M. Freitag, W. Zhu, P. Avouris, F. Xia, “Tunable infrared plasmonic devices using graphene/insulator stacks,” Nat. Nanotechnol. 7(5), 330–334 (2012). [CrossRef] [PubMed]
  36. H. Raether, Surface Plasmons: On Smooth and Rough Surfaces and on Gratings; Springer: Berlin, 1998.
  37. P. Y. Chen, A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011). [CrossRef] [PubMed]
  38. K. Hasegawa, J. U. Nockel, M. Deutsch, “Curvature-induced radiation of surface plasmon polaritons propagating around bends,” Phys. Rev. A 75(6), 063816 (2007). [CrossRef]
  39. M. Faddaoui, A. Folacci, P. Gabrielli, “Surface polaritons of a left-handed curved slab,” http://arxiv.org/abs/1007.1337 .

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4 Fig. 5
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited