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Shape approaches for enhancing plasmon propagation in graphene Mario Miscuglio, Davide Spirito, Remo Proietti Zaccaria, and Roman Krahne ACS Photonics, Just Accepted Manuscript • DOI: 10.1021/acsphotonics.6b00667 • Publication Date (Web): 25 Oct 2016 Downloaded from http://pubs.acs.org on October 26, 2016

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Shape approaches for enhancing plasmon propagation in graphene Mario Miscuglio1,2, Davide Spirito1,3, Remo Proietti Zaccaria1, and Roman Krahne1,3,* 1

Nanochemistry Department, Istituto Italiano di Tecnologia, Via Morego 30, Genoa, 16163, Italy 2

Dipartimento di Chimica e Chimica Industriale, Università degli studi di Genova, Via Dodecaneso 33, 16146 Genoa, Italy 3

Graphene Labs, Istituto Italiano Tecnologia, Via Morego 30, Genova, Italia

Corresponding author email: [email protected]

KEYWORDS: Graphene, Plasmons, Surface Plasmon Polariton, FDTD Simulations

ABSTRACT. Graphene plasmonics is a promising alternative for on-chip high speed communication that integrates optics and electronics, where the strong confinement of the electromagnetic energy at sub-wavelength scale and the tunability of the plasmon frequency via an external gate voltage are key advantages. The main drawback of graphene plasmons is their rather short decay and propagation length, which is due to intrinsic losses and substrate-related

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defects. Towards plasmonic devices, noble metal antennas represent a viable approach for plasmon launching in graphene waveguides, with the challenge of efficient coupling and plasmon propagation that are feasible for on chip communication. Here we discuss and analyze, using numerical simulations, different designs of metal antennas and their coupling to graphene plasmons, as well as graphene based nanopatterned waveguides that can lead to a more efficient GP propagation. A Yagi-Uda antenna leads to stronger coupling to GPs and allows for directive propagation as compared to a simple dipole antenna. This is especially advantageous to launch plasmons in graphene nanowire waveguides, where propagation up to 3 microns and frequency and phase control can be achieved. In tapered graphene waveguides the constructive interference of the plasmon reflection at the edges can lead to strong plasmon signals up to 8 microns distant from the launching dipole antenna. Nanostructuring of rectangular waveguides into asymmetric chains of truncated triangles greatly enhances directionality of GP propagation and conserves phase information. A comparison of the propagation length and electric near-field strength of these different approaches is presented, and confronted with the efficiency of GP launching by light scattering on scanning near field optical microscopy (SNOM) tips.

Plasmons in graphene have unique properties such as tunability of frequency in the midinfrared and terahertz range via charge carrier density, 1-3 and short plasmon wavelength together with large electric field confinement. Additional manipulation of the plasmon properties can be achieved by micro- and nanostructuring graphene.4-5 Finite size of the graphene leads to plasmon reflection at the borders and enables spatial mapping with near field optical techniques (for example by SNOM) in graphene sheets. 6 In such experiments the SNOM tip in proximity of the graphene sheet was used also as efficient means for plasmon launching

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, and systems

consisting of monolayer, bilayer and multilayer graphene regions were investigated.9 Graphene


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nanostructures sustain confined plasmons where the plasmon resonance not only depends on the intrinsic properties of the graphene sheet, but also on its size and shape.12 GP can be excited with metallic nanostructures, which represents a viable approach towards practical implementations, for example, in on chip optical signal routing, photodetection, and sensing.1 One major drawback in this respect is the relative short propagation length of GPs due to intrinsic losses and defects from the underlying substrate.13 Highly defect free interfaces can be achieved with graphene sandwiched between layers of hexagonal boron nitride (hBN), which increases the plasmon propagation length significantly.14-16 However, the fabrication of such layered structures is tedious, and currently cannot be realized on the large scale. In this work, we show by finite elements numerical simulations how the metal antenna design, combined with appropriate shape of the graphene sheet, can result in a significant enhancement of the plasmon propagation length. The proposed concepts can be applied to CVD grown graphene layers and are therefore compatible with the requirement for practical device fabrication. We used the COMSOL software-RF module to evaluate the shape and architecture of the metal antennas for efficient launching of GPs, with emphasis on maximizing the propagation length, and control on coupling and directionality. Since GPs get reflected at the borders of graphene flakes 17, we show how the shape of the graphene flake can be tailored such that those reflections result in greatly enhanced propagation length. Furthermore, we introduce a novel concept of nanostructuring graphene flakes that enables to exploit both reflections at the edges and localized plasmon resonances. This approach promises plasmon propagation lengths of several microns in CVD graphene on SiO2 (as opposed to few hundred nm in unstructured graphene), and opens pathways for plasmon modulation via design of propagation channels. For our study we assume a monolayer graphene sheet on top of a SiO2/Si substrate, with 280 nm


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oxide layer and p++ doped Si which functions as a back gate for tuning the carrier density in the graphene. The metal antennas are placed on top of the graphene and modeled with a Drude approximation, taking the parameters of gold18. The design of our structures is threedimensional, as illustrated in Figure 1a. The conductivity of graphene was calculated according to the random phase approximation (RPA)13, 19 with a MATLAB code (see Supplementary Information for details). Following the work of Alonso et al. 13, we assumed graphene with Fermi energy of 0.44 eV and carrier mobility of 1136 cm2/(V·s). These values correspond to the relaxation time of charge carriers of 0.05 ps. We assume perfect reflection at the graphene edges and implemented this by boundary conditions with negligible losses, i.e. we neglect scattering due to disorder, edge type etc.. This assumption should be justified as long as the plasmon wavelength is much larger than the variations at the graphene edge.9 In the supporting information (SI) we show that purely dissipative edge effects (in a region that is much smaller than the GP wavelength) do not result in significant losses. The surrounding of the device was taken as air, which was implemented by an outer box with a Perfectly Matched Layer (PML) that minimized unphysical reflections of the scattered wave. The system was illuminated at normal incidence with a linearly polarized plane wave at 10.9 µm wavelength (corresponding to a typical CO2 laser source). In case of nanostructured graphene the simulation yields the eigenmodes near the plasmon frequency, giving insight into fundamental resonant frequencies of the localized plasmons. The mesh resolution was chosen such that steady and mesh independent results for the electric field distribution were obtained, with the largest mesh dimension at least a factor 2 smaller than the plasmon wavelength and skin depth. A segregated solver was chosen for the solution method, and an iterative solver was adopted to solve the linear system equations. The propagation length


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of the plasmon, δGP, is taken as the distance over which the intensity of the vertical component of the electric field decays from 90% to 10% of its initial value. First, we confirmed that our model reproduces the results reported by Alonso et al.

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for a

simple Au dipole antenna on a graphene sheet, as shown in SI section 1. In this system, the size of the antenna is 2.9 x 0.6 µm, the GP wavelength is 250 nm, and the propagation length is around 1 µm, in good agreement with ref. 13.


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Figure 1. Yagi-Uda Antenna on a monolayer of graphene as it could be fabricated by chemical vapor deposition (CVD). (a) Illustration of the graphene sheet and antenna geometry. (b) Directivity for a Yagi Uda antenna in the two major planes, as a reference the far field directivity of a dipole antenna is shown by dashed lines. (c) Real part of the normalized vertical near-field component of the antennas for λ0 = 10.9 µm on a graphene flake. (d) Near-field profile along the black, dashed line in (c), normalized to the maximum amplitude of the near-field generated by the dipole antenna (dashed line – see also Fig. S1). (e,f) Absolute value of the Fourier transform of the near-field in (c) on a SiO2 (e) and graphene surface. The scale bar shows the amplitude of the graphene plasmon wave vector. Compared to a simple dipole antenna, the Yagi-Uda design enables control on directivity, and leads to stronger coupling as shown in Figure 1. We use a 5 element Yagi-Uda antenna (Fig. 1a) that covers an area of approximately 3x5 µm, and therefore is still feasible for integration on graphene sheets. We find optimal directivity of 4.97 (at 10.9 µm wavelength) for distances of around λ/π between neighboring elements, except for the distance between reflector and feed, which gave best results for λ/4, as shown by Hofmann et al

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. This directivity is 3.8 times

higher than for the simple dipole. Figure 1b shows the normalized far-field and highlights the directionality of the Yagi-Uda antenna with a front to back lobe ratio of 3. The graphene plasmon propagates mainly within the major lobe produced by the antenna. Furthermore, the near-field in proximity of the antenna (Fig. 1c) is increased by a factor 2 with respect to a dipole antenna. Therefore, although the propagation length δGP of the signal is not larger compared to a dipole antenna, the absolute near field amplitude is significantly increased, which facilitates plasmon modulation and detection. Figure 1d shows a line profile of the near-field in propagation direction, demonstrating that the


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modulation is still clearly evident at a distance of 2µm from the antenna edge. The Fourier transform of the near-field evidences the directivity in y-direction. Here = 2⁄ , and = 2⁄ , where = 10.9 μ

is the excitation wavelength and = 275 the GP

wavelength. Furthermore, the FT signal is distributed over a large range in k space, and therefore the Yagi-Uda antenna couples efficiently to GPs over a broad range of carrier density in the graphene (see figure S3 in the SI). The Yagi-Uda design also leads to small absorption losses (see Fig. S2a in SI) and good frequency selectivity with respect to the excitation wavelength (Fig. S2b in SI) manifested by a narrow resonance.21


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Figure 2. (a) Eigenvalue analysis of a rectangular (a,b) and triangular (c,d) shaped waveguide. (a,c) Real part of the vertical near-field component produced by the dipole antenna for λ0 = 10.9 µm in a rectangular (a) and triangular (c) shaped graphene waveguide. (b,d) 3D plot of the vertical near-field component in the forward propagation region of the waveguide. Next we will discuss how the shape of the graphene sheet can be used to increase the GP propagation length. Figure 2 compares a standard rectangular GP waveguide with a tapered


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triangular shape. For this comparison we use a dipole gold antenna to launch the GPs. In the rectangular waveguide in Figure 2a,b the GPs get reflected at the lateral edges and there is very little plasmon propagation along the stripe, with near-field enhancement only at the edges

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This occurs because the eigenmodes of the waveguides at the GP frequency are mostly edge modes. In case of the tapered triangular waveguide (Fig. 2c,d) the reflections of the eigenmodes at the edges result in constructive interference that leads to strong electric near field (with enhancement factors of up to 20). This occurs all the way to the tip of the triangle, which is 8 µm distant from the point where the plasmon was launched (the edge of the antenna). This behavior is triggered by symmetry breaking of the graphene waveguide, which leads to a resonance of the tip contribution with the cavity modes of the triangular graphene sheet 6. Note that here the signal is propagated, although at the edges, in direction along the long axis of the waveguide, and therefore useful for communication purposes. As shown in Figure 2d the highest plasmon signal is obtained at the lateral edges of the sharp triangular tip, therefore this concept can be explored for plasmon propagation in specific direction over large distance to locations where detectors24-25 could be implemented. Moreover, the resonance effect in the tapered waveguide can be used for logic operations, since it can be tuned either by the incident wavelength on the antenna, or by varying the GP resonance via the charge carrier density.


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Figure 3. (a) Eigenvalue analysis of a chain of truncated triangles in graphene. (b) Real part of the vertical near-field component produced by the dipole antenna for λ0 = 10.9 µm. (c) Electric near-field profile along the center of tapered triangle.

Figure 2a illustrated that a micron size rectangular waveguide combined with a dipole antenna is not suitable for GP propagation along its long axis. In Figure 3 we show how nanostructuring of such waveguide can lead to directional and efficient GP propagation. We consider the rectangular waveguide, however consisting of nano-patterned triangular motifs engineered to have constructive interference and maximized field enhancement in the “forward” direction at their truncated tips. The GPs are launched by a dipole antenna as before. Figure 3a shows the


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resonance of a chain of truncated triangles at the plasmon frequency. The plasmon is sustained by the coexistence of the enhancement of the electric field at the truncated tip,26 and the constructive interference of the reflections at the lateral edges9, 17 of the triangles. This results in an asymmetric distribution of the electric field that can be exploited for GP propagation. A rectangular graphene waveguide patterned with an array of such truncated triangle chains in the vicinity of a gold dipole antenna is depicted in Figure 3b. For the given width of the dipole antenna, the inner three chains of nano-triangles couple to the excitation. The pattern sustains an in-phase coherent interference that results in a strong transmission peak which can lead to a propagation length δGP of 4 µm. We note that wavelength and phase of the transmitted peak remains unaltered (Figure 3c), which facilitates the preservation of information in such waveguide structures. This nanostructuring approach has the additional advantage that the resonance energy of the GP depends on the dimensions of the nanostructure, and consequently can be tuned into an energy range that is significantly higher than the mid-IR that we use in this example. With lateral sizes of the order of 100 nm, plasmon resonance energies can be in the near IR, which allows the use of smaller metal antenna structures that resonate in that range, as well as more standard diode lasers for excitation.

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Figure 4. GP propagation in parallel nanowire waveguides. (a) Electric near-field distribution at resonance for a dipole antenna under 10.9 µm laser excitation with an array of wire-shaped waveguides patterned in the vicinity of its lateral sides. The regions without graphene on the SiO2 surface are sketched by the white rectangular boxes. The length of the long wires is 3 µm (b) Line plots of the electric near-field profile along the center of the two long nanowire waveguides in (a). The plasmons in the left and right wire oscillate out of phase. (c) Electric near field distribution for an array of wire-shaped waveguides patterned near a Yagi-Uda antenna. The red box marks a region of different potential (as could be realized by a local buried gate) that leads to a different Fermi energy in the graphene. (d) Line plots of the electric near-field profile along the center of the two long nanowire waveguides in (c). The phase and wavelength can be controlled by a back gate.


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A different nanostructuring approach is based on nanowire shaped waveguides. Figure 4 shows how an array of parallel graphene nanowires 27 oriented perpendicular to the plasmon launching antenna can lead to significantly increased plasmon propagation δGP up to 3 µm (compared to δGP ~1 µm for unstructured graphene – see section 1 in the SI). Here the width of the nanowires was chosen such that an almost parallel wave front is obtained inside the waveguide. The position of the waveguides at the lateral side of the metal stripes of the antennas has the advantage that plasmon waves with opposite phase are launched in wires located at the left and right side (in Fig 4a), which is evident in the line plots shown in Figure 4b. This design allows for plasmon propagation up to 3 µm for CVD graphene on SiO2. Inside the wire the signal exhibits an exponential decay, followed by a more abrupt decrease at the wire end due to the free dispersion of the plasmon when the 1D confinement is relieved. Comparison of a dipole antenna (a,b) with a Yagi-Uda antenna (c,d) for plasmon launching shows that the electric near field signal is almost a factor of 2 larger for the Yagi-Uda case. Furthermore we demonstrate in Figure 4 (c,d) the possibility to tune the phase of the propagating plasmon wave by varying locally the potential, as could be achieved by local gate electrodes 28-29. In this scenario the plasmons in the two nanowire waveguides are out of phase at zero gate potential, due to their position with respect to the antenna polarization. A change in potential alters the wavelength and the phase of the plasmon in the left waveguide, as is evident from the red trace in Fig. 4d. If the two nanowire waveguides are brought in proximity over a certain length section (not shown) this concept can potentially be used for information processing via plasmon interference 30.


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Figure 5. Vertical (z) component of the electric field for three different scatterers. (a) Dipole antenna, (b) gold sphere with 5 nm radius on the SiO2 substrate, and (c) nanotip with 5 nm curvature under excitation with a Gaussian beam with 10 µm diameter in z direction. (d) zcomponent of the electric near field in a graphene layer on SiO2 (i.e. GP amplitude) generated by scattering of a laser beam at 10.9 µm wavelength on the metallized nanotip. Finally we compare the GP launching efficiency of metal antennas with nano-scatterers, placed in- and out-of plane with the graphene layer. In detail, we consider metal spheres as could be realized by Au nanoparticles, and a tapered cone as it is the case in the SNOM experiments reported in ref.

5, 9, 11, 27-28.

Figure 5 shows the near field intensity produced by an in-plane

dipole antenna (a), and of a spherical scatterer with 5 nm radius (b), and of a tapered metal tip with 5 nm tip radius (c) placed on top of a silicon oxide substrate. The excitation at 10.9 µm is in resonance with the dipole antenna, but out of resonance with the metal nanostructures in (b) and (c) such that these act solely as scatterers. The simulations show that an out-of-plane scatterer results in a much stronger z-component of the electric near field, which in turn leads to stronger plasmon excitation in the graphene sheet. This is evidenced in Figure 5d where the plasmon signal in a graphene layer launched by a tapered waveguide is a factor of 5 stronger than that of a


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planar dipole antenna. Consequently, three-dimensional antenna designs can be a promising alternative for future devices that rely on plasmon propagation. In conclusion, we calculated the electric field in graphene waveguides coupled to metal antennas and demonstrate how the plasmon propagation in graphene can be enhanced and directed by antenna and waveguide design. On one hand the metal antenna shape can be optimized for coupling to the GP and for directivity, which was demonstrated in the Yagi-Uda design. On the other hand, the graphene waveguide can be altered with the aim to explore resonance and reflection effects. Here tapered graphene waveguides enable the propagation of edge plasmons towards the tip for distances larger than 8 µm, and nanopatterning of rectangular graphene waveguides results in the propagation of localized plasmons over several micron distance. In nanowire waveguides the large propagation length can be combined with phase control by underlying local gate electrodes. The proposed concepts can be applied to graphene on a variety of planar substrates as well as to encapsulated graphene, and can drive the fabrication of graphene based devices for optical on-chip communication.

Supporting Information. The following files are available free of charge. Supporting information (PDF) Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Funding Sources


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This work was supported by the EC under the Graphene Flagship program (contract no. CNECT-ICT-604391). Notes ACKNOWLEDGMENT This work was supported by the EC under the Graphene Flagship program (contract no. CNECT-ICT-604391).

ABBREVIATIONS GP, graphene plasmon; YU Yagi-Uda antenna; CVD, chemical vapour deposition; SiO2, Silicon dioxide; RPA, Random Phase Approximation; TOC image

REFERENCES 1. 2.

3.

4.

Grigorenko, A. N.; Polini, M.; Novoselov, K. S., Graphene plasmonics. Nat. Photon. 2012, 6, 749-758. Ju, L.; Geng, B.; Horng, J.; Girit, C.; Martin, M.; Hao, Z.; Bechtel, H. A.; Liang, X.; Zettl, A.; Shen, Y. R.; Wang, F., Graphene plasmonics for tunable terahertz metamaterials. Nat. Nano. 2011, 6, 630-634. Yan, H.; Low, T.; Zhu, W.; Wu, Y.; Freitag, M.; Li, X.; Guinea, F.; Avouris, P.; Xia, F., Damping pathways of mid-infrared plasmons in graphene nanostructures. Nat. Photon. 2013, 7, 394399. Cox, J. D.; Javier García de Abajo, F., Electrically tunable nonlinear plasmonics in graphene nanoislands. Nat. Commun. 2014, 5.


16

Page 17 of 18

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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5.

6.

7. 8. 9.

10. 11. 12. 13.

14.

15.

16.

17. 18. 19. 20.

Fei, Z.; Goldflam, M. D.; Wu, J. S.; Dai, S.; Wagner, M.; McLeod, A. S.; Liu, M. K.; Post, K. W.; Zhu, S.; Janssen, G. C. A. M.; Fogler, M. M.; Basov, D. N., Edge and Surface Plasmons in Graphene Nanoribbons. Nano Lett. 2015, 15, 8271-8276. Chen, J.; Badioli, M.; Alonso-Gonzalez, P.; Thongrattanasiri, S.; Huth, F.; Osmond, J.; Spasenovic, M.; Centeno, A.; Pesquera, A.; Godignon, P.; Zurutuza Elorza, A.; Camara, N.; de Abajo, F. J. G.; Hillenbrand, R.; Koppens, F. H. L., Optical nano-imaging of gate-tunable graphene plasmons. Nature 2012, 487, 77-81. Arrazola, I.; Hillenbrand, R.; Nikitin, A. Y., Plasmons in graphene on uniaxial substrates. Appl. Phys. Lett. 2014, 104, 011111. Basov, D. N.; Fogler, M. M.; Lanzara, A.; Wang, F.; Zhang, Y., Graphene spectroscopy. Rev. Mod. Phys. 2014, 86, 959-994. Fei, Z.; Rodin, A. S.; Andreev, G. O.; Bao, W.; McLeod, A. S.; Wagner, M.; Zhang, L. M.; Zhao, Z.; Thiemens, M.; Dominguez, G.; Fogler, M. M.; Neto, A. H. C.; Lau, C. N.; Keilmann, F.; Basov, D. N., Gate-tuning of graphene plasmons revealed by infrared nano-imaging. Nature 2012, 487, 82-85. García de Abajo, F. J., Graphene Plasmonics: Challenges and Opportunities. ACS Photon. 2014, 1, 135-152. Koppens, F. H. L.; Chang, D. E.; García de Abajo, F. J., Graphene Plasmonics: A Platform for Strong Light–Matter Interactions. Nano Lett. 2011, 11, 3370-3377. Brar, V. W.; Jang, M. S.; Sherrott, M.; Lopez, J. J.; Atwater, H. A., Highly Confined Tunable Mid-Infrared Plasmonics in Graphene Nanoresonators. Nano Lett. 2013, 13, 2541-2547. Alonso-González, P.; Nikitin, A. Y.; Golmar, F.; Centeno, A.; Pesquera, A.; Vélez, S.; Chen, J.; Navickaite, G.; Koppens, F.; Zurutuza, A.; Casanova, F.; Hueso, L. E.; Hillenbrand, R., Controlling graphene plasmons with resonant metal antennas and spatial conductivity patterns. Science 2014, 344, 1369-1373. Xue, J.; Sanchez-Yamagishi, J.; Bulmash, D.; Jacquod, P.; Deshpande, A.; Watanabe, K.; Taniguchi, T.; Jarillo-Herrero, P.; LeRoy, B. J., Scanning tunnelling microscopy and spectroscopy of ultra-flat graphene on hexagonal boron nitride. Nat. Mater. 2011, 10, 2825. Dean, C. R.; Young, A. F.; Meric, I.; Lee, C.; Wang, L.; Sorgenfrei, S.; Watanabe, K.; Taniguchi, T.; Kim, P.; Shepard, K. L.; Hone, J., Boron nitride substrates for high-quality graphene electronics. Nat. Nanotechnol. 2010, 5, 722-6. DaiS; MaQ; Liu, M. K.; AndersenT; FeiZ; Goldflam, M. D.; WagnerM; WatanabeK; TaniguchiT; ThiemensM; KeilmannF; Janssen, G. C. A. M.; Zhu, S. E.; Jarillo Herrero, P.; Fogler, M. M.; Basov, D. N., Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial. Nat. Nano. 2015, 10, 682-686. Rosolen, G.; Maes, B., Patterned graphene edges for tailored reflection of plasmonic modes. Opt. Lett. 2015, 40, 2727-2730. Rakic, A. D.; Djurisic, A. B.; Elazar, J. M.; Majewski, M. L., Optical properties of metallic films for vertical-cavity optoelectronic devices. Appl. Opt. 1998, 37, 5271-83. Hwang, E. H.; Das Sarma, S., Dielectric function, screening, and plasmons in twodimensional graphene. Phys. Rev. B 2007, 75, 205418. Mühlschlegel, P.; Eisler, H.-J.; Martin, O. J. F.; Hecht, B.; Pohl, D. W., Resonant Optical Antennas. Science 2005, 308, 1607-1609.


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21. Kosako, T.; Kadoya, Y.; Hofmann, H. F., Directional control of light by a nano-optical YagiUda antenna. Nat. Photon. 2010, 4, 312-315. 22. Holger, F. H.; Terukazu, K.; Yutaka, K., Design parameters for a nano-optical Yagi–Uda antenna. New J. Phys. 2007, 9, 217. 23. Nikitin, A. Y.; Guinea, F.; García-Vidal, F. J.; Martín-Moreno, L., Edge and waveguide terahertz surface plasmon modes in graphene microribbons. Phys. Rev. B 2011, 84, 161407. 24. Lundeberg, M. B.; Gao, Y.; Woessner, A.; Tan, C.; Alonso-González, P.; Watanabe, K.; Taniguchi, T.; Hone, J.; Hillenbrand, R.; Koppens, F. H. L. Thermoelectric detection of propagating plasmons in graphene ArXiv [Online], 2016. http://arxiv.org/abs/1601.01977. 25. Torre, I.; Tomadin, A.; Krahne, R.; Pellegrini, V.; Polini, M., Electrical plasmon detection in graphene waveguides. Phys. Rev. B 2015, 91, 081402. 26. Si, G.; Zhao, Y.; Lv, J.; Wang, F.; Liu, H.; Teng, J.; Liu, Y. J., Direct and accurate patterning of plasmonic nanostructures with ultrasmall gaps. Nanoscale 2013, 5, 4309-4313. 27. FeiZ; Rodin, A. S.; GannettW; DaiS; ReganW; WagnerM; Liu, M. K.; McLeod, A. S.; DominguezG; ThiemensM; Castro NetoAntonio, H.; KeilmannF; ZettlA; HillenbrandR; Fogler, M. M.; Basov, D. N., Electronic and plasmonic phenomena at graphene grain boundaries. Nat. Nano. 2013, 8, 821-825. 28. Woessner, A.; Lundeberg, M. B.; Gao, Y.; Principi, A.; Alonso-González, P.; Carrega, M.; Watanabe, K.; Taniguchi, T.; Vignale, G.; Polini, M.; Hone, J.; Hillenbrand, R.; Koppens, F. H. L., Highly confined low-loss plasmons in graphene–boron nitride heterostructures. Nat. Mater. 2015, 14, 421-425. 29. Christensen, J.; Manjavacas, A.; Thongrattanasiri, S.; Koppens, F. H. L.; García de Abajo, F. J., Graphene Plasmon Waveguiding and Hybridization in Individual and Paired Nanoribbons. ACS Nano 2012, 6, 431-440. 30. Fakonas, J. S.; Lee, H.; Kelaita, Y. A.; Atwater, H. A., Two-plasmon quantum interference. Nat. Photon. 2014, 8, 317-320.


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