Abstract

Graphene-based plasmonic structures feature large tunability, high spatial confinement, and potentially low loss, and are therefore an emerging technology for unconventional manipulation of light. In this paper, we demonstrate electrically tunable terahertz plasmonic crystals consisting of square-lattice graphene periodic anti-dot arrays on a SiO2/Si substrate. Transmission spectroscopy reveals multiple distinct resonances arising from excitations of graphene surface-plasmon–polariton (SPP) modes on different branches of the SPP dispersion curves inherent to the periodic structures. The resonance frequencies are readily tuned electrostatically with the Si back-gate and exhibit the dependency on the carrier density unique to SPP in graphene. Simulations show excellent agreement with the experiments and further illustrate the symmetry-based selection rule for the excited graphene SPP modes. Such graphene plasmonic crystals may lead to a broad range of applications including plasmonic waveguide and transformation optics. Exploiting higher-order graphene SPP modes is an effective way to further facilitate field localization and enhancement.

© 2015 Optical Society of America

1. INTRODUCTION

Among other extraordinary electronic and optical properties of graphene [1], its ability to support highly confined surface-plasmon-polariton (SPP) waves in the mid-infrared to terahertz (THz) frequency range with large tunability and potentially low loss has motivated considerable research efforts in recent years [215], in light of a broad range of potential applications such as tunable plasmonic waveguides [16], reconfigurable metasurfaces [17], transformation optics [18], optical modulators [19], photo-detectors [20], chemical sensors [21], and so on. Similarly to SPP waves at a metal-dielectric interface [22], as a result of their high spatial confinement, SPP waves in an intact graphene sheet do not couple to free-space electro-magnetic (EM) waves due to a large momentum mismatch. Various approaches to bridge the momentum gap and achieve excitation of graphene SPP with free-space EM waves have been theoretically studied and/or experimentally demonstrated, including patterning graphene to form lower-dimensional structures (e.g., ribbons and disks) as cavities for localized SPP modes [610], or exciting SPP waves in continuous graphene with a near-field high-momentum components of light scattered by sub-wavelength structures such as a sharp metal tip [12,13] or a grating [14]. Alternatively, efficient coupling can be accomplished with periodically modulated graphene such as a graphene anti-dot array which possesses modified dispersion relations of SPP waves compared to that of pristine graphene [23]. In a fashion analogous to photonic crystal slabs [24,25], multiple branches of graphene SPP dispersion curves emerge and form a band-structure in the first Brillouin zone of the anti-dot array as a result of the Bragg scattering from the periodic lattice, thus allowing for direct coupling of free-space EM waves to selected SPP modes above the light line. In addition to the large tunability intrinsic to graphene-based structures, the plasmonic band-structure of a graphene anti-dot array can be tailored by its structural details, making such structures promising versatile building blocks for more complex devices in different applications. Periodic anti-dot arrays have previously been studied in the context of two-dimensional electron gas (2DEG) in semiconductor hetero-structures [2629] where intriguing collective carrier excitations (plasmonic and magneto-plasmonic modes) brought forth by the anti-dot arrays were observed; however, those investigations were limited at cryogenic temperatures. Plasmonic crystals employing graphene anti-dot arrays operating at room temperature have been demonstrated recently [30,31] where resonance features in the transmission spectra attributed to graphene SPP modes were observed in hexagonal-lattice graphene anti-dot arrays. However, neither electrostatic tuning of these resonances nor resolved multi-band resonances inherent to the periodic structures was reported.

In this paper we demonstrate various large-area electrically tunable THz plasmonic crystals consisting of graphene periodic anti-dot arrays in the square-lattice configuration. Transmission characterizations evidently reveal multiple resonances, corresponding to modes on different branches of the graphene SPP dispersion curves. Carrier density (n) dependent measurements are conducted by employing electrostatic doping with the Si back-gate, which confirm that the resonance frequencies (ωSP) shift according to the scaling law unique to SPP waves in monolayer graphene (ωSPn1/4). The experimentally observed resonances show excellent agreement with the full-wave simulation results which further reveal the symmetry-based selection rule for the excited SPP modes.

2. DESIGNS OF THE GRAPHENE ANTI-DOT ARRAY THz PLASMONIC CRYSTALS

We focus on square-lattice anti-dot array structures with round apertures in part due to their isotropic nature, high symmetry, and structural simplicity [only two structural parameters, i.e., the lattice constant and the aperture diameter as illustrated in Fig. 1(a)]. Another key motivation for studying such square-lattice structures is that in general half of the higher-order dispersion curves in the associated SPP band-structure host modes that can be efficiently excited by free-space EM waves (referred to as coupled SPP modes later), whereas this ratio is 1/3 for hexagonal-lattice structures. This is a consequence of the symmetry-based selection rule for the coupled SPP modes in such 2D crystal type structures [32]. Similarly to photonic crystal slab structures [24,25], the SPP band-structure of a graphene periodic anti-dot array [30] is a combined result of the zone-folding of the single SPP dispersion curve of an intact graphene sheet into the first Brillouin zone by different orders of lattice-induced Bragg scatterings, and the mixing and degeneracy-lifting due to the finite-sized apertures. As a first-order estimate, such a band-structure can also be analytically obtained with the empty lattice approximation [25], and an example is presented in Fig. S1 (Supplement 1). Near the Γ-point (center) of the first Brillouin zone, each SPP dispersion curve except for the lowest branch lies above the light line and hence it is possible for the associated SPP modes to couple to free-space EM waves. Such a coupling would be manifested as enhanced absorption and reflection, and thus reduced transmission in the form of a resonance at the frequency of the SPP mode. However, since the Γ-point is a high-symmetry point, the field profile (or equivalently the charge distribution) of any SPP mode in the vicinity of the Γ-point also preserves certain symmetry properties of the lattice structure, which belong to the C4V point group for the case of a square lattice [32]. Besides the momentum-matching requirement, the symmetry property of a SPP mode also has to be compatible with that of the incident EM wave of a specific polarization to achieve efficient coupling. More specifically, for the square-lattice structures studied in this work, the profiles of the z-direction electric field of coupled SPP modes in the plane of the lattice structure (xy–plane) should be symmetric under one mirror reflection while anti-symmetric under the orthogonal mirror reflection. SPP modes above the light line but with different symmetry properties are consequently uncoupled modes. Such a symmetry-based selection rule for coupled SPP modes can be more intuitively perceived from the simulation results in Fig. 1. The simulated transmission, reflection and absorption spectra of a graphene anti-dot array on a SiO2/Si substrate are plotted in Fig. 1(b). Two sharp resonances associated with two different graphene SPP modes are present in the frequency range concerned, with their electric field profiles shown in Fig. 1(c). Both field profiles, under mirror reflection operations, are symmetric with respect to the x=0 plane and anti-symmetric with respect to the y=0 plane, indeed matching the symmetry of the incident EM wave which is linearly polarized in the y-direction. It is worth noticing that the higher-order mode in Fig. 1(b) is considerably stronger than the simulated higher-order mode of a hexagonal-lattice graphene anti-dot array with a similar filling factor of the apertures in Ref. [30]. From the perspective that different branches of the SPP dispersion curves are due to Bragg scatterings associated with different reciprocal lattice vectors [23,29], the reciprocal lattice vectors corresponding to the field profiles in Fig. 1(c) are [0,1] (top) and [0,2] (bottom), respectively. However, as the relatively large apertures introduce strong mixing of different orders of Bragg scatterings, both modes also contain significant contributions from the reciprocal lattice vector [1,1] as is markedly revealed by the 2D FFT of the field profiles in Fig. 1(c). Since the spatial confinement factor λ0/λSP of graphene SPP (λSP being the SPP wavelength) decreases with the free-space wavelength λ0 [4], exploiting higher-order modes in the THz frequency range is an effective way to achieve high spatial confinement comparable to that in the mid-infrared [12,13] and significantly higher than that of noble-metal-based plasmonics [4].

 

Fig. 1. (a) Schematic of a square-lattice graphene periodic anti-dot array; (b) simulated transmission, reflection, and absorption spectra of a graphene periodic anti-dot array on a SiO2/Si substrate with a lattice constant of 3 μm and an aperture diameter of 2 μm. Fermi energy is set to 0.4eV and the carrier relaxation time 1 ps; (c) simulated z-direction electric field profiles (in an xy–plane right above the graphene sheet) of the two resonances in part b (left) and the 2D fast Fourier-transform (FFT) of each field profile (right). Top, lower-frequency mode; bottom, higher-frequency mode. In the 2D FFT of the field profiles, each square pixel corresponds to a reciprocal lattice vector (e.g., the center pixel is for [0,0], the one above the center is for [0,1], and so on) and its brightness represents the amplitude of the corresponding spatial frequency component.

Download Full Size | PPT Slide | PDF

3. SAMPLE FABRICATION AND BASIC CHARACTERIZATIONS

Square-lattice graphene periodic anti-dot arrays with various dimensions are designed and implemented on large-area monolayer graphene on a SiO2/Si substrate. The details of the investigated structures are listed in Table 1. These structures are designed to ensure that the dominant coupled graphene SPP modes are in the THz frequency range and well below the frequency of the surface optical phonon mode in the SiO2 substrate at 485cm1 (14.5 THz) [10]. The graphene sheet is patterned with deep-UV photolithography and O2 plasma etching (fabrication details in Supplement 1). Each graphene anti-dot array structure has a dimension of 3mm×3mm. An SEM image detailing the microscopic structure of a fabricated sample is shown in Fig. 2(a). The fabrication process unavoidably introduces small discrepancies between the diameters of the etched apertures (also listed in Table 1) and their designed values, which are taken into account when analyzing the experimental data. Metal electrodes are deposited to form contacts with the graphene structure in a field-effect transistor-type configuration with the Si substrate as the back-gate, facilitating electrostatic tuning of the carrier density and characterizations of the electrical properties of the graphene sheet. Several unpatterned graphene samples are prepared in a similar configuration, and electrical characterizations show that the graphene sheet is naturally p-doped with an average hole mobility of 1000cm2/Vs (Fig. S2, Supplement 1). Characterizations on the patterned graphene samples suggest that the carrier mobility is not significantly affected by the fabrication process. Raman spectroscopy is performed on several graphene anti-dot arrays, and signature Raman spectra of monolayer graphene are observed [Fig. 2(b)].

Tables Icon

Table 1. Details of Different Graphene Anti-Dot Arrays

 

Fig. 2. (a) Scanning electron microscopy (SEM) image of a fabricated graphene anti-dot array sample; (b) typical Raman spectrum of the graphene anti-dot array samples.

Download Full Size | PPT Slide | PDF

4. EXPERIMENTAL DEMONSTRATION OF TUNABLE MULTI-BAND SPP EXCITATIONS

To probe the coupled SPP modes of the graphene anti-dot arrays, transmission spectroscopy is carried out with a Fourier-transform infrared (FTIR) spectrometer (Bruker Vertex 80v). The samples are placed in the vacuum compartment of the FTIR, and all the measurements are conducted at room temperature. Due to the isotropic nature of the square-lattice anti-dot arrays with round apertures, the transmission should not depend on the polarization of the incident illumination (experimentally verified); therefore, unpolarized broadband emission from a Globar is employed as the illumination beam in a nearly normal-incident (slightly focusing) scheme for the measurements. Following the conventional procedure [6], the transmission spectra of each anti-dot array are measured at various back-gate voltages and hence different carrier densities including the charge neutrality point (CNP). Transmission extinction spectra at biases away from the CNP defined as 1-(T/TCNP) are extracted, which clearly reveal the carrier-density-dependent spectral features of the graphene-based structure by reliably eliminating the background spectral information due to the substrate and the measurement setup. Figure 3 shows the extinction spectra of four different anti-dot arrays (SQ1–SQ4) in comparison with those of an unpatterned graphene sample, whereas the spectra for the other investigated structures (SQ5–SQ7) are presented in Fig. S3 (Supplement 1). In sharp contrast to the extinction spectra of the unpatterned graphene sample [Fig. 3(e)], the only feature of which is a Drude-type tail progressing with increasing carrier density, distinct peaks with rising prominences are observed in the extinction spectra of all the graphene anti-dot arrays [Figs. 3(a)3(d)]. Moreover, in each set of spectra shown in Figs. 3(b)3(d), two peaks are clearly visible despite their relatively broad profiles. The positions of all the peaks shift towards the high-frequency side with increasing carrier density, and further quantitative analyses show that the frequency shift is consistent with the carrier-density-dependent frequency scaling law (ωn1/4|EF|1/2), where EF is the Fermi energy, unique to SPP waves in monolayer graphene [Fig. 3(f)], confirming the graphene SPP origin of all the observed resonance peaks. The separated resonances in each of Figs. 3(b)3(d) originate from SPP modes on different branches of the SPP dispersion curves associated with the corresponding graphene anti-dot array, which are further analyzed and confirmed by the simulation results presented in a subsequent paragraph. To the best of our knowledge, such direct experimental observation of the multi-band nature of SPP dispersion curves inherent to the periodic structures of graphene anti-dot arrays has not been reported yet. Higher-order SPP modes were also rarely observed in semiconductor-based 2DEG anti-dot arrays despite their much higher carrier mobility at cryogenic temperatures [28].

 

Fig. 3. Transmission extinction spectra at various back-gate voltages for the following; (a)–(d) samples SQ1–SQ4; (e) unpatterned graphene sample; (f) symbols are the plasmonic resonance frequency (in wavenumbers) as a function of the square root of the carrier density and equivalently the Fermi energy for all the resonance peaks in SQ1–SQ4. Height of the symbols corresponds to the typical error bar in extracting the peak position using different fitting functions and ranges. Solid curves are fits of the data points (symbols in the matching color) with functions in the form of y=ax1/2 with a being a fitting parameter. Experimental results on the other structures are included in Supplement 1.

Download Full Size | PPT Slide | PDF

5. SIMULATED PROFILES OF THE EXCITED SPP MODES

Full-wave simulations of the transmission spectra are performed for all the studied graphene anti-dot arrays using finite-element frequency domain methods (details in Supplement 1). For the simulation results presented, the Fermi energy EF is set to 0.45eV which roughly corresponds to the highest carrier (hole) density achieved experimentally (1.5×1013cm2), and two different values of carrier relaxation time τ, 1 and 0.1 ps, are assumed where the latter is relatively close to that of the graphene material used. Figure 4 shows the simulated extinction spectra in comparison with the experimental results of the same four structures in Fig. 3, whereas results for the other structures are included in Fig. S4 (Supplement 1). The simulated spectra corresponding to τ=0.1ps (red curves) show excellent agreement with the experimental results in terms of the number of observable peaks and their positions, although the resonance peaks are more prominent in the simulated spectra, suggesting that the carrier relaxation time of the real samples is even shorter. Scatterings due to the etched graphene edges [8] and the SiO2 surface optical phonon [8,10] may have significant impact on the plasmon damping rate. Furthermore, the spectra corresponding to τ=1ps (blue curves) unveil more details on the origins of the observed broader higher-frequency peaks in Figs. 4(c) and 4(d) as well as Figs. 3(c) and 3(d), i.e., they do not stem from a single SPP resonance but contain contributions from multiple SPP resonances on different branches of SPP dispersion curves. These individual resonances are to be clearly distinguished only in structures with much higher carrier mobility.

 

Fig. 4. Simulated transmission extinction spectra for the same graphene anti-dot arrays in Figs. 3(a)3(d) assuming two different carrier relaxation times: τ=1ps (blue curves) and τ=0.1ps (red curves) in comparison with the experimental results (black curves).

Download Full Size | PPT Slide | PDF

To further gain insight of the individual coupled SPP modes, electric field profiles are calculated for each SPP resonance in all the structures. Figure 5 shows the z-direction electric field profiles (in an xy–plane right above the graphene sheet) associated with the four prominent resonances in Fig. 4(d). Two distinctive features are noticeable from the field profiles of all the investigated structures. The first feature is that all of the field profiles have the same symmetry properties under mirror reflection operations as those in Fig. 1(c), indeed complying with the symmetry property of the linearly polarized (in the y–direction) normal-incident plane wave, as required by the previously mentioned symmetry-based selection rule. The second feature is that each field profile has certain dominant spatial frequencies corresponding to specific reciprocal lattice vectors, which are clearly revealed in the 2D FFT of the field profiles (see the insets). In general, modes with higher energy are associated with higher-order reciprocal lattice vectors and have more enhanced spatial confinement. Due to the large ratio of the aperture diameter to the lattice constant (d/l), the mixing of Bragg scatterings of different orders is significant and hence each mode is associated with multiple dominant reciprocal lattice vectors.

 

Fig. 5. Simulated z-direction electric field profiles of the SPP modes corresponding to the four prominent resonance peaks in Fig. 4(d). Plots are numbered in the ascending order of the resonance frequency. Insets, 2D FFT of the field profiles plotted similarly as in Fig. 1(c).

Download Full Size | PPT Slide | PDF

6. CONCLUSION

In summary, various large-area graphene periodic anti-dot arrays in the square-lattice configuration were investigated, and multiple electrically tunable resonances in the transmission extinction spectra (originating from excitations of graphene SPP modes on different bands of SPP dispersion curves inherent to the periodic structures) are evidently resolved at room temperature. Numerical simulations confirm the experimental observations and further reveal the symmetry-based selection rule for the excited SPP modes. The presented experimental and simulation results further illustrate the high flexibility of band-structure engineering of such graphene-based plasmonic crystals, demonstrate their advantages over noble-metal-based plasmonics, and can be utilized as design guidelines for more complex structures and devices such as tunable plasmonic waveguides, reconfigurable metasurfaces, and transformation optics. The excitation of higher-order SPP modes observed in such structures is of significant technological interest due to the more enhanced mode spatial confinement and field localization, and also provides an interesting platform for further study of higher-order magneto-plasmonic responses in periodic anti-dot arrays.

FUNDING INFORMATION

European Commission (EC) through project GOSFEL; Swiss National Science Foundation (SNSF) through NCCR QSIT.

ACKNOWLEDGMENT

The authors thank Sergey Mikhailov for valuable discussions and Christofer Hierold for granting access to a micro-Raman spectrometer. The cleanroom facility FIRST at ETH Zurich is also acknowledged.

 

See Supplement 1 for supporting content.

REFERENCES

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

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

3. S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett. 99, 016803 (2007). [CrossRef]  

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

5. F. H. L. Koppens, D. E. Chang, and F. J. Garcia de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).

6. 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, 630–634 (2011). [CrossRef]  

7. 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, 330–334 (2012). [CrossRef]  

8. H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7, 394–399 (2013). [CrossRef]  

9. V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, and H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett. 13, 25412547 (2013).

10. I. J. Luxmoore, C. H. Gan, P. Q. Liu, F. Valmorra, P. Li, J. Faist, and G. R. Nash, “Strong coupling in the far-infrared between graphene plasmons and the surface optical phonons of silicon dioxide,” ACS Photonics 1, 1151–1155 (2014).

11. I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, and A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12, 2470–2474 (2012).

12. J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).

13. Z. Fei, A. S. Rodin, G. O. Adreev, 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, 82–85 (2012).

14. W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, “Excitation and active control of propagating surface plasmon polaritons in graphene,” Nano Lett. 13, 3698–3702 (2013).

15. T. Low and P. Avouris, “Graphene plasmonics for terahertz to midinfrared applications,” ACS Nano 8, 1086–1101 (2014). [CrossRef]  

16. A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84, 161407 (2011).

17. M. Tamagnone, J. S. Gomez-Diaz, J. R. Mosig, and J. Perruisseau-Carrier, “Reconfigurable terahertz plasmonic antenna concept using a graphene stack,” Appl. Phys. Lett. 101, 214102 (2012). [CrossRef]  

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

19. B. Sensale-Rodriguez, R. Yan, M. Zhu, D. Jena, L. Liu, and X. G. Xing, “Efficient terahertz electro-absorption modulation employing graphene plasmonic structures,” Appl. Phys. Lett. 101, 261115 (2012). [CrossRef]  

20. M. Freitag, T. Low, W. Zhu, H. Yan, F. Xia, and P. Avouris, “Photocurrent in graphene harnessed by tunable intrinsic plasmons,” Nat. Commun. 4, 1951 (2013). [CrossRef]  

21. Y. Li, H. Yan, D. B. Farmer, X. Meng, W. Zhu, R. M. Osgood, T. F. Heinz, and P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14, 1573–1577 (2014).

22. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, 1988).

23. A. Y. Nikitin, F. Guinea, and L. Martin-Moreno, “Resonant plasmonic effects in periodic graphene antidot arrays,” Appl. Phys. Lett. 101, 151119 (2012). [CrossRef]  

24. S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).

25. K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, and O. Solgaard, “Airbridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006).

26. K. Kern, D. Heitmann, P. Grambow, Y. H. Zhang, and K. Ploog, “Collective excitations in antidots,” Phys. Rev. Lett. 66, 1618–1621 (1991). [CrossRef]  

27. Y. Zhao, D. C. Tsui, M. Santos, M. Shayegan, R. A. Ghanbari, D. A. Antoniadis, and H. I. Smith, “Magneto-optical absorption in a two-dimensional electron grid,” Appl. Phys. Lett. 60, 1510–1512 (1992). [CrossRef]  

28. M. Hochgraefe, R. Krahne, Ch. Heyn, and D. Heitmann, “Anticyclotron motion in antidot arrays,” Phys. Rev. B 60, 10680 (1999).

29. S. A. Mikhailov, “Theory of electromagnetic response and collective excitations of a square lattice of antidots,” Phys. Rev. B 54, 14293 (1996).

30. K. Y. M. Yeung, J. Chee, H. Yoon, Y. Song, J. Kong, and D. Ham, “Farinfrared graphene plasmonic crystals for plasmonic band engineering,” Nano Lett. 14, 2479–2484 (2014).

31. X. Zhu, W. Wang, W. Yan, M. B. Larsen, P. Boggild, T. G. Pedersen, S. Xiao, J. Zi, and N. A. Mortensen, “Plasmon−phonon coupling in largearea graphene dot and antidot arrays fabricated by nanosphere lithography,” Nano Lett. 14, 2907–2913 (2014).

32. K. Sakoda, Optical Properties of Photonic Crystals (Springer, 2005).

References

  • View by:
  • |
  • |
  • |

  1. K. S. Novoselov, V. I. Fal’ko, L. Colombo, P. R. Gellert, M. G. Schwab, K. Kim, “A roadmap for graphene,” Nature 490, 192–200 (2012).
    [Crossref]
  2. E. H. Hwang, S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B 75, 205418 (2007).
  3. S. A. Mikhailov, K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett. 99, 016803 (2007).
    [Crossref]
  4. M. Jablan, H. Buljan, M. Soljacic, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).
  5. F. H. L. Koppens, D. E. Chang, F. J. Garcia de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).
  6. L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
    [Crossref]
  7. 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, 330–334 (2012).
    [Crossref]
  8. H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7, 394–399 (2013).
    [Crossref]
  9. V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett. 13, 25412547 (2013).
  10. I. J. Luxmoore, C. H. Gan, P. Q. Liu, F. Valmorra, P. Li, J. Faist, G. R. Nash, “Strong coupling in the far-infrared between graphene plasmons and the surface optical phonons of silicon dioxide,” ACS Photonics 1, 1151–1155 (2014).
  11. I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12, 2470–2474 (2012).
  12. J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).
  13. Z. Fei, A. S. Rodin, G. O. Adreev, 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, 82–85 (2012).
  14. W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, Q. Xu, “Excitation and active control of propagating surface plasmon polaritons in graphene,” Nano Lett. 13, 3698–3702 (2013).
  15. T. Low, P. Avouris, “Graphene plasmonics for terahertz to midinfrared applications,” ACS Nano 8, 1086–1101 (2014).
    [Crossref]
  16. A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, L. Martin-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84, 161407 (2011).
  17. M. Tamagnone, J. S. Gomez-Diaz, J. R. Mosig, J. Perruisseau-Carrier, “Reconfigurable terahertz plasmonic antenna concept using a graphene stack,” Appl. Phys. Lett. 101, 214102 (2012).
    [Crossref]
  18. A. Vakil, N. Engheta, “Transformation optics using graphene,” Science 332, 1291–1294 (2011).
    [Crossref]
  19. B. Sensale-Rodriguez, R. Yan, M. Zhu, D. Jena, L. Liu, X. G. Xing, “Efficient terahertz electro-absorption modulation employing graphene plasmonic structures,” Appl. Phys. Lett. 101, 261115 (2012).
    [Crossref]
  20. M. Freitag, T. Low, W. Zhu, H. Yan, F. Xia, P. Avouris, “Photocurrent in graphene harnessed by tunable intrinsic plasmons,” Nat. Commun. 4, 1951 (2013).
    [Crossref]
  21. Y. Li, H. Yan, D. B. Farmer, X. Meng, W. Zhu, R. M. Osgood, T. F. Heinz, P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14, 1573–1577 (2014).
  22. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, 1988).
  23. A. Y. Nikitin, F. Guinea, L. Martin-Moreno, “Resonant plasmonic effects in periodic graphene antidot arrays,” Appl. Phys. Lett. 101, 151119 (2012).
    [Crossref]
  24. S. Fan, J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).
  25. K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, O. Solgaard, “Airbridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006).
  26. K. Kern, D. Heitmann, P. Grambow, Y. H. Zhang, K. Ploog, “Collective excitations in antidots,” Phys. Rev. Lett. 66, 1618–1621 (1991).
    [Crossref]
  27. Y. Zhao, D. C. Tsui, M. Santos, M. Shayegan, R. A. Ghanbari, D. A. Antoniadis, H. I. Smith, “Magneto-optical absorption in a two-dimensional electron grid,” Appl. Phys. Lett. 60, 1510–1512 (1992).
    [Crossref]
  28. M. Hochgraefe, R. Krahne, Ch. Heyn, D. Heitmann, “Anticyclotron motion in antidot arrays,” Phys. Rev. B 60, 10680 (1999).
  29. S. A. Mikhailov, “Theory of electromagnetic response and collective excitations of a square lattice of antidots,” Phys. Rev. B 54, 14293 (1996).
  30. K. Y. M. Yeung, J. Chee, H. Yoon, Y. Song, J. Kong, D. Ham, “Farinfrared graphene plasmonic crystals for plasmonic band engineering,” Nano Lett. 14, 2479–2484 (2014).
  31. X. Zhu, W. Wang, W. Yan, M. B. Larsen, P. Boggild, T. G. Pedersen, S. Xiao, J. Zi, N. A. Mortensen, “Plasmon−phonon coupling in largearea graphene dot and antidot arrays fabricated by nanosphere lithography,” Nano Lett. 14, 2907–2913 (2014).
  32. K. Sakoda, Optical Properties of Photonic Crystals (Springer, 2005).

2014 (5)

I. J. Luxmoore, C. H. Gan, P. Q. Liu, F. Valmorra, P. Li, J. Faist, G. R. Nash, “Strong coupling in the far-infrared between graphene plasmons and the surface optical phonons of silicon dioxide,” ACS Photonics 1, 1151–1155 (2014).

T. Low, P. Avouris, “Graphene plasmonics for terahertz to midinfrared applications,” ACS Nano 8, 1086–1101 (2014).
[Crossref]

Y. Li, H. Yan, D. B. Farmer, X. Meng, W. Zhu, R. M. Osgood, T. F. Heinz, P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14, 1573–1577 (2014).

K. Y. M. Yeung, J. Chee, H. Yoon, Y. Song, J. Kong, D. Ham, “Farinfrared graphene plasmonic crystals for plasmonic band engineering,” Nano Lett. 14, 2479–2484 (2014).

X. Zhu, W. Wang, W. Yan, M. B. Larsen, P. Boggild, T. G. Pedersen, S. Xiao, J. Zi, N. A. Mortensen, “Plasmon−phonon coupling in largearea graphene dot and antidot arrays fabricated by nanosphere lithography,” Nano Lett. 14, 2907–2913 (2014).

2013 (4)

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, Q. Xu, “Excitation and active control of propagating surface plasmon polaritons in graphene,” Nano Lett. 13, 3698–3702 (2013).

M. Freitag, T. Low, W. Zhu, H. Yan, F. Xia, P. Avouris, “Photocurrent in graphene harnessed by tunable intrinsic plasmons,” Nat. Commun. 4, 1951 (2013).
[Crossref]

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7, 394–399 (2013).
[Crossref]

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett. 13, 25412547 (2013).

2012 (8)

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, 330–334 (2012).
[Crossref]

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

M. Tamagnone, J. S. Gomez-Diaz, J. R. Mosig, J. Perruisseau-Carrier, “Reconfigurable terahertz plasmonic antenna concept using a graphene stack,” Appl. Phys. Lett. 101, 214102 (2012).
[Crossref]

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12, 2470–2474 (2012).

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).

Z. Fei, A. S. Rodin, G. O. Adreev, 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, 82–85 (2012).

B. Sensale-Rodriguez, R. Yan, M. Zhu, D. Jena, L. Liu, X. G. Xing, “Efficient terahertz electro-absorption modulation employing graphene plasmonic structures,” Appl. Phys. Lett. 101, 261115 (2012).
[Crossref]

A. Y. Nikitin, F. Guinea, L. Martin-Moreno, “Resonant plasmonic effects in periodic graphene antidot arrays,” Appl. Phys. Lett. 101, 151119 (2012).
[Crossref]

2011 (4)

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

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, L. Martin-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84, 161407 (2011).

F. H. L. Koppens, D. E. Chang, F. J. Garcia de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref]

2009 (1)

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

2007 (2)

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

S. A. Mikhailov, K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett. 99, 016803 (2007).
[Crossref]

2006 (1)

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, O. Solgaard, “Airbridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006).

2002 (1)

S. Fan, J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).

1999 (1)

M. Hochgraefe, R. Krahne, Ch. Heyn, D. Heitmann, “Anticyclotron motion in antidot arrays,” Phys. Rev. B 60, 10680 (1999).

1996 (1)

S. A. Mikhailov, “Theory of electromagnetic response and collective excitations of a square lattice of antidots,” Phys. Rev. B 54, 14293 (1996).

1992 (1)

Y. Zhao, D. C. Tsui, M. Santos, M. Shayegan, R. A. Ghanbari, D. A. Antoniadis, H. I. Smith, “Magneto-optical absorption in a two-dimensional electron grid,” Appl. Phys. Lett. 60, 1510–1512 (1992).
[Crossref]

1991 (1)

K. Kern, D. Heitmann, P. Grambow, Y. H. Zhang, K. Ploog, “Collective excitations in antidots,” Phys. Rev. Lett. 66, 1618–1621 (1991).
[Crossref]

Adreev, G. O.

Z. Fei, A. S. Rodin, G. O. Adreev, 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, 82–85 (2012).

Ajayan, P. M.

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, Q. Xu, “Excitation and active control of propagating surface plasmon polaritons in graphene,” Nano Lett. 13, 3698–3702 (2013).

Alonso-Gonzalez, P.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).

Antoniadis, D. A.

Y. Zhao, D. C. Tsui, M. Santos, M. Shayegan, R. A. Ghanbari, D. A. Antoniadis, H. I. Smith, “Magneto-optical absorption in a two-dimensional electron grid,” Appl. Phys. Lett. 60, 1510–1512 (1992).
[Crossref]

Atwater, H. A.

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett. 13, 25412547 (2013).

Avouris, P.

T. Low, P. Avouris, “Graphene plasmonics for terahertz to midinfrared applications,” ACS Nano 8, 1086–1101 (2014).
[Crossref]

Y. Li, H. Yan, D. B. Farmer, X. Meng, W. Zhu, R. M. Osgood, T. F. Heinz, P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14, 1573–1577 (2014).

M. Freitag, T. Low, W. Zhu, H. Yan, F. Xia, P. Avouris, “Photocurrent in graphene harnessed by tunable intrinsic plasmons,” Nat. Commun. 4, 1951 (2013).
[Crossref]

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7, 394–399 (2013).
[Crossref]

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, 330–334 (2012).
[Crossref]

Badioli, M.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).

Bao, W.

Z. Fei, A. S. Rodin, G. O. Adreev, 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, 82–85 (2012).

Basov, D. N.

Z. Fei, A. S. Rodin, G. O. Adreev, 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, 82–85 (2012).

Bechtel, H. A.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref]

Boggild, P.

X. Zhu, W. Wang, W. Yan, M. B. Larsen, P. Boggild, T. G. Pedersen, S. Xiao, J. Zi, N. A. Mortensen, “Plasmon−phonon coupling in largearea graphene dot and antidot arrays fabricated by nanosphere lithography,” Nano Lett. 14, 2907–2913 (2014).

Brar, V. W.

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett. 13, 25412547 (2013).

Buljan, H.

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

Camara, N.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).

Castro Neto, A. H.

Z. Fei, A. S. Rodin, G. O. Adreev, 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, 82–85 (2012).

Centeno, A.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).

Chandra, B.

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, 330–334 (2012).
[Crossref]

Chang, D. E.

F. H. L. Koppens, D. E. Chang, F. J. Garcia de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).

Chee, J.

K. Y. M. Yeung, J. Chee, H. Yoon, Y. Song, J. Kong, D. Ham, “Farinfrared graphene plasmonic crystals for plasmonic band engineering,” Nano Lett. 14, 2479–2484 (2014).

Chen, J.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12, 2470–2474 (2012).

Colombo, L.

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

Crassee, I.

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12, 2470–2474 (2012).

Crozier, K. B.

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, O. Solgaard, “Airbridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006).

Das Sarma, S.

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

Dominguez, G.

Z. Fei, A. S. Rodin, G. O. Adreev, 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, 82–85 (2012).

Engheta, N.

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

Faist, J.

I. J. Luxmoore, C. H. Gan, P. Q. Liu, F. Valmorra, P. Li, J. Faist, G. R. Nash, “Strong coupling in the far-infrared between graphene plasmons and the surface optical phonons of silicon dioxide,” ACS Photonics 1, 1151–1155 (2014).

Fal’ko, V. I.

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

Fan, S.

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, O. Solgaard, “Airbridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006).

S. Fan, J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).

Farmer, D. B.

Y. Li, H. Yan, D. B. Farmer, X. Meng, W. Zhu, R. M. Osgood, T. F. Heinz, P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14, 1573–1577 (2014).

Fei, Z.

Z. Fei, A. S. Rodin, G. O. Adreev, 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, 82–85 (2012).

Fogler, M. M.

Z. Fei, A. S. Rodin, G. O. Adreev, 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, 82–85 (2012).

Freitag, M.

M. Freitag, T. Low, W. Zhu, H. Yan, F. Xia, P. Avouris, “Photocurrent in graphene harnessed by tunable intrinsic plasmons,” Nat. Commun. 4, 1951 (2013).
[Crossref]

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7, 394–399 (2013).
[Crossref]

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, 330–334 (2012).
[Crossref]

Gan, C. H.

I. J. Luxmoore, C. H. Gan, P. Q. Liu, F. Valmorra, P. Li, J. Faist, G. R. Nash, “Strong coupling in the far-infrared between graphene plasmons and the surface optical phonons of silicon dioxide,” ACS Photonics 1, 1151–1155 (2014).

Gao, W.

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, Q. Xu, “Excitation and active control of propagating surface plasmon polaritons in graphene,” Nano Lett. 13, 3698–3702 (2013).

Gaponenko, I.

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12, 2470–2474 (2012).

Garcia de Abajo, F. J.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).

F. H. L. Koppens, D. E. Chang, F. J. Garcia de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).

Garcia-Vidal, F. J.

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, L. Martin-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84, 161407 (2011).

Gellert, P. R.

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

Geng, B.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref]

Ghanbari, R. A.

Y. Zhao, D. C. Tsui, M. Santos, M. Shayegan, R. A. Ghanbari, D. A. Antoniadis, H. I. Smith, “Magneto-optical absorption in a two-dimensional electron grid,” Appl. Phys. Lett. 60, 1510–1512 (1992).
[Crossref]

Girit, C.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref]

Godignon, P.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).

Gomez-Diaz, J. S.

M. Tamagnone, J. S. Gomez-Diaz, J. R. Mosig, J. Perruisseau-Carrier, “Reconfigurable terahertz plasmonic antenna concept using a graphene stack,” Appl. Phys. Lett. 101, 214102 (2012).
[Crossref]

Grambow, P.

K. Kern, D. Heitmann, P. Grambow, Y. H. Zhang, K. Ploog, “Collective excitations in antidots,” Phys. Rev. Lett. 66, 1618–1621 (1991).
[Crossref]

Guinea, F.

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7, 394–399 (2013).
[Crossref]

A. Y. Nikitin, F. Guinea, L. Martin-Moreno, “Resonant plasmonic effects in periodic graphene antidot arrays,” Appl. Phys. Lett. 101, 151119 (2012).
[Crossref]

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, L. Martin-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84, 161407 (2011).

Ham, D.

K. Y. M. Yeung, J. Chee, H. Yoon, Y. Song, J. Kong, D. Ham, “Farinfrared graphene plasmonic crystals for plasmonic band engineering,” Nano Lett. 14, 2479–2484 (2014).

Hao, Z.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref]

Heinz, T. F.

Y. Li, H. Yan, D. B. Farmer, X. Meng, W. Zhu, R. M. Osgood, T. F. Heinz, P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14, 1573–1577 (2014).

Heitmann, D.

M. Hochgraefe, R. Krahne, Ch. Heyn, D. Heitmann, “Anticyclotron motion in antidot arrays,” Phys. Rev. B 60, 10680 (1999).

K. Kern, D. Heitmann, P. Grambow, Y. H. Zhang, K. Ploog, “Collective excitations in antidots,” Phys. Rev. Lett. 66, 1618–1621 (1991).
[Crossref]

Heyn, Ch.

M. Hochgraefe, R. Krahne, Ch. Heyn, D. Heitmann, “Anticyclotron motion in antidot arrays,” Phys. Rev. B 60, 10680 (1999).

Hillenbrand, R.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).

Hochgraefe, M.

M. Hochgraefe, R. Krahne, Ch. Heyn, D. Heitmann, “Anticyclotron motion in antidot arrays,” Phys. Rev. B 60, 10680 (1999).

Horng, J.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref]

Huth, F.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).

Hwang, E. H.

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

Jablan, M.

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

Jang, M. S.

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett. 13, 25412547 (2013).

Jena, D.

B. Sensale-Rodriguez, R. Yan, M. Zhu, D. Jena, L. Liu, X. G. Xing, “Efficient terahertz electro-absorption modulation employing graphene plasmonic structures,” Appl. Phys. Lett. 101, 261115 (2012).
[Crossref]

Jin, Z.

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, Q. Xu, “Excitation and active control of propagating surface plasmon polaritons in graphene,” Nano Lett. 13, 3698–3702 (2013).

Joannopoulos, J. D.

S. Fan, J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).

Ju, L.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref]

Keilmann, F.

Z. Fei, A. S. Rodin, G. O. Adreev, 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, 82–85 (2012).

Kern, K.

K. Kern, D. Heitmann, P. Grambow, Y. H. Zhang, K. Ploog, “Collective excitations in antidots,” Phys. Rev. Lett. 66, 1618–1621 (1991).
[Crossref]

Kilic, O.

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, O. Solgaard, “Airbridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006).

Kim, K.

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

Kim, S.

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, O. Solgaard, “Airbridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006).

Kong, J.

K. Y. M. Yeung, J. Chee, H. Yoon, Y. Song, J. Kong, D. Ham, “Farinfrared graphene plasmonic crystals for plasmonic band engineering,” Nano Lett. 14, 2479–2484 (2014).

Kono, J.

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, Q. Xu, “Excitation and active control of propagating surface plasmon polaritons in graphene,” Nano Lett. 13, 3698–3702 (2013).

Koppens, F. H. L.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).

F. H. L. Koppens, D. E. Chang, F. J. Garcia de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).

Krahne, R.

M. Hochgraefe, R. Krahne, Ch. Heyn, D. Heitmann, “Anticyclotron motion in antidot arrays,” Phys. Rev. B 60, 10680 (1999).

Kuzmenko, A. B.

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12, 2470–2474 (2012).

Larsen, M. B.

X. Zhu, W. Wang, W. Yan, M. B. Larsen, P. Boggild, T. G. Pedersen, S. Xiao, J. Zi, N. A. Mortensen, “Plasmon−phonon coupling in largearea graphene dot and antidot arrays fabricated by nanosphere lithography,” Nano Lett. 14, 2907–2913 (2014).

Lau, C. N.

Z. Fei, A. S. Rodin, G. O. Adreev, 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, 82–85 (2012).

Li, P.

I. J. Luxmoore, C. H. Gan, P. Q. Liu, F. Valmorra, P. Li, J. Faist, G. R. Nash, “Strong coupling in the far-infrared between graphene plasmons and the surface optical phonons of silicon dioxide,” ACS Photonics 1, 1151–1155 (2014).

Li, X.

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7, 394–399 (2013).
[Crossref]

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, 330–334 (2012).
[Crossref]

Li, Y.

Y. Li, H. Yan, D. B. Farmer, X. Meng, W. Zhu, R. M. Osgood, T. F. Heinz, P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14, 1573–1577 (2014).

Liang, X.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref]

Liu, L.

B. Sensale-Rodriguez, R. Yan, M. Zhu, D. Jena, L. Liu, X. G. Xing, “Efficient terahertz electro-absorption modulation employing graphene plasmonic structures,” Appl. Phys. Lett. 101, 261115 (2012).
[Crossref]

Liu, P. Q.

I. J. Luxmoore, C. H. Gan, P. Q. Liu, F. Valmorra, P. Li, J. Faist, G. R. Nash, “Strong coupling in the far-infrared between graphene plasmons and the surface optical phonons of silicon dioxide,” ACS Photonics 1, 1151–1155 (2014).

Lopez, J. J.

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett. 13, 25412547 (2013).

Lousse, V.

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, O. Solgaard, “Airbridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006).

Low, T.

T. Low, P. Avouris, “Graphene plasmonics for terahertz to midinfrared applications,” ACS Nano 8, 1086–1101 (2014).
[Crossref]

M. Freitag, T. Low, W. Zhu, H. Yan, F. Xia, P. Avouris, “Photocurrent in graphene harnessed by tunable intrinsic plasmons,” Nat. Commun. 4, 1951 (2013).
[Crossref]

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7, 394–399 (2013).
[Crossref]

Luxmoore, I. J.

I. J. Luxmoore, C. H. Gan, P. Q. Liu, F. Valmorra, P. Li, J. Faist, G. R. Nash, “Strong coupling in the far-infrared between graphene plasmons and the surface optical phonons of silicon dioxide,” ACS Photonics 1, 1151–1155 (2014).

Martin, M.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref]

Martin-Moreno, L.

A. Y. Nikitin, F. Guinea, L. Martin-Moreno, “Resonant plasmonic effects in periodic graphene antidot arrays,” Appl. Phys. Lett. 101, 151119 (2012).
[Crossref]

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, L. Martin-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84, 161407 (2011).

McLeod, A. S.

Z. Fei, A. S. Rodin, G. O. Adreev, 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, 82–85 (2012).

Meng, X.

Y. Li, H. Yan, D. B. Farmer, X. Meng, W. Zhu, R. M. Osgood, T. F. Heinz, P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14, 1573–1577 (2014).

Mikhailov, S. A.

S. A. Mikhailov, K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett. 99, 016803 (2007).
[Crossref]

S. A. Mikhailov, “Theory of electromagnetic response and collective excitations of a square lattice of antidots,” Phys. Rev. B 54, 14293 (1996).

Mortensen, N. A.

X. Zhu, W. Wang, W. Yan, M. B. Larsen, P. Boggild, T. G. Pedersen, S. Xiao, J. Zi, N. A. Mortensen, “Plasmon−phonon coupling in largearea graphene dot and antidot arrays fabricated by nanosphere lithography,” Nano Lett. 14, 2907–2913 (2014).

Mosig, J. R.

M. Tamagnone, J. S. Gomez-Diaz, J. R. Mosig, J. Perruisseau-Carrier, “Reconfigurable terahertz plasmonic antenna concept using a graphene stack,” Appl. Phys. Lett. 101, 214102 (2012).
[Crossref]

Nash, G. R.

I. J. Luxmoore, C. H. Gan, P. Q. Liu, F. Valmorra, P. Li, J. Faist, G. R. Nash, “Strong coupling in the far-infrared between graphene plasmons and the surface optical phonons of silicon dioxide,” ACS Photonics 1, 1151–1155 (2014).

Nikitin, A. Y.

A. Y. Nikitin, F. Guinea, L. Martin-Moreno, “Resonant plasmonic effects in periodic graphene antidot arrays,” Appl. Phys. Lett. 101, 151119 (2012).
[Crossref]

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, L. Martin-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84, 161407 (2011).

Novoselov, K. S.

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

Orlita, M.

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12, 2470–2474 (2012).

Osgood, R. M.

Y. Li, H. Yan, D. B. Farmer, X. Meng, W. Zhu, R. M. Osgood, T. F. Heinz, P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14, 1573–1577 (2014).

Osmond, J.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).

Ostler, M.

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12, 2470–2474 (2012).

Pedersen, T. G.

X. Zhu, W. Wang, W. Yan, M. B. Larsen, P. Boggild, T. G. Pedersen, S. Xiao, J. Zi, N. A. Mortensen, “Plasmon−phonon coupling in largearea graphene dot and antidot arrays fabricated by nanosphere lithography,” Nano Lett. 14, 2907–2913 (2014).

Perruisseau-Carrier, J.

M. Tamagnone, J. S. Gomez-Diaz, J. R. Mosig, J. Perruisseau-Carrier, “Reconfigurable terahertz plasmonic antenna concept using a graphene stack,” Appl. Phys. Lett. 101, 214102 (2012).
[Crossref]

Pesquera, A.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).

Ploog, K.

K. Kern, D. Heitmann, P. Grambow, Y. H. Zhang, K. Ploog, “Collective excitations in antidots,” Phys. Rev. Lett. 66, 1618–1621 (1991).
[Crossref]

Potemski, M.

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12, 2470–2474 (2012).

Raether, H.

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, 1988).

Rodin, A. S.

Z. Fei, A. S. Rodin, G. O. Adreev, 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, 82–85 (2012).

Sakoda, K.

K. Sakoda, Optical Properties of Photonic Crystals (Springer, 2005).

Santos, M.

Y. Zhao, D. C. Tsui, M. Santos, M. Shayegan, R. A. Ghanbari, D. A. Antoniadis, H. I. Smith, “Magneto-optical absorption in a two-dimensional electron grid,” Appl. Phys. Lett. 60, 1510–1512 (1992).
[Crossref]

Schwab, M. G.

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

Sensale-Rodriguez, B.

B. Sensale-Rodriguez, R. Yan, M. Zhu, D. Jena, L. Liu, X. G. Xing, “Efficient terahertz electro-absorption modulation employing graphene plasmonic structures,” Appl. Phys. Lett. 101, 261115 (2012).
[Crossref]

Seyller, T.

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12, 2470–2474 (2012).

Shayegan, M.

Y. Zhao, D. C. Tsui, M. Santos, M. Shayegan, R. A. Ghanbari, D. A. Antoniadis, H. I. Smith, “Magneto-optical absorption in a two-dimensional electron grid,” Appl. Phys. Lett. 60, 1510–1512 (1992).
[Crossref]

Shen, Y. R.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref]

Sherrott, M.

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett. 13, 25412547 (2013).

Shi, G.

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, Q. Xu, “Excitation and active control of propagating surface plasmon polaritons in graphene,” Nano Lett. 13, 3698–3702 (2013).

Shu, J.

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, Q. Xu, “Excitation and active control of propagating surface plasmon polaritons in graphene,” Nano Lett. 13, 3698–3702 (2013).

Smith, H. I.

Y. Zhao, D. C. Tsui, M. Santos, M. Shayegan, R. A. Ghanbari, D. A. Antoniadis, H. I. Smith, “Magneto-optical absorption in a two-dimensional electron grid,” Appl. Phys. Lett. 60, 1510–1512 (1992).
[Crossref]

Solgaard, O.

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, O. Solgaard, “Airbridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006).

Soljacic, M.

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

Song, Y.

K. Y. M. Yeung, J. Chee, H. Yoon, Y. Song, J. Kong, D. Ham, “Farinfrared graphene plasmonic crystals for plasmonic band engineering,” Nano Lett. 14, 2479–2484 (2014).

Spasenovic, M.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).

Tamagnone, M.

M. Tamagnone, J. S. Gomez-Diaz, J. R. Mosig, J. Perruisseau-Carrier, “Reconfigurable terahertz plasmonic antenna concept using a graphene stack,” Appl. Phys. Lett. 101, 214102 (2012).
[Crossref]

Thiemens, M.

Z. Fei, A. S. Rodin, G. O. Adreev, 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, 82–85 (2012).

Thongrattanasiri, S.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).

Tsui, D. C.

Y. Zhao, D. C. Tsui, M. Santos, M. Shayegan, R. A. Ghanbari, D. A. Antoniadis, H. I. Smith, “Magneto-optical absorption in a two-dimensional electron grid,” Appl. Phys. Lett. 60, 1510–1512 (1992).
[Crossref]

Tulevski, G.

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, 330–334 (2012).
[Crossref]

Vajtai, R.

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, Q. Xu, “Excitation and active control of propagating surface plasmon polaritons in graphene,” Nano Lett. 13, 3698–3702 (2013).

Vakil, A.

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

Valmorra, F.

I. J. Luxmoore, C. H. Gan, P. Q. Liu, F. Valmorra, P. Li, J. Faist, G. R. Nash, “Strong coupling in the far-infrared between graphene plasmons and the surface optical phonons of silicon dioxide,” ACS Photonics 1, 1151–1155 (2014).

Wagner, M.

Z. Fei, A. S. Rodin, G. O. Adreev, 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, 82–85 (2012).

Walter, A. L.

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12, 2470–2474 (2012).

Wang, F.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref]

Wang, W.

X. Zhu, W. Wang, W. Yan, M. B. Larsen, P. Boggild, T. G. Pedersen, S. Xiao, J. Zi, N. A. Mortensen, “Plasmon−phonon coupling in largearea graphene dot and antidot arrays fabricated by nanosphere lithography,” Nano Lett. 14, 2907–2913 (2014).

Wu, Y.

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7, 394–399 (2013).
[Crossref]

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, 330–334 (2012).
[Crossref]

Xia, F.

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7, 394–399 (2013).
[Crossref]

M. Freitag, T. Low, W. Zhu, H. Yan, F. Xia, P. Avouris, “Photocurrent in graphene harnessed by tunable intrinsic plasmons,” Nat. Commun. 4, 1951 (2013).
[Crossref]

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, 330–334 (2012).
[Crossref]

Xiao, S.

X. Zhu, W. Wang, W. Yan, M. B. Larsen, P. Boggild, T. G. Pedersen, S. Xiao, J. Zi, N. A. Mortensen, “Plasmon−phonon coupling in largearea graphene dot and antidot arrays fabricated by nanosphere lithography,” Nano Lett. 14, 2907–2913 (2014).

Xing, X. G.

B. Sensale-Rodriguez, R. Yan, M. Zhu, D. Jena, L. Liu, X. G. Xing, “Efficient terahertz electro-absorption modulation employing graphene plasmonic structures,” Appl. Phys. Lett. 101, 261115 (2012).
[Crossref]

Xu, Q.

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, Q. Xu, “Excitation and active control of propagating surface plasmon polaritons in graphene,” Nano Lett. 13, 3698–3702 (2013).

Yan, H.

Y. Li, H. Yan, D. B. Farmer, X. Meng, W. Zhu, R. M. Osgood, T. F. Heinz, P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14, 1573–1577 (2014).

M. Freitag, T. Low, W. Zhu, H. Yan, F. Xia, P. Avouris, “Photocurrent in graphene harnessed by tunable intrinsic plasmons,” Nat. Commun. 4, 1951 (2013).
[Crossref]

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7, 394–399 (2013).
[Crossref]

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, 330–334 (2012).
[Crossref]

Yan, R.

B. Sensale-Rodriguez, R. Yan, M. Zhu, D. Jena, L. Liu, X. G. Xing, “Efficient terahertz electro-absorption modulation employing graphene plasmonic structures,” Appl. Phys. Lett. 101, 261115 (2012).
[Crossref]

Yan, W.

X. Zhu, W. Wang, W. Yan, M. B. Larsen, P. Boggild, T. G. Pedersen, S. Xiao, J. Zi, N. A. Mortensen, “Plasmon−phonon coupling in largearea graphene dot and antidot arrays fabricated by nanosphere lithography,” Nano Lett. 14, 2907–2913 (2014).

Yeung, K. Y. M.

K. Y. M. Yeung, J. Chee, H. Yoon, Y. Song, J. Kong, D. Ham, “Farinfrared graphene plasmonic crystals for plasmonic band engineering,” Nano Lett. 14, 2479–2484 (2014).

Yoon, H.

K. Y. M. Yeung, J. Chee, H. Yoon, Y. Song, J. Kong, D. Ham, “Farinfrared graphene plasmonic crystals for plasmonic band engineering,” Nano Lett. 14, 2479–2484 (2014).

Zettl, A.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref]

Zhang, L. M.

Z. Fei, A. S. Rodin, G. O. Adreev, 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, 82–85 (2012).

Zhang, Q.

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, Q. Xu, “Excitation and active control of propagating surface plasmon polaritons in graphene,” Nano Lett. 13, 3698–3702 (2013).

Zhang, Y. H.

K. Kern, D. Heitmann, P. Grambow, Y. H. Zhang, K. Ploog, “Collective excitations in antidots,” Phys. Rev. Lett. 66, 1618–1621 (1991).
[Crossref]

Zhao, Y.

Y. Zhao, D. C. Tsui, M. Santos, M. Shayegan, R. A. Ghanbari, D. A. Antoniadis, H. I. Smith, “Magneto-optical absorption in a two-dimensional electron grid,” Appl. Phys. Lett. 60, 1510–1512 (1992).
[Crossref]

Zhao, Z.

Z. Fei, A. S. Rodin, G. O. Adreev, 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, 82–85 (2012).

Zhu, M.

B. Sensale-Rodriguez, R. Yan, M. Zhu, D. Jena, L. Liu, X. G. Xing, “Efficient terahertz electro-absorption modulation employing graphene plasmonic structures,” Appl. Phys. Lett. 101, 261115 (2012).
[Crossref]

Zhu, W.

Y. Li, H. Yan, D. B. Farmer, X. Meng, W. Zhu, R. M. Osgood, T. F. Heinz, P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14, 1573–1577 (2014).

M. Freitag, T. Low, W. Zhu, H. Yan, F. Xia, P. Avouris, “Photocurrent in graphene harnessed by tunable intrinsic plasmons,” Nat. Commun. 4, 1951 (2013).
[Crossref]

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7, 394–399 (2013).
[Crossref]

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, 330–334 (2012).
[Crossref]

Zhu, X.

X. Zhu, W. Wang, W. Yan, M. B. Larsen, P. Boggild, T. G. Pedersen, S. Xiao, J. Zi, N. A. Mortensen, “Plasmon−phonon coupling in largearea graphene dot and antidot arrays fabricated by nanosphere lithography,” Nano Lett. 14, 2907–2913 (2014).

Zi, J.

X. Zhu, W. Wang, W. Yan, M. B. Larsen, P. Boggild, T. G. Pedersen, S. Xiao, J. Zi, N. A. Mortensen, “Plasmon−phonon coupling in largearea graphene dot and antidot arrays fabricated by nanosphere lithography,” Nano Lett. 14, 2907–2913 (2014).

Ziegler, K.

S. A. Mikhailov, K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett. 99, 016803 (2007).
[Crossref]

Zurutuza Elorza, A.

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).

ACS Nano (1)

T. Low, P. Avouris, “Graphene plasmonics for terahertz to midinfrared applications,” ACS Nano 8, 1086–1101 (2014).
[Crossref]

ACS Photonics (1)

I. J. Luxmoore, C. H. Gan, P. Q. Liu, F. Valmorra, P. Li, J. Faist, G. R. Nash, “Strong coupling in the far-infrared between graphene plasmons and the surface optical phonons of silicon dioxide,” ACS Photonics 1, 1151–1155 (2014).

Appl. Phys. Lett. (4)

M. Tamagnone, J. S. Gomez-Diaz, J. R. Mosig, J. Perruisseau-Carrier, “Reconfigurable terahertz plasmonic antenna concept using a graphene stack,” Appl. Phys. Lett. 101, 214102 (2012).
[Crossref]

B. Sensale-Rodriguez, R. Yan, M. Zhu, D. Jena, L. Liu, X. G. Xing, “Efficient terahertz electro-absorption modulation employing graphene plasmonic structures,” Appl. Phys. Lett. 101, 261115 (2012).
[Crossref]

A. Y. Nikitin, F. Guinea, L. Martin-Moreno, “Resonant plasmonic effects in periodic graphene antidot arrays,” Appl. Phys. Lett. 101, 151119 (2012).
[Crossref]

Y. Zhao, D. C. Tsui, M. Santos, M. Shayegan, R. A. Ghanbari, D. A. Antoniadis, H. I. Smith, “Magneto-optical absorption in a two-dimensional electron grid,” Appl. Phys. Lett. 60, 1510–1512 (1992).
[Crossref]

Nano Lett. (7)

K. Y. M. Yeung, J. Chee, H. Yoon, Y. Song, J. Kong, D. Ham, “Farinfrared graphene plasmonic crystals for plasmonic band engineering,” Nano Lett. 14, 2479–2484 (2014).

X. Zhu, W. Wang, W. Yan, M. B. Larsen, P. Boggild, T. G. Pedersen, S. Xiao, J. Zi, N. A. Mortensen, “Plasmon−phonon coupling in largearea graphene dot and antidot arrays fabricated by nanosphere lithography,” Nano Lett. 14, 2907–2913 (2014).

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, Q. Xu, “Excitation and active control of propagating surface plasmon polaritons in graphene,” Nano Lett. 13, 3698–3702 (2013).

Y. Li, H. Yan, D. B. Farmer, X. Meng, W. Zhu, R. M. Osgood, T. F. Heinz, P. Avouris, “Graphene plasmon enhanced vibrational sensing of surface-adsorbed layers,” Nano Lett. 14, 1573–1577 (2014).

I. Crassee, M. Orlita, M. Potemski, A. L. Walter, M. Ostler, T. Seyller, I. Gaponenko, J. Chen, A. B. Kuzmenko, “Intrinsic terahertz plasmons and magnetoplasmons in large scale monolayer graphene,” Nano Lett. 12, 2470–2474 (2012).

F. H. L. Koppens, D. E. Chang, F. J. Garcia de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011).

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett. 13, 25412547 (2013).

Nat. Commun. (1)

M. Freitag, T. Low, W. Zhu, H. Yan, F. Xia, P. Avouris, “Photocurrent in graphene harnessed by tunable intrinsic plasmons,” Nat. Commun. 4, 1951 (2013).
[Crossref]

Nat. Nanotechnol. (2)

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6, 630–634 (2011).
[Crossref]

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, 330–334 (2012).
[Crossref]

Nat. Photonics (1)

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, F. Xia, “Damping pathways of mid-infrared plasmons in graphene nanostructures,” Nat. Photonics 7, 394–399 (2013).
[Crossref]

Nature (3)

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

J. Chen, M. Badioli, P. Alonso-Gonzalez, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenovic, A. Centeno, A. Pesquera, P. Godignon, A. Zurutuza Elorza, N. Camara, F. J. Garcia de Abajo, R. Hillenbrand, F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487, 77–81 (2012).

Z. Fei, A. S. Rodin, G. O. Adreev, 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, 82–85 (2012).

Phys. Rev. B (7)

A. Y. Nikitin, F. Guinea, F. J. Garcia-Vidal, L. Martin-Moreno, “Edge and waveguide terahertz surface plasmon modes in graphene microribbons,” Phys. Rev. B 84, 161407 (2011).

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

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

S. Fan, J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).

K. B. Crozier, V. Lousse, O. Kilic, S. Kim, S. Fan, O. Solgaard, “Airbridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006).

M. Hochgraefe, R. Krahne, Ch. Heyn, D. Heitmann, “Anticyclotron motion in antidot arrays,” Phys. Rev. B 60, 10680 (1999).

S. A. Mikhailov, “Theory of electromagnetic response and collective excitations of a square lattice of antidots,” Phys. Rev. B 54, 14293 (1996).

Phys. Rev. Lett. (2)

K. Kern, D. Heitmann, P. Grambow, Y. H. Zhang, K. Ploog, “Collective excitations in antidots,” Phys. Rev. Lett. 66, 1618–1621 (1991).
[Crossref]

S. A. Mikhailov, K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett. 99, 016803 (2007).
[Crossref]

Science (1)

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

Other (2)

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, 1988).

K. Sakoda, Optical Properties of Photonic Crystals (Springer, 2005).

Supplementary Material (1)

» Supplement 1: PDF (1276 KB)     

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1. (a) Schematic of a square-lattice graphene periodic anti-dot array; (b) simulated transmission, reflection, and absorption spectra of a graphene periodic anti-dot array on a SiO 2 / Si substrate with a lattice constant of 3 μm and an aperture diameter of 2 μm. Fermi energy is set to 0.4 eV and the carrier relaxation time 1 ps; (c) simulated z -direction electric field profiles (in an x y –plane right above the graphene sheet) of the two resonances in part b (left) and the 2D fast Fourier-transform (FFT) of each field profile (right). Top, lower-frequency mode; bottom, higher-frequency mode. In the 2D FFT of the field profiles, each square pixel corresponds to a reciprocal lattice vector (e.g., the center pixel is for [0,0], the one above the center is for [0,1], and so on) and its brightness represents the amplitude of the corresponding spatial frequency component.
Fig. 2.
Fig. 2. (a) Scanning electron microscopy (SEM) image of a fabricated graphene anti-dot array sample; (b) typical Raman spectrum of the graphene anti-dot array samples.
Fig. 3.
Fig. 3. Transmission extinction spectra at various back-gate voltages for the following; (a)–(d) samples SQ1–SQ4; (e) unpatterned graphene sample; (f) symbols are the plasmonic resonance frequency (in wavenumbers) as a function of the square root of the carrier density and equivalently the Fermi energy for all the resonance peaks in SQ1–SQ4. Height of the symbols corresponds to the typical error bar in extracting the peak position using different fitting functions and ranges. Solid curves are fits of the data points (symbols in the matching color) with functions in the form of y = a x 1 / 2 with a being a fitting parameter. Experimental results on the other structures are included in Supplement 1.
Fig. 4.
Fig. 4. Simulated transmission extinction spectra for the same graphene anti-dot arrays in Figs. 3(a)3(d) assuming two different carrier relaxation times: τ = 1 ps (blue curves) and τ = 0.1 ps (red curves) in comparison with the experimental results (black curves).
Fig. 5.
Fig. 5. Simulated z -direction electric field profiles of the SPP modes corresponding to the four prominent resonance peaks in Fig. 4(d). Plots are numbered in the ascending order of the resonance frequency. Insets, 2D FFT of the field profiles plotted similarly as in Fig. 1(c).

Tables (1)

Tables Icon

Table 1. Details of Different Graphene Anti-Dot Arrays

Metrics