Abstract

Dielectric loaded graphene plasmon waveguide (DLGPW) is proposed and investigated. An analytical model based on effective-index method is presented and verified by the finite element method simulations. The mode effective index, propagation loss, cutoff wavelength of higher order modes and single-mode operation region were derived at mid-infrared spectral region. By changing Fermi energy level, the propagation properties of fundamental mode could be tuned flexibly. The structure of the DLGPW is simple and easy for fabrication. It provided a new freedom to manipulate the graphene surface plasmons, which may led to new applications in actively tunable integrated optical devices.

© 2015 Optical Society of America

1. Introduction

Surface plasmons (SPs) offer a promising way to confine and control electromagnetic (EM) waves at subwavelength scale which is quite required to realize highly compact optical circuits in nanotechnology [1]. Noble metals are usually used to support SPs in the visible to near-infrared frequencies and various SPs waveguide structures have been studied intensively [211]. However in the mid-infrared to terahertz frequency, only loosely bound surfaced waves could be supported by noble meals. Graphene, a newly emerged two dimensional (2D) atomically thin material, is believed as noval plasmonic material from the terahertz to the infrared spectral region [12,13]. Recently, the excitation, propagation and tunability of graphene surface plasmons (GSPs) in mid-infrared frequencies have been experimentally demonstrated [14,15]. Compared with noble metals, GSP could confine EM field at an extremely subwavelength scale in the mid-infrared spectral region. Moreover, GSP could be actively tuned by electrostatically gating or chemical doping which may lead to dynamically tunable plasmonic devices. These extraordinary properties make graphene a promising candidate for mid-infrared to terahertz SP waveguide. GSP modes on graphene sheets [16], graphene nanoribbons [1719], graphene-coated nanowire [20] and graphene groove/wedge [21] were investigated intensively. These GSP waveguides could be classified into two classes. One is based on graphene patterning. However, the edge shape of graphene could strongly influence the propagation properties of GSP modes, and it is still a challenge to control the edge shape with desired atomic arrangement [22]. The other is based on substrate engineering, which may bring fabrication difficulties.

In this paper, we investigate the GSP modes of dielectric loaded graphene plasmon waveguide (DLGPW) in mid-infrared spectral region. This concept originated from dielectric loaded metal plasmon waveguides in visible to near-infrared spectral region [811]. The DLGPW is not influenced by the edge shape of graphene and could be produced in a straightforward way by, for example, standard processes of lithography. Moreover the DLGPW could be combined with substrate engineering structures, providing more freedom to manipulate GSPs. So, it is of great significance to characterize the properties of GSP modes in DLGPW. Here, we first present an analytical model based on effective-index method [23,24] to solve eigen guided modes in DLGPW. Then dispersion relation and propagation loss is derived. The single-mode operation region is also illustrated. In the last part, the tunablity of the fundamental mode is dicussed.

2. Analytical model

The geometry of the DLGPW is shown in Fig. 1(a). A dielectric strip with width of W and height of h is deposited onto a graphene sheet. The relative permittivity of the strip is εr2. For simplicity, the substrate is supposed to be a half space dielectric with relative permittivity of εr1, and the cladding is air. The dielectric strip results in a higher refractive index for GSP modes on the graphene-dielectric interface compared to graphene-air interface, giving rise to GSP modes bound by the dielectric strip. This is similar to guided modes in dielectric planar waveguides. The effective-index method (EIM) is one of the simple methods for analyze photonic and SP waveguide [9,23,24]. Here, we use this method to present an analytical model for DLGPW.

 figure: Fig. 1

Fig. 1 (a) Schematic of the dielectric loaded graphene plasmon waveguide. (b) The equivalent three-layer planar waveguide structure for the derivation of Eq. (1). (b) The equivalent three-layer planar waveguide structure for the derivation of Eq. (3).

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In this method, the dielectric strip serves as the core of a three-layer dielectric planar waveguide (Fig. 1(c)). The refractive index of the core ncore is independent on the width of dielectric strip, and is equal to the effective mode index of the highly confined GSP mode (TM mode) in planar graphene sheet sandwiched between dielectrics of relative permittivity εr1 and εr2 (Fig. 1(b)) and is written as [12]

ncore=kGSP1/k0=ε0εr1+εr222icσ(ω).
where σ (ω) is the optical conductivity of graphene, k0 is the vacuum wave number. The refractive index of the cladding nclad is equal to the effective mode index of the GSP mode (TM mode) in planar graphene sheet sandwiched between dielectrics of relative permittivity εr1 and air and is expressed as
nclad=kGSP2/k0=ε0εr1+122icσ(ω).
Then, by simple algebra operation, eigen equation of the equivalent dielectric planar waveguide for the m-th order guided TE mode is given as
μcladTtan(Tw2mπ2)μcoreτ=0.
Where μclad = μcore = 1 is the relative permeability, T=k0ncore2neff2,τ=k0neff2nclad2, w is the width of the dielectric strip, neff is the effective mode refractive index of the DLGPW. The cutoff condition of the guided modes is τ = 0. Then, the cutoff wavelength of m-th order guided mode is
λcm=Re(2wmncore2nclad2).
By numerical solving Eq. (3), the effective mode index neff of m-th order mode could be derived. The real part of neff corresponds to the GSP wavelength λGSP = λ0/Re(neff), where λ0 is the vacuum wavelength. The imaginary part of neff corresponds to the propagation loss, and determines the propagation length L by L = λ0/[2π⋅Im(neff)].

It should be noted that, in developing the analytical modal for the DLGPW, the influence of the height of the dielectric strip has not been taken into account. This is based on the fact that the GSP mode is highly confined at the interface of graphene sheet (Fig. 2 (c)) and the EM field surpass the top of the dielctric strip could be neglected, if the dielectric strip is not too thin. However, the analytical modal proposed here could be easily expanded to the case of thin dielectric strip or more complicated structure: e. g. the recently proposed graphene based hybrid plasmonic waveguide [25]. In these cases, the eigen equations of planar four-layer or five-layer waveguide structure should be solved first to get the effective refractive index of the core layer.

 figure: Fig. 2

Fig. 2 Effective mode indices of the GSP modes in DLGPW with a width of 200 nm: (a) Real part, (b) Imaginary part of the effective mode index. The insets of (b) show the amplitudes of Ey for 1-th mode at the wavelength of 10 μm and 13 μm, respectively. Solid lines are numerical solutions of Eq. (3), symbols are obtained by Comsol simulations, and dashed lines correspond to numerical solutions of Eq. (1) and (2). (c) Mode patterns (the amplitudes of Ey) of the first 4 order modes at the wavelength of 8 μm.

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3. Results and discuss

We first numerically solve Eq. (3), the dispersion relation is demonstrated. Then we use commercial software (COMSOL) based on the finite element method (FEM) to verify the proposed analytical model. Next we numerically solve Eq. (4), the single mode operation range is derived. In our calculation, the height of the dielectric strip is 100nm, relative permittivity of the substrate and the dielectric strip are both 3.92. Graphene is modeled as a 0.5nm thick anisotropic layer. The out-of-plane relative permittivity is 2.5. The in-plane relative permittivity is ε//(ω)=2.5+iσ(ω)/(ωε0t), where the optical conductivity of graphene is derived using the random-phase approximation in the local limit [26]:

σ(ω)=i2e2kBTπ2(ω+iτ1)In[2cosh(EF2kBT)]+e24[12+1πarctan(ω2EF2kBT)i2πIn(ω+2EF)2(ω+2EF)2+4(kBT)2]
where T = 300 K is the temperature, kB is the Boltzmann constant, ω is the frequency, EF is the Fermi energy level and τ=μEF/eVF2 is the carrier relaxation lifetime (μ is the carrier mobility of graphene and VF=106m/s is the Fermi velocity). In recent experiments, the Fermi energy level has reached as high as 1.17 eV [27]. The carrier mobility ranges from ~1000 cm2/(V⋅s) [28] in chemical vapor deposition (CVD) grown graphene to 230000 cm2/(V⋅s) [29] in suspended exfoliated graphene. Here, we use moderate Fermi energy level of 0.5eV and carrier mobility of 10000 cm2/(V⋅s), unless otherwise stated.

Figure 2 shows the effective mode indices of GSP modes in DLGPW with a width of 200 nm. Numerical solutions of the analytical model show good agreement with the FEM simulation results, when the wavelength is away from the cutoff wavelength. The guided GSP modes are confined between ncore and nclad, which is the same as dielectric planar waveguide. However, when the modes are approaching cutoff, the results of analytical model show slight deviations from the FEM results. This is because when approaching cutoff, the mode confinement become weak (see the insets of Fig. 2(b)), and the EM field in the corner regions is no longer negligible. However, the effective-index method doesn’t account for the EM field in the corner regions. Effective mode indices decrease monotonically as wavelength increases. The fundamental mode (m = 0) has higher real part of effective mode index than higher order modes, which indicates the shorter GSP wavelength. Moreover the fundamental mode is cutoff-free. The higher order modes cutoff when the real parts of neff approache that of nclad. The propagation loss of higher order mode decreases sharply as the wavelength approaches the cutoff wavelength. However, this is at the expense of poor confinement of the GSP modes. Away from the cutoff wavelength, the fundamental mode has relatively small propagation loss.

Single-mode operation is highly preferred for many applications, as multi-mode propagation may lead to signal fading and unwanted mode conversion. By solving Eq. (4), single-mode and multi-modes operation region as a function of the width of the dielectric strip is shown in Fig. 3(a). The white dashed curves are numerical solutions of Eq. (4). At a fixed wavelength, the numbers of guided modes decrease as the width of the dielectric strip decrease. The single-mode operation region (labeled 1) lies in the right of the 1-th order mode cutoff wavelength. As the width of the dielectric strip increase, the single-mode operation region starts at a longer wavelength. Propagation properties of the GSP modes in DLGPW could be manipulated by tuning the Fermi energy level. Figure 3(b) shows the cutoff wavelength of 1-th order mode at different Fermi energy level. The single-mode operation region moves to longer wavelength as the Fermi energy level decrease. When the Fermi energy level changes from 0.3 eV to 0.9 eV and the width is fixed as 50 nm, only fundamental mode is supported for wavelength longer than 10 μm. Then we fix the width as 50nm, and study the dispersion relation of the fundamental mode.

 figure: Fig. 3

Fig. 3 (a) Single-mode and multi-modes operation regions calculated by Eq. (4). The numbers of modes supported by the DLGPW are labeled. (b) The cutoff wavelength of 1-th order mode at different Fermi energy levels.

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Figure 4(a) shows the real part of the effective mode indices of the fundamental mode in DLGPW with a width of 50 nm. By varying the Fermi energy level, effective mode indices of the fundamental mode could be effectively manipulated. Effective mode indices increase as the Fermi energy level decrease. At a Fermi energy level of 0.3 eV, real part of the effective mode index is larger than 70 for a wavelength of 12 μm, indicating that the GSP mode is tightly confined. However there is a well-known tradeoff between mode confinement and propagation length. The propagation length increases conspicuously as the Fermi energy level increases (Fig. 4(b)). This is due to poor confinement of the GSP mode and increment of the carrier relaxation lifetime (indicating reduction of the intrinsic loss of graphene), as the Fermi energy level increases. The carrier mobility has a great influence on the propagation length (Fig. 4(d)). Higher carrier mobility leads to longer propagation length. But, the real part of the effective mode indices is insensitive to the carrier mobility (Fig. 4(c)). So graphene with lower Fermi energy level and higher carrier mobility is better for long distance propagation of highly confined GSP mode.

 figure: Fig. 4

Fig. 4 Real part of the effective mode indices (a) and the propagation length (b) of the fundamental mode at different Fermi energy levels. The carrier mobility is fixed as 10000 cm2/(V⋅s). Real part of the effective mode indices (c) and the propagation length (d) of the fundamental mode at different carrier mobility. The Fermi energy level is fixed as 0.5 eV, and the width of the dielectric strip is 50 nm.

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4. Conclusions

In summary, we proposed the concept of dielectric loaded graphene plasmon waveguide. This waveguide is not influenced by the edge shape of graphene and easy to fabricate. An analytical model based on effective-index method was presented and verified by FEM simulations, which provided a simple way to analysis the mode properties of DLGPW. The mode effective index, propagation loss, cutoff wavelength of higher order modes and single-mode operation region were derived. The number of GSP modes supported by the DLGPW increases as either the wavelength decrease or the dielectric strip width increase. By changing Fermi energy level, the propagation properties of fundamental mode could be tuned flexibly. Higher Fermi engery level led to smaller propagation loss at the expense of poorer confinement. The DLGPW provided a new freedom to manipulate the GSP, which may led to new applications in actively tunable integrated optical devices.

Acknowledgments

This work is supported by the State Key Program for Basic Research of China (No. 2012CB933501) and the National Natural Science Foundation of China (Grant Nos. 61177051, 11304389, 61404174, and 61205087).

References and links

1. D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010). [CrossRef]  

2. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett. 95(4), 046802 (2005). [CrossRef]   [PubMed]  

3. E. Moreno, F. J. Garcia-Vidal, S. G. Rodrigo, L. Martin-Moreno, and S. I. Bozhevolnyi, “Channel plasmon-polaritons: modal shape, dispersion, and losses,” Opt. Lett. 31(23), 3447–3449 (2006). [CrossRef]   [PubMed]  

4. C. L. Zou, F. W. Sun, Y. F. Xiao, C. H. Dong, X. D. Chen, J. M. Cui, Q. Gong, Z. F. Han, and G. C. Guo, “Plasmon modes of silver nanowire on a silica substrate,” Appl. Phys. Lett. 97(18), 183102 (2010). [CrossRef]  

5. J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-sacle localization,” Phys. Rev. B 73(3), 035407 (2006). [CrossRef]  

6. I. Avrutsky, R. Soref, and W. Buchwald, “Sub-wavelength plasmonic modes in a conductor-gap-dielectric system with a nanoscale gap,” Opt. Express 18(1), 348–363 (2010). [CrossRef]   [PubMed]  

7. R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-rang propagation,” Nat. Photonics 2(8), 496–500 (2008). [CrossRef]  

8. B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. Aussenegg, A. Leitner, and J. Krenn, “Dielectric stipes on gold as surface plasmon waveguides,” Appl. Phys. Lett. 88(9), 094104 (2006). [CrossRef]  

9. T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides,” Phys. Rev. B 75(24), 245405 (2007). [CrossRef]  

10. S. Randhawa, A. V. Krasavin, T. Holmgaard, J. Renger, S. I. Bozhevolnyi, A. V. Zayats, and R. Quidant, “Experimental demonstration of dielectric-loaded plasmonic waveguide disk resonators at telecom wavelengths,” Appl. Phys. Lett. 98(16), 161102 (2011). [CrossRef]  

11. Z. H. Zhu, C. E. Garcia-Ortiz, Z. H. Han, I. P. Radko, and S. I. Bozhevolnyi, “Compact and broadband directional coupling and demultiplexing in dielectric-loaded surface plasmon polariton waveguides based on the multimode interference effect,” Appl. Phys. Lett. 103(6), 061108 (2013). [CrossRef]  

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

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

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

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

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

17. J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. Koppens, and F. J. García de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6(1), 431–440 (2012). [CrossRef]   [PubMed]  

18. F. J. García de Abajo, “Graphene plasmonics: challenges and opportunities,” ACS Photon. 1(3), 135–152 (2014). [CrossRef]  

19. E. Forati and G. W. Hanson, “Surface plasmon polaritons on soft-boundary graphene nanoribbons and their application in switching/demultiplexing,” Appl. Phys. Lett. 103(13), 133104 (2013). [CrossRef]  

20. Y. Gao, G. Ren, B. Zhu, H. Liu, Y. Lian, and S. Jian, “Analytical model for plasmon modes in graphene-coated nanowire,” Opt. Express 22(20), 24322–24331 (2014). [CrossRef]   [PubMed]  

21. P. Liu, X. Zhang, Z. Ma, W. Cai, L. Wang, and J. Xu, “Surface plasmon modes in graphene wedge and groove waveguides,” Opt. Express 21(26), 32432–32440 (2013). [PubMed]  

22. J. Kotakoski, D. Santos-Cottin, and A. V. Krasheninnikov, “Stability of graphene edges under electron beam: equilibrium energetics versus dynamic effects,” ACS Nano 6(1), 671–676 (2012). [CrossRef]   [PubMed]  

23. A. B. Buckman, Guided-Wave Photonics, 1 st ed. (Saunders College Publishing, 1992).

24. A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, and S. I. Bozhevolnyi, “Integrated optical components utilizing long-rang surface plasmon polaritons,” J. Lightwave Technol. 23(1), 413–422 (2005). [CrossRef]  

25. X. Zhou, T. Zhang, L. Chen, W. Hong, and X. Li, “A graphene-based hybrid plasmonic waveguide with ultra-deep subwavelength confinement,” J. Lightwave Technol. 32(21), 4199–4203 (2014). [CrossRef]  

26. L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B 76(15), 153410 (2007). [CrossRef]  

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

28. L. Ju, B. S. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. G. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011). [CrossRef]   [PubMed]  

29. K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. L. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146(9-10), 351–355 (2008). [CrossRef]  

References

  • View by:

  1. D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
    [Crossref]
  2. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett. 95(4), 046802 (2005).
    [Crossref] [PubMed]
  3. E. Moreno, F. J. Garcia-Vidal, S. G. Rodrigo, L. Martin-Moreno, and S. I. Bozhevolnyi, “Channel plasmon-polaritons: modal shape, dispersion, and losses,” Opt. Lett. 31(23), 3447–3449 (2006).
    [Crossref] [PubMed]
  4. C. L. Zou, F. W. Sun, Y. F. Xiao, C. H. Dong, X. D. Chen, J. M. Cui, Q. Gong, Z. F. Han, and G. C. Guo, “Plasmon modes of silver nanowire on a silica substrate,” Appl. Phys. Lett. 97(18), 183102 (2010).
    [Crossref]
  5. J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-sacle localization,” Phys. Rev. B 73(3), 035407 (2006).
    [Crossref]
  6. I. Avrutsky, R. Soref, and W. Buchwald, “Sub-wavelength plasmonic modes in a conductor-gap-dielectric system with a nanoscale gap,” Opt. Express 18(1), 348–363 (2010).
    [Crossref] [PubMed]
  7. R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-rang propagation,” Nat. Photonics 2(8), 496–500 (2008).
    [Crossref]
  8. B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. Aussenegg, A. Leitner, and J. Krenn, “Dielectric stipes on gold as surface plasmon waveguides,” Appl. Phys. Lett. 88(9), 094104 (2006).
    [Crossref]
  9. T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides,” Phys. Rev. B 75(24), 245405 (2007).
    [Crossref]
  10. S. Randhawa, A. V. Krasavin, T. Holmgaard, J. Renger, S. I. Bozhevolnyi, A. V. Zayats, and R. Quidant, “Experimental demonstration of dielectric-loaded plasmonic waveguide disk resonators at telecom wavelengths,” Appl. Phys. Lett. 98(16), 161102 (2011).
    [Crossref]
  11. Z. H. Zhu, C. E. Garcia-Ortiz, Z. H. Han, I. P. Radko, and S. I. Bozhevolnyi, “Compact and broadband directional coupling and demultiplexing in dielectric-loaded surface plasmon polariton waveguides based on the multimode interference effect,” Appl. Phys. Lett. 103(6), 061108 (2013).
    [Crossref]
  12. M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrafred frequencies,” Phys. Rev. B 80(24), 245435 (2009).
    [Crossref]
  13. F. H. L. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: A platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
    [Crossref] [PubMed]
  14. Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
    [PubMed]
  15. J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
    [PubMed]
  16. A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
    [Crossref] [PubMed]
  17. J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. Koppens, and F. J. García de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6(1), 431–440 (2012).
    [Crossref] [PubMed]
  18. F. J. García de Abajo, “Graphene plasmonics: challenges and opportunities,” ACS Photon. 1(3), 135–152 (2014).
    [Crossref]
  19. E. Forati and G. W. Hanson, “Surface plasmon polaritons on soft-boundary graphene nanoribbons and their application in switching/demultiplexing,” Appl. Phys. Lett. 103(13), 133104 (2013).
    [Crossref]
  20. Y. Gao, G. Ren, B. Zhu, H. Liu, Y. Lian, and S. Jian, “Analytical model for plasmon modes in graphene-coated nanowire,” Opt. Express 22(20), 24322–24331 (2014).
    [Crossref] [PubMed]
  21. P. Liu, X. Zhang, Z. Ma, W. Cai, L. Wang, and J. Xu, “Surface plasmon modes in graphene wedge and groove waveguides,” Opt. Express 21(26), 32432–32440 (2013).
    [PubMed]
  22. J. Kotakoski, D. Santos-Cottin, and A. V. Krasheninnikov, “Stability of graphene edges under electron beam: equilibrium energetics versus dynamic effects,” ACS Nano 6(1), 671–676 (2012).
    [Crossref] [PubMed]
  23. A. B. Buckman, Guided-Wave Photonics, 1 st ed. (Saunders College Publishing, 1992).
  24. A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, and S. I. Bozhevolnyi, “Integrated optical components utilizing long-rang surface plasmon polaritons,” J. Lightwave Technol. 23(1), 413–422 (2005).
    [Crossref]
  25. X. Zhou, T. Zhang, L. Chen, W. Hong, and X. Li, “A graphene-based hybrid plasmonic waveguide with ultra-deep subwavelength confinement,” J. Lightwave Technol. 32(21), 4199–4203 (2014).
    [Crossref]
  26. L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B 76(15), 153410 (2007).
    [Crossref]
  27. D. K. Efetov and P. Kim, “Controlling electron-phonon interactions in graphene at ultrahigh carrier densities,” Phys. Rev. Lett. 105(25), 256805 (2010).
    [Crossref] [PubMed]
  28. L. Ju, B. S. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. G. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
    [Crossref] [PubMed]
  29. K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. L. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146(9-10), 351–355 (2008).
    [Crossref]

2014 (3)

F. J. García de Abajo, “Graphene plasmonics: challenges and opportunities,” ACS Photon. 1(3), 135–152 (2014).
[Crossref]

Y. Gao, G. Ren, B. Zhu, H. Liu, Y. Lian, and S. Jian, “Analytical model for plasmon modes in graphene-coated nanowire,” Opt. Express 22(20), 24322–24331 (2014).
[Crossref] [PubMed]

X. Zhou, T. Zhang, L. Chen, W. Hong, and X. Li, “A graphene-based hybrid plasmonic waveguide with ultra-deep subwavelength confinement,” J. Lightwave Technol. 32(21), 4199–4203 (2014).
[Crossref]

2013 (3)

P. Liu, X. Zhang, Z. Ma, W. Cai, L. Wang, and J. Xu, “Surface plasmon modes in graphene wedge and groove waveguides,” Opt. Express 21(26), 32432–32440 (2013).
[PubMed]

E. Forati and G. W. Hanson, “Surface plasmon polaritons on soft-boundary graphene nanoribbons and their application in switching/demultiplexing,” Appl. Phys. Lett. 103(13), 133104 (2013).
[Crossref]

Z. H. Zhu, C. E. Garcia-Ortiz, Z. H. Han, I. P. Radko, and S. I. Bozhevolnyi, “Compact and broadband directional coupling and demultiplexing in dielectric-loaded surface plasmon polariton waveguides based on the multimode interference effect,” Appl. Phys. Lett. 103(6), 061108 (2013).
[Crossref]

2012 (4)

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

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

J. Kotakoski, D. Santos-Cottin, and A. V. Krasheninnikov, “Stability of graphene edges under electron beam: equilibrium energetics versus dynamic effects,” ACS Nano 6(1), 671–676 (2012).
[Crossref] [PubMed]

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. Koppens, and F. J. García de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6(1), 431–440 (2012).
[Crossref] [PubMed]

2011 (4)

L. Ju, B. S. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. G. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

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

S. Randhawa, A. V. Krasavin, T. Holmgaard, J. Renger, S. I. Bozhevolnyi, A. V. Zayats, and R. Quidant, “Experimental demonstration of dielectric-loaded plasmonic waveguide disk resonators at telecom wavelengths,” Appl. Phys. Lett. 98(16), 161102 (2011).
[Crossref]

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

2010 (4)

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[Crossref]

C. L. Zou, F. W. Sun, Y. F. Xiao, C. H. Dong, X. D. Chen, J. M. Cui, Q. Gong, Z. F. Han, and G. C. Guo, “Plasmon modes of silver nanowire on a silica substrate,” Appl. Phys. Lett. 97(18), 183102 (2010).
[Crossref]

I. Avrutsky, R. Soref, and W. Buchwald, “Sub-wavelength plasmonic modes in a conductor-gap-dielectric system with a nanoscale gap,” Opt. Express 18(1), 348–363 (2010).
[Crossref] [PubMed]

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

2009 (1)

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

2008 (2)

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-rang propagation,” Nat. Photonics 2(8), 496–500 (2008).
[Crossref]

K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. L. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146(9-10), 351–355 (2008).
[Crossref]

2007 (2)

L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B 76(15), 153410 (2007).
[Crossref]

T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides,” Phys. Rev. B 75(24), 245405 (2007).
[Crossref]

2006 (3)

E. Moreno, F. J. Garcia-Vidal, S. G. Rodrigo, L. Martin-Moreno, and S. I. Bozhevolnyi, “Channel plasmon-polaritons: modal shape, dispersion, and losses,” Opt. Lett. 31(23), 3447–3449 (2006).
[Crossref] [PubMed]

B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. Aussenegg, A. Leitner, and J. Krenn, “Dielectric stipes on gold as surface plasmon waveguides,” Appl. Phys. Lett. 88(9), 094104 (2006).
[Crossref]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-sacle localization,” Phys. Rev. B 73(3), 035407 (2006).
[Crossref]

2005 (2)

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett. 95(4), 046802 (2005).
[Crossref] [PubMed]

A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, and S. I. Bozhevolnyi, “Integrated optical components utilizing long-rang surface plasmon polaritons,” J. Lightwave Technol. 23(1), 413–422 (2005).
[Crossref]

Alonso-González, P.

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

Andreev, G. O.

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

Atwater, H. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-sacle localization,” Phys. Rev. B 73(3), 035407 (2006).
[Crossref]

Aussenegg, F.

B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. Aussenegg, A. Leitner, and J. Krenn, “Dielectric stipes on gold as surface plasmon waveguides,” Appl. Phys. Lett. 88(9), 094104 (2006).
[Crossref]

Avrutsky, I.

Badioli, M.

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

Bao, W.

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

Basov, D. N.

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

Bechtel, H. A.

L. Ju, B. S. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. G. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

Bolotin, K. I.

K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. L. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146(9-10), 351–355 (2008).
[Crossref]

Boltasseva, A.

Bozhevolnyi, S. I.

Z. H. Zhu, C. E. Garcia-Ortiz, Z. H. Han, I. P. Radko, and S. I. Bozhevolnyi, “Compact and broadband directional coupling and demultiplexing in dielectric-loaded surface plasmon polariton waveguides based on the multimode interference effect,” Appl. Phys. Lett. 103(6), 061108 (2013).
[Crossref]

S. Randhawa, A. V. Krasavin, T. Holmgaard, J. Renger, S. I. Bozhevolnyi, A. V. Zayats, and R. Quidant, “Experimental demonstration of dielectric-loaded plasmonic waveguide disk resonators at telecom wavelengths,” Appl. Phys. Lett. 98(16), 161102 (2011).
[Crossref]

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[Crossref]

T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides,” Phys. Rev. B 75(24), 245405 (2007).
[Crossref]

E. Moreno, F. J. Garcia-Vidal, S. G. Rodrigo, L. Martin-Moreno, and S. I. Bozhevolnyi, “Channel plasmon-polaritons: modal shape, dispersion, and losses,” Opt. Lett. 31(23), 3447–3449 (2006).
[Crossref] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett. 95(4), 046802 (2005).
[Crossref] [PubMed]

A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, and S. I. Bozhevolnyi, “Integrated optical components utilizing long-rang surface plasmon polaritons,” J. Lightwave Technol. 23(1), 413–422 (2005).
[Crossref]

Buchwald, W.

Buljan, H.

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

Cai, W.

Camara, N.

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

Castro Neto, A. H.

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

Centeno, A.

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

Chang, D. E.

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

Chen, J.

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

Chen, L.

X. Zhou, T. Zhang, L. Chen, W. Hong, and X. Li, “A graphene-based hybrid plasmonic waveguide with ultra-deep subwavelength confinement,” J. Lightwave Technol. 32(21), 4199–4203 (2014).
[Crossref]

Chen, X. D.

C. L. Zou, F. W. Sun, Y. F. Xiao, C. H. Dong, X. D. Chen, J. M. Cui, Q. Gong, Z. F. Han, and G. C. Guo, “Plasmon modes of silver nanowire on a silica substrate,” Appl. Phys. Lett. 97(18), 183102 (2010).
[Crossref]

Christensen, J.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. Koppens, and F. J. García de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6(1), 431–440 (2012).
[Crossref] [PubMed]

Cui, J. M.

C. L. Zou, F. W. Sun, Y. F. Xiao, C. H. Dong, X. D. Chen, J. M. Cui, Q. Gong, Z. F. Han, and G. C. Guo, “Plasmon modes of silver nanowire on a silica substrate,” Appl. Phys. Lett. 97(18), 183102 (2010).
[Crossref]

Devaux, E.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett. 95(4), 046802 (2005).
[Crossref] [PubMed]

Dionne, J. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-sacle localization,” Phys. Rev. B 73(3), 035407 (2006).
[Crossref]

Ditlbacher, H.

B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. Aussenegg, A. Leitner, and J. Krenn, “Dielectric stipes on gold as surface plasmon waveguides,” Appl. Phys. Lett. 88(9), 094104 (2006).
[Crossref]

Dominguez, G.

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

Dong, C. H.

C. L. Zou, F. W. Sun, Y. F. Xiao, C. H. Dong, X. D. Chen, J. M. Cui, Q. Gong, Z. F. Han, and G. C. Guo, “Plasmon modes of silver nanowire on a silica substrate,” Appl. Phys. Lett. 97(18), 183102 (2010).
[Crossref]

Drezet, A.

B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. Aussenegg, A. Leitner, and J. Krenn, “Dielectric stipes on gold as surface plasmon waveguides,” Appl. Phys. Lett. 88(9), 094104 (2006).
[Crossref]

Ebbesen, T. W.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett. 95(4), 046802 (2005).
[Crossref] [PubMed]

Efetov, D. K.

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

Elorza, A. Z.

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

Engheta, N.

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

Falkovsky, L. A.

L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B 76(15), 153410 (2007).
[Crossref]

Fei, Z.

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

Fogler, M. M.

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

Forati, E.

E. Forati and G. W. Hanson, “Surface plasmon polaritons on soft-boundary graphene nanoribbons and their application in switching/demultiplexing,” Appl. Phys. Lett. 103(13), 133104 (2013).
[Crossref]

Fudenberg, G.

K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. L. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146(9-10), 351–355 (2008).
[Crossref]

Gao, Y.

García de Abajo, F. J.

F. J. García de Abajo, “Graphene plasmonics: challenges and opportunities,” ACS Photon. 1(3), 135–152 (2014).
[Crossref]

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. Koppens, and F. J. García de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6(1), 431–440 (2012).
[Crossref] [PubMed]

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

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

Garcia-Ortiz, C. E.

Z. H. Zhu, C. E. Garcia-Ortiz, Z. H. Han, I. P. Radko, and S. I. Bozhevolnyi, “Compact and broadband directional coupling and demultiplexing in dielectric-loaded surface plasmon polariton waveguides based on the multimode interference effect,” Appl. Phys. Lett. 103(6), 061108 (2013).
[Crossref]

Garcia-Vidal, F. J.

Geng, B. S.

L. Ju, B. S. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. G. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

Genov, D. A.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-rang propagation,” Nat. Photonics 2(8), 496–500 (2008).
[Crossref]

Girit, C.

L. Ju, B. S. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. G. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

Godignon, P.

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

Gong, Q.

C. L. Zou, F. W. Sun, Y. F. Xiao, C. H. Dong, X. D. Chen, J. M. Cui, Q. Gong, Z. F. Han, and G. C. Guo, “Plasmon modes of silver nanowire on a silica substrate,” Appl. Phys. Lett. 97(18), 183102 (2010).
[Crossref]

Gramotnev, D. K.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[Crossref]

Guo, G. C.

C. L. Zou, F. W. Sun, Y. F. Xiao, C. H. Dong, X. D. Chen, J. M. Cui, Q. Gong, Z. F. Han, and G. C. Guo, “Plasmon modes of silver nanowire on a silica substrate,” Appl. Phys. Lett. 97(18), 183102 (2010).
[Crossref]

Han, Z. F.

C. L. Zou, F. W. Sun, Y. F. Xiao, C. H. Dong, X. D. Chen, J. M. Cui, Q. Gong, Z. F. Han, and G. C. Guo, “Plasmon modes of silver nanowire on a silica substrate,” Appl. Phys. Lett. 97(18), 183102 (2010).
[Crossref]

Han, Z. H.

Z. H. Zhu, C. E. Garcia-Ortiz, Z. H. Han, I. P. Radko, and S. I. Bozhevolnyi, “Compact and broadband directional coupling and demultiplexing in dielectric-loaded surface plasmon polariton waveguides based on the multimode interference effect,” Appl. Phys. Lett. 103(6), 061108 (2013).
[Crossref]

Hanson, G. W.

E. Forati and G. W. Hanson, “Surface plasmon polaritons on soft-boundary graphene nanoribbons and their application in switching/demultiplexing,” Appl. Phys. Lett. 103(13), 133104 (2013).
[Crossref]

Hao, Z.

L. Ju, B. S. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. G. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

Hillenbrand, R.

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

Hohenau, A.

B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. Aussenegg, A. Leitner, and J. Krenn, “Dielectric stipes on gold as surface plasmon waveguides,” Appl. Phys. Lett. 88(9), 094104 (2006).
[Crossref]

Holmgaard, T.

S. Randhawa, A. V. Krasavin, T. Holmgaard, J. Renger, S. I. Bozhevolnyi, A. V. Zayats, and R. Quidant, “Experimental demonstration of dielectric-loaded plasmonic waveguide disk resonators at telecom wavelengths,” Appl. Phys. Lett. 98(16), 161102 (2011).
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T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides,” Phys. Rev. B 75(24), 245405 (2007).
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K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. L. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146(9-10), 351–355 (2008).
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Hong, W.

X. Zhou, T. Zhang, L. Chen, W. Hong, and X. Li, “A graphene-based hybrid plasmonic waveguide with ultra-deep subwavelength confinement,” J. Lightwave Technol. 32(21), 4199–4203 (2014).
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Horng, J.

L. Ju, B. S. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. G. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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Huth, F.

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

Jablan, M.

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrafred frequencies,” Phys. Rev. B 80(24), 245435 (2009).
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Jian, S.

Jiang, Z.

K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. L. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146(9-10), 351–355 (2008).
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L. Ju, B. S. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. G. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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Keilmann, F.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
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D. K. Efetov and P. Kim, “Controlling electron-phonon interactions in graphene at ultrahigh carrier densities,” Phys. Rev. Lett. 105(25), 256805 (2010).
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K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. L. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146(9-10), 351–355 (2008).
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Kjaer, K.

Klima, M.

K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. L. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146(9-10), 351–355 (2008).
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Koppens, F. H.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. Koppens, and F. J. García de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6(1), 431–440 (2012).
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Koppens, F. H. L.

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

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

J. Kotakoski, D. Santos-Cottin, and A. V. Krasheninnikov, “Stability of graphene edges under electron beam: equilibrium energetics versus dynamic effects,” ACS Nano 6(1), 671–676 (2012).
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S. Randhawa, A. V. Krasavin, T. Holmgaard, J. Renger, S. I. Bozhevolnyi, A. V. Zayats, and R. Quidant, “Experimental demonstration of dielectric-loaded plasmonic waveguide disk resonators at telecom wavelengths,” Appl. Phys. Lett. 98(16), 161102 (2011).
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J. Kotakoski, D. Santos-Cottin, and A. V. Krasheninnikov, “Stability of graphene edges under electron beam: equilibrium energetics versus dynamic effects,” ACS Nano 6(1), 671–676 (2012).
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B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. Aussenegg, A. Leitner, and J. Krenn, “Dielectric stipes on gold as surface plasmon waveguides,” Appl. Phys. Lett. 88(9), 094104 (2006).
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Lau, C. N.

Z. Fei, A. S. Rodin, G. O. Andreev, W. Bao, A. S. McLeod, M. Wagner, L. M. Zhang, Z. Zhao, M. Thiemens, G. Dominguez, M. M. Fogler, A. H. Castro Neto, C. N. Lau, F. Keilmann, and D. N. Basov, “Gate-tuning of graphene plasmons revealed by infrared nano-imaging,” Nature 487(7405), 82–85 (2012).
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B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. Aussenegg, A. Leitner, and J. Krenn, “Dielectric stipes on gold as surface plasmon waveguides,” Appl. Phys. Lett. 88(9), 094104 (2006).
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Leosson, K.

Li, X.

X. Zhou, T. Zhang, L. Chen, W. Hong, and X. Li, “A graphene-based hybrid plasmonic waveguide with ultra-deep subwavelength confinement,” J. Lightwave Technol. 32(21), 4199–4203 (2014).
[Crossref]

Lian, Y.

Liang, X. G.

L. Ju, B. S. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. G. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

Liu, H.

Liu, P.

Ma, Z.

Manjavacas, A.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. Koppens, and F. J. García de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6(1), 431–440 (2012).
[Crossref] [PubMed]

Martin, M.

L. Ju, B. S. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. G. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

Martin-Moreno, L.

McLeod, A. S.

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

Moreno, E.

Nikolajsen, T.

Osmond, J.

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

Oulton, R. F.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-rang propagation,” Nat. Photonics 2(8), 496–500 (2008).
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L. A. Falkovsky and S. S. Pershoguba, “Optical far-infrared properties of a graphene monolayer and multilayer,” Phys. Rev. B 76(15), 153410 (2007).
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J. Chen, M. Badioli, P. Alonso-González, S. Thongrattanasiri, F. Huth, J. Osmond, M. Spasenović, A. Centeno, A. Pesquera, P. Godignon, A. Z. Elorza, N. Camara, F. J. García de Abajo, R. Hillenbrand, and F. H. L. Koppens, “Optical nano-imaging of gate-tunable graphene plasmons,” Nature 487(7405), 77–81 (2012).
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Pile, D. F. P.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-rang propagation,” Nat. Photonics 2(8), 496–500 (2008).
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Polman, A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-sacle localization,” Phys. Rev. B 73(3), 035407 (2006).
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Quidant, R.

S. Randhawa, A. V. Krasavin, T. Holmgaard, J. Renger, S. I. Bozhevolnyi, A. V. Zayats, and R. Quidant, “Experimental demonstration of dielectric-loaded plasmonic waveguide disk resonators at telecom wavelengths,” Appl. Phys. Lett. 98(16), 161102 (2011).
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Radko, I. P.

Z. H. Zhu, C. E. Garcia-Ortiz, Z. H. Han, I. P. Radko, and S. I. Bozhevolnyi, “Compact and broadband directional coupling and demultiplexing in dielectric-loaded surface plasmon polariton waveguides based on the multimode interference effect,” Appl. Phys. Lett. 103(6), 061108 (2013).
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Randhawa, S.

S. Randhawa, A. V. Krasavin, T. Holmgaard, J. Renger, S. I. Bozhevolnyi, A. V. Zayats, and R. Quidant, “Experimental demonstration of dielectric-loaded plasmonic waveguide disk resonators at telecom wavelengths,” Appl. Phys. Lett. 98(16), 161102 (2011).
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Ren, G.

Renger, J.

S. Randhawa, A. V. Krasavin, T. Holmgaard, J. Renger, S. I. Bozhevolnyi, A. V. Zayats, and R. Quidant, “Experimental demonstration of dielectric-loaded plasmonic waveguide disk resonators at telecom wavelengths,” Appl. Phys. Lett. 98(16), 161102 (2011).
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Rodin, A. S.

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

Rodrigo, S. G.

Santos-Cottin, D.

J. Kotakoski, D. Santos-Cottin, and A. V. Krasheninnikov, “Stability of graphene edges under electron beam: equilibrium energetics versus dynamic effects,” ACS Nano 6(1), 671–676 (2012).
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Shen, Y. R.

L. Ju, B. S. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. G. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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Sikes, K. J.

K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. L. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146(9-10), 351–355 (2008).
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Soljacic, M.

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrafred frequencies,” Phys. Rev. B 80(24), 245435 (2009).
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Soref, R.

Sorger, V. J.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-rang propagation,” Nat. Photonics 2(8), 496–500 (2008).
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Spasenovic, M.

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

B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. Aussenegg, A. Leitner, and J. Krenn, “Dielectric stipes on gold as surface plasmon waveguides,” Appl. Phys. Lett. 88(9), 094104 (2006).
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Stepanov, A. L.

B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. Aussenegg, A. Leitner, and J. Krenn, “Dielectric stipes on gold as surface plasmon waveguides,” Appl. Phys. Lett. 88(9), 094104 (2006).
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Stormer, H. L.

K. I. Bolotin, K. J. Sikes, Z. Jiang, M. Klima, G. Fudenberg, J. Hone, P. Kim, and H. L. Stormer, “Ultrahigh electron mobility in suspended graphene,” Solid State Commun. 146(9-10), 351–355 (2008).
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Sun, F. W.

C. L. Zou, F. W. Sun, Y. F. Xiao, C. H. Dong, X. D. Chen, J. M. Cui, Q. Gong, Z. F. Han, and G. C. Guo, “Plasmon modes of silver nanowire on a silica substrate,” Appl. Phys. Lett. 97(18), 183102 (2010).
[Crossref]

Sweatlock, L. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-sacle localization,” Phys. Rev. B 73(3), 035407 (2006).
[Crossref]

Thiemens, M.

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

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

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. Koppens, and F. J. García de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6(1), 431–440 (2012).
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S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channel plasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev. Lett. 95(4), 046802 (2005).
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Wagner, M.

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

Wang, F.

L. Ju, B. S. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. G. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
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Wang, L.

Xiao, Y. F.

C. L. Zou, F. W. Sun, Y. F. Xiao, C. H. Dong, X. D. Chen, J. M. Cui, Q. Gong, Z. F. Han, and G. C. Guo, “Plasmon modes of silver nanowire on a silica substrate,” Appl. Phys. Lett. 97(18), 183102 (2010).
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Xu, J.

Zayats, A. V.

S. Randhawa, A. V. Krasavin, T. Holmgaard, J. Renger, S. I. Bozhevolnyi, A. V. Zayats, and R. Quidant, “Experimental demonstration of dielectric-loaded plasmonic waveguide disk resonators at telecom wavelengths,” Appl. Phys. Lett. 98(16), 161102 (2011).
[Crossref]

Zettl, A.

L. Ju, B. S. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. G. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

Zhang, L. M.

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

Zhang, T.

X. Zhou, T. Zhang, L. Chen, W. Hong, and X. Li, “A graphene-based hybrid plasmonic waveguide with ultra-deep subwavelength confinement,” J. Lightwave Technol. 32(21), 4199–4203 (2014).
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Zhang, X.

P. Liu, X. Zhang, Z. Ma, W. Cai, L. Wang, and J. Xu, “Surface plasmon modes in graphene wedge and groove waveguides,” Opt. Express 21(26), 32432–32440 (2013).
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R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-rang propagation,” Nat. Photonics 2(8), 496–500 (2008).
[Crossref]

Zhao, Z.

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

Zhou, X.

X. Zhou, T. Zhang, L. Chen, W. Hong, and X. Li, “A graphene-based hybrid plasmonic waveguide with ultra-deep subwavelength confinement,” J. Lightwave Technol. 32(21), 4199–4203 (2014).
[Crossref]

Zhu, B.

Zhu, Z. H.

Z. H. Zhu, C. E. Garcia-Ortiz, Z. H. Han, I. P. Radko, and S. I. Bozhevolnyi, “Compact and broadband directional coupling and demultiplexing in dielectric-loaded surface plasmon polariton waveguides based on the multimode interference effect,” Appl. Phys. Lett. 103(6), 061108 (2013).
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Zou, C. L.

C. L. Zou, F. W. Sun, Y. F. Xiao, C. H. Dong, X. D. Chen, J. M. Cui, Q. Gong, Z. F. Han, and G. C. Guo, “Plasmon modes of silver nanowire on a silica substrate,” Appl. Phys. Lett. 97(18), 183102 (2010).
[Crossref]

ACS Nano (2)

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. Koppens, and F. J. García de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6(1), 431–440 (2012).
[Crossref] [PubMed]

J. Kotakoski, D. Santos-Cottin, and A. V. Krasheninnikov, “Stability of graphene edges under electron beam: equilibrium energetics versus dynamic effects,” ACS Nano 6(1), 671–676 (2012).
[Crossref] [PubMed]

ACS Photon. (1)

F. J. García de Abajo, “Graphene plasmonics: challenges and opportunities,” ACS Photon. 1(3), 135–152 (2014).
[Crossref]

Appl. Phys. Lett. (5)

E. Forati and G. W. Hanson, “Surface plasmon polaritons on soft-boundary graphene nanoribbons and their application in switching/demultiplexing,” Appl. Phys. Lett. 103(13), 133104 (2013).
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C. L. Zou, F. W. Sun, Y. F. Xiao, C. H. Dong, X. D. Chen, J. M. Cui, Q. Gong, Z. F. Han, and G. C. Guo, “Plasmon modes of silver nanowire on a silica substrate,” Appl. Phys. Lett. 97(18), 183102 (2010).
[Crossref]

B. Steinberger, A. Hohenau, H. Ditlbacher, A. L. Stepanov, A. Drezet, F. Aussenegg, A. Leitner, and J. Krenn, “Dielectric stipes on gold as surface plasmon waveguides,” Appl. Phys. Lett. 88(9), 094104 (2006).
[Crossref]

S. Randhawa, A. V. Krasavin, T. Holmgaard, J. Renger, S. I. Bozhevolnyi, A. V. Zayats, and R. Quidant, “Experimental demonstration of dielectric-loaded plasmonic waveguide disk resonators at telecom wavelengths,” Appl. Phys. Lett. 98(16), 161102 (2011).
[Crossref]

Z. H. Zhu, C. E. Garcia-Ortiz, Z. H. Han, I. P. Radko, and S. I. Bozhevolnyi, “Compact and broadband directional coupling and demultiplexing in dielectric-loaded surface plasmon polariton waveguides based on the multimode interference effect,” Appl. Phys. Lett. 103(6), 061108 (2013).
[Crossref]

J. Lightwave Technol. (2)

A. Boltasseva, T. Nikolajsen, K. Leosson, K. Kjaer, M. S. Larsen, and S. I. Bozhevolnyi, “Integrated optical components utilizing long-rang surface plasmon polaritons,” J. Lightwave Technol. 23(1), 413–422 (2005).
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X. Zhou, T. Zhang, L. Chen, W. Hong, and X. Li, “A graphene-based hybrid plasmonic waveguide with ultra-deep subwavelength confinement,” J. Lightwave Technol. 32(21), 4199–4203 (2014).
[Crossref]

Nano Lett. (1)

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

Nat. Nanotechnol. (1)

L. Ju, B. S. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. G. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

Nat. Photonics (2)

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-rang propagation,” Nat. Photonics 2(8), 496–500 (2008).
[Crossref]

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
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Nature (2)

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Figures (4)

Fig. 1
Fig. 1 (a) Schematic of the dielectric loaded graphene plasmon waveguide. (b) The equivalent three-layer planar waveguide structure for the derivation of Eq. (1). (b) The equivalent three-layer planar waveguide structure for the derivation of Eq. (3).
Fig. 2
Fig. 2 Effective mode indices of the GSP modes in DLGPW with a width of 200 nm: (a) Real part, (b) Imaginary part of the effective mode index. The insets of (b) show the amplitudes of Ey for 1-th mode at the wavelength of 10 μm and 13 μm, respectively. Solid lines are numerical solutions of Eq. (3), symbols are obtained by Comsol simulations, and dashed lines correspond to numerical solutions of Eq. (1) and (2). (c) Mode patterns (the amplitudes of Ey) of the first 4 order modes at the wavelength of 8 μm.
Fig. 3
Fig. 3 (a) Single-mode and multi-modes operation regions calculated by Eq. (4). The numbers of modes supported by the DLGPW are labeled. (b) The cutoff wavelength of 1-th order mode at different Fermi energy levels.
Fig. 4
Fig. 4 Real part of the effective mode indices (a) and the propagation length (b) of the fundamental mode at different Fermi energy levels. The carrier mobility is fixed as 10000 cm2/(V⋅s). Real part of the effective mode indices (c) and the propagation length (d) of the fundamental mode at different carrier mobility. The Fermi energy level is fixed as 0.5 eV, and the width of the dielectric strip is 50 nm.

Equations (5)

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n core = k GSP1 / k 0 = ε 0 ε r1 + ε r2 2 2ic σ(ω) .
n clad = k GSP2 / k 0 = ε 0 ε r1 +1 2 2ic σ(ω) .
μ clad Ttan( Tw 2 mπ 2 ) μ core τ=0.
λ c m =Re( 2w m n core 2 n clad 2 ).
σ(ω)= i2 e 2 k B T π 2 (ω+i τ 1 ) In[ 2cosh( E F 2 k B T ) ]+ e 2 4 [ 1 2 + 1 π arctan( ω2 E F 2 k B T ) i 2π In (ω+2 E F ) 2 (ω+2 E F ) 2 +4 ( k B T) 2 ]

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