Abstract

Graphene, as a type of flexible and electrically adjustable two-dimensional material, has exceptional optical and electrical properties that make it possible to be used in modulators. However, the poor interaction between optical fields and a single atom graphene layer prevents the easy implementation of graphene modulators. Currently available devices often require a larger overlap area of graphene to obtain the desired phase or amplitude modulation, which results in a rather large footprint and high capacitance and consequently increases the energy consumption and reduces the modulation speed. In this paper, a localized plasmonic-enhanced waveguide modulator with high-speed tunability using graphene is proposed for telecommunication applications. Strong modulation of the transmission takes place due to the enhanced interaction between the ultrathin plasmon patches and the graphene, when the plasmons are tuned on- and off-resonance by the gate-tunable graphene. A 400 GHz modulation rate using low gated-voltages with an active device area of 0.2 μm2 and a low consumption of only 0.5 fJ/bit is achieved, which paves the way for ultrafast low-energy optical waveguide modulation and switching.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Photonic interconnection plays a vital role in future supercomputers, large data centres, and high-speed intra-/inter-chip data connections. A high-speed and compact electro-optic modulator is one of the core components in a photonic integration system. Since the silicon CMOS technology is more and more mature with reliable performance at low cost, the development of high-speed and reliable electro-optic modulator-based silicon has become one focus in photonic integration [1–3]. However, a pure silicon modulator always has a low rate of modulation and a large footprint due to the weak plasma dispersion effect of silicon. Alternatively, graphene, as a type of flexible and electrically adjustable two-dimensional material, has exceptional electrical and optical properties, such as good thermal conductivity, stability, ultra-broad absorption bandwidth and outstanding carrier mobility, which make it an excellent electro-optic material for modulators [4–7]. In 2011, Liu et al. first introduced graphene into modulators by placing single- or double-layer graphene on a silicon waveguide to modulate the absorption [8, 9]. Subsequently, some graphene-embedded silicon modulators and multi-layer graphene silicon modulators have been proposed [10, 11] to enhance the light-matter interaction. An electrical bandwidth of 100 GHz and energy consumption of 17.6 fJ/bit have been reported [10]. However, the modulator is still bulky due to the minimal overlap between the optical mode and graphene sheet [12]. For microring resonator modulators [13–15], an measured electrical bandwidth of 30 GHz and energy consumption of 0.8 pJ/bit have been demonstrated [16]. The graphene strongly interacts with the resonant field, resulting in strong resonance enhance with only a few micrometers device footprints [17, 18]. However, resonant modulators suffer from bandwidth limitations and are sensitive to temperature fluctuations and fabrication tolerances. Benefiting from the subwavelength confinement, plasmonic waveguide modulators [19–21] can provide higher light-matter interaction. For example, an electrical bandwidth of 0.4 THz and energy consumption of 145 fJ/bit in our previous work have been proposed [22]. However, the plasmonic waveguide modulators based on graphene still commonly require a few micrometers long active graphene channel [23, 24]. Therefore, the power consumption is intrinsically high due to the large device footprint and capacitance. Therefore, reducing the overlapping area of the active part of graphene (reducing the capacitance) becomes the key target for high-speed low-energy graphene modulators.

Localized plasmon resonance has the ability to concentrate light at subwavelength scale, making it applicable in many fields, such as optical absorber [25], biochemical sensing [26, 27], spectrum detection [28] and optical switching [29, 30]. Recently, some graphene spatial light modulators loaded with the metal nanoantennas working in the terahertz, infrared and visible light spectrum were developed [31–33]. The use of plasmonic antennas and graphene makes it possible to electrically manipulate spatial light at the nanoscale [34, 35]. In this work, a novel waveguide modulator combining metal patch nanoantennas and graphene is proposed for the first time to the knowledge of authors. The localized plasmon resonance caused by the effective coupling between the ultrathin patch antennas and the waveguide mode greatly enhances the light–graphene interaction. This design realizes a high-speed modulator with dramatically reduced footprint and capacitance, which is promising for the implementation of electro-optic modulators with high speed and low energy consumption.

2. Structure and discussion

2.1 Structural description

Figures 1(a) and 1(b) show the 3D view and the cross-sectional view of the proposed waveguide electro-optic modulator integrated with metal patches and a layer of graphene. The metal patches are placed on top of the graphene, where wx and wz are the widths of the patches in the x and z directions, respectively. The outer edges of the patches along the z direction are aligned with the edge of the waveguide, where the width of the waveguide is fixed at 400 nm (see Fig. 1(b)). The gap between patches in the z direction is wgap, and the thickness of the metal patch is t. A 10-nm-thick Al2O3 layer working as the capacitor dielectric layer is placed between the graphene and the silicon waveguide. A 50-nm-thick silicon layer is used to connect the 220-nm-thick silicon waveguide and one of the metal electrodes, and the other electrode is grown on top of the graphene layer on the other side.

 

Fig. 1 (a) 3D view and (b) cross-sectional view of the proposed waveguide electro-optic modulator integrated with metal patches and graphene. The outer edges of the patches along the z direction are aligned with the edge of the waveguide, where the spacing of edges is 400 nm. The gap between patches in the z direction is wgap, and the thickness of the metal patches is t. wx and wz are the widths of the patch in the x and z directions, respectively. The inset in Fig. 1(a) shows an electric field intensity cutplane aligned with the x-z plane at the middle of the metal patch thickness where t = 3 nm, wx = wz = 110 nm and wgap = 100 nm, and wavelength is 1.55 µm.

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In this structure, nanoscale metal structures on top of the silicon waveguide have the unique capability to concentrate light into a deep subwavelength scale as shown in the inset of Fig. 1(a). The plasmon resonance can be tailored via electrostatic gating of graphene at optical telecommunication wavelengths. The simulation is performed by Lumerical FDTD. All the materials in the structure, except for graphene, are standard available materials provided by the simulation software. In this theoretical study, silver is chosen as the material of the metal patches and is simulated using the Lumerical built-in material data fitted from Johnson and Christy’s experimental data [36, 37]. It can be replaced by other metals in the fabrication where the same phenomenon can be achieved.

2.2 Transmission characteristics without graphene

Before discussing the modulation characteristics of the device, it is instructive to first study the influence of loading the ultrathin metal patches on the light propagation in the silicon waveguide without graphene. A 220 nm × 400 nm ridge waveguide on a silicon-on-insulator (SOI) wafer is selected for quasi TE light transmission. Different from the plane wave in free space, the quasi TE polarized light in the silicon waveguide is mainly distributed in the horizontal direction (x direction) and in the propagation direction (z direction) as shown in Fig. 2(a). To make use of the dominant two directional E-fields distribution, the plasmon resonances excited in both directions are considered by placing a 2 × 2 metal patch array along the transverse and the propagation directions. As shown from the transmission characteristics in Fig. 2(b), there are two distinct resonant peaks in the transmission spectrum. The insets of Fig. 2(b) show the |Ex| and |Ez| distributions of the metal patches in the x-z plane. It can be seen that the metal patches have a very strong electric field in the z and x directions corresponding to resonance 1 and 2, respectively.

 

Fig. 2 Transmission characteristics of the waveguides. (a) Electric field profile of the silicon waveguide in the x-z cutplane without the metal patches. The areas of the dotted boxes represent the locations where the patch array will be placed. (b) Optical transmission spectrum with t = 3 nm, wx = 110 nm, wz = 100 nm and wgap = 100 nm. The two insets show the electric field resonant intensity profiles of the metal patches in the z and x directions corresponding to the two resonant peaks of the transmission spectrum, respectively.

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To verify the two distinct resonant peaks caused by the patch array, the transmission spectra of the waveguide loading with metal patches of different sizes along the x direction and the z direction are calculated, as shown in Fig. 3. We fix wz (wx) at 110 nm and vary wx (wz) from 90 to 120 nm with a 10-nm step as shown in Fig. 3(a) left (right). In all of the above simulations, the thickness of the metal patch t is 3 nm, and the gap size wgap is 100 nm.

 

Fig. 3 Transmission spectra of the waveguide with different patches’ sizes. The thickness of the metal patch t is 3 nm, and the gap size wgap is 100 nm. In the left of Fig. 3(a), wz is 110 nm, and wx varies from 90 to 120 nm with a 10-nm step. In the right of Fig. 3(a), wx is at 110 nm, and wz varies from 90 to 120 nm with a 10-nm step. (b) The transmission spectra with patch sizes of wx = wz = 95 nm, 100 nm, 105 nm and 110 nm, respectively. (c) The electric field distribution corresponding to the three resonance peaks of two transmission spectrum with patch sizes of wx = 110 nm, wz = 100 nm, and wx = wz = 110 nm as red circle marked in Figs. 3(a) and 3(b).

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Obviously, the resonant wavelength denoted by the dotted black line is nearly unchanged around 1.59 µm, whereas the other resonant peak marked with a triangle exhibits a significant red shift due to the increase of wx (or wz) as shown in Fig. 3(a). Another interesting phenomenon is that when the sizes of the ultrathin metal patches in two directions are the same, the resonant frequency in the two directions is overlapped, thus the intensity of the resonance is significantly enhanced. As shown in Fig. 3(b), the transmission spectra are plot with the square patch sizes of wx = wz = 95, 100, 105 and 110 nm, respectively. In Fig. 3(c), we draw the electric field distribution corresponding to the three resonance peaks of two transmission spectrum with patch sizes of wx = 110 nm, wz = 100 nm, and wx = wz = 110 nm as red circle marked in Figs. 3(a) and 3(b). Obviously, resonance point 1 is a z-directional polarization, resonance point 2 is an x-directional polarization, and resonance point 3 is x-, z- directional polarizations at the same time.

Based on these results, we concluded that by using the metal patches, plasmon resonance in two directions can be achieved, which can be tuned with different patch sizes in two directions separately. Thus, we can achieve the desired frequency resonance, and even broadband resonance, by changing the sizes of the metal patches. It is important to us to design a high speed, compact device in the following studies, because a sufficiently strong resonance can be obtained with fewer metal patches.

2.3 Transmission characteristics with graphene

The resonance of a metal nanoantenna is affected not only by the antenna size but also by the surrounding medium. According to the perturbation theory [31], the resonant frequency of an antenna, ω, can be expressed as

(Δω/ω)=(Δε|E|2dr3/2ε|E|2dr3)
where Δω=ωω0is a variant in angular frequency. The denominator in the right item is the stored electromagnetic energy, and the numerator is the change in electromagnetic energy caused by a material perturbation. Δε is a variant of the dielectric constant of the surrounding medium, and E is the undisturbed electric field intensity. The theory indicates that a large Δωcan be achieved by increasing the product of the material perturbation and the optical fields: Δε|E|2, which is the light-graphene interaction. In addition, since the denominator is always positive, whether the actual frequency is red- or blue-shifted completely depends on whether the value of is positive or negative, i.e. the change of the real part of the permittivity of graphene, which is subject to the bias voltage.

The photonic properties of graphene depends on its conductivity, σ, which is mainly controlled by electron–hole pair excitations and can be divided into intra-band and inter-band contributions [38]. The complex conductivity of graphene can be dynamically tuned by an applied voltage, which can be expressed as

σ(ω,μc,τ,T)=ie2(ω+iτ1)π2[1(ω+iτ1)20ξ(fd(ξ)ξfd(ξ)ξ)dξ0fd(ξ)fd(ξ)(ω+iτ1)24(ξ/)2dξ]
where fd(ξ)=1/{exp[(ξμc)/kBT]+1} is the Fermi–Dirac distribution function, τ is the relaxation time, is the reduced Planck’s constant, and e is the electron charge. The chemical potential, μc, can be tuned by an applied voltage, |μc|=vFπao|VgVDirac|, where VDirac is the voltage deviation caused by natural doping. Here, it is simply the ideal state. Vg is the applied voltage, vF106m/s represents the Fermi velocity, and ao=εrεo/de is obtained from the simple capacitor model [22]. Its permittivity can be expressed as the in-plane permittivity, ε||, and out-of-plane permittivity, ε. ε||=2.5+iσ/(ωε0Δ), whereas ε is a constant of 2.5 based on the permittivity of graphite [39]. In the simulation, we fixed the thickness of graphene, Δ, to 0.5 nm. The patch array with a mesh size of 2 nm × 2 nm × 0.2 nm, and the graphene is modelled by two layers of FDTD mesh cells with the smallest mesh size at 0.1 nm.

A graphene layer is placed between the patch array and the waveguide. The impacts of different doping concentrations of graphene on the transmission characteristics of the silicon waveguide when loading metal patches are studied in detail. Figure 4(a) shows the transmission properties of the device. The corresponding properties of resonance wavelength, intensity and peak width on graphene chemical potential are extracted as shown in Figs. 4(d)–4(f). When the chemical potential of graphene changed from 0 eV to 0.8 eV, the resonant frequency in Fig. 4(d) first red shift and then blue shift in the near infrared region. This is different from the mid infrared region in which the resonant frequency blue shift as the doping concentration of graphene increases [35]. The resonant intensity in Fig. 4(e) shows a step-like decrease along with higher doping concentrations. Also shown in Fig. 4(f), the resonant width defined as the full-width-half-maximum of the transmission spectra displays a step-like decrease with the increase in doping concentration.

 

Fig. 4 Electrical control of the plasmon resonance. (a) Transmission spectra (colour scale) are plotted as a function of the wavelength and chemical potential with t = 3 nm, wx = wz = 110 nm and wgap = 100 nm. (b–c) Real (εr) and imaginary (εi) parts of the graphene in-plane permittivity are calculated using the Kubo formula at temperature T = 300 K for different wavelengths in single-layer graphene. The carrier relaxation time used in the calculation is τ = 10−13 s. (d–f) The corresponding properties of resonance wavelength, intensity and peak width as a function of chemical potential in graphene.

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The phenomenon mentioned above can be explained by the optical absorption properties of graphene. The Pauli blocking caused by the high doping concentration inhibits the photon absorption of graphene, which largely change the conductivity and permittivity of graphene. Figures 4(b) and 4(c) shows the real (εr) and imaginary (εi) parts of the graphene in-plane permittivity for different wavelengths in single-layer graphene. When the chemical potential is less than ½ of the photon energy, the contribution from the interband transition becomes dominant, and the real part of the in-plane permittivity increases as the doping concentration increases. On the contrary, when the chemical potential is more than ½ of the photon energy, interband transitions will diminish due to Pauli blocking, and the intraband transitions will play an important role. Then, the real part of the in-plane permittivity decreases with an increase of doping concentration. Thus, when the chemical potential is less than ½ of the photon energy, Δε>0,Δω<0, and the resonance is red shifted; conversely, when Δε<0,Δω>0, the resonance is blue shifted. The changes in the resonant width and resonant intensity are attributed to the change in the imaginary part of the in-plane permittivity or the change in the loss. This is because of the strong interband optical absorption of graphene in optical frequencies, which provides an efficient dissipation channel and increases the damping rate of the surface plasmon oscillation.

2.4 Effect of metal patch thickness on modulation

The above simulation results are obtained using the 3-nm-thick patch antennas. In fact, the patch array thickness provides an extra degree of freedom to control the plasmon resonance. The plasmon resonant wavelength as a function of the chemical potential of graphene for different metal patch thicknesses is depicted in Fig. 5. When the chemical potential changed from 0.4 eV to 0.8 eV, the resonant wavelengths dramatically shifted from 1.66 μm to 1.54 μm and from 1.47 μm to 1.41 μm, corresponding to the metal thicknesses of t = 3 nm and 4 nm, respectively. This indicates that a thinner metal leads to a larger dynamic tunable range of the resonant waveguide within the chemical potential of 0.4 to 0.8 eV. That is because, the decrease in the metal patch thickness will squeeze the localized plasmon to be near the location of the graphene, and apparently the strong field localization will enhance the light-graphene interaction. Thus, higher modulation ability can be obtained by using thinner metal patches

 

Fig. 5 The plasmon resonant wavelength as a function of chemical potential of graphene with different thicknesses, t = 3-4 nm, of the metal patches (width of wx = wz = 115 nm, and gap size of wgap = 100 nm).

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3. Design

We have clarified that the graphene has an excellent modulation effect on the resonant frequency, the resonant intensity, and the resonant width when combined with the ultrathin metal antennas. Here, we designed an ultra-compact, low-energy and high-speed graphene modulator at the near infrared region by taking advantage of the excellent modulation effects of graphene on the resonant frequency and resonant strength.

To achieve a working wavelength of 1.55 μm and to meet the requirements of a low insertion loss (IL, less than 3 dB) for optical transmission, the size of the ultrathin metal patch is finalized as 110 nm × 110 nm × 3 nm, and wgap = 100 nm. The transmission spectra of the modulator corresponding to different bias voltages is plotted in Fig. 6, from which, a wideband modulation of 40 nm or more can be achieved with different bias voltages as shown in the inset of Fig. 6.

 

Fig. 6 Optical modulation based on the active graphene sheet. The transmission spectra of the device as a function of different bias voltages of graphene with wx = wz = 110 nm, t = 3 nm and wgap = 100 nm. When the bias voltage is 1.9 V, the modulator is in the states of ON, and when the bias voltage is more than 2.4 V, the modulator is in the states of OFF. So with different bias voltages, a wideband modulation can be achieved as shown in the inset.

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We selected 0.5 eV and 0.4 eV for the graphene Fermi level for the OFF and ON states of the modulator, and the corresponding bias voltages were 2.9 V and 1.9 V, respectively. The bandwidth of the modulator can be evaluated by 1/(2πRC), which is mainly determined by the device capacitance and resistance. The fundamental limitation of the device resistance mainly comes from the graphene resistance and the contact resistance [13]. The capacitance can also be calculated by the simple capacitor model. Benefited from the enhanced coupling due to the ultrathin metal patches, the overlapping area between the graphene and the silicon waveguide is only 0.2 μm2 (500 nm × 400 nm), Therefore, the modulation speed will be able to achieve as high as 400 GHz by taking R ∼200 Ω. The energy consumption was determined to be 0.5 fJ/bit using 1/4CVpp2 with a peak-to-peak voltage of 1 V and a bias voltage of 2.4 V, which is better than most of the existing waveguide modulators [8–23]. An extinction ratio (ER) of optical modulation of more than 6 dB can be achieved for operating wavelength range from 1520 to 1560 nm. In addition, because the modulator can be used for monolithic photonic integration without additional couplers, unnecessary coupling loss will be avoided.

4. Conclusion

We have demonstrated an ultra-compact, low-energy and high-speed electro-optic waveguide modulator based on a novel plasmonic structure at near infrared wavelengths using graphene. An interaction enhancement between graphene and light, as well as an excellent modulation performance, are acquired by using ultrathin metal patch array. Because of the plasmon resonance in two directions can be excited by a single metal patch placed on the waveguide, we achieved the desired resonant intensity using a 2 × 2 patch elements, which greatly reduces the capacitance of the device and finally allows for low-energy high-speed modulation. A low insertion loss electro-optic modulator with a 400 GHz modulation rate, an energy consumption of 0.5 fJ/bit, and an optical bandwidth of 1530-1560 nm are also achieved. In a broader context, the highly enhanced light–matter interaction on the deep subwavelength scale by using an ultrathin metal patches placed on the waveguide opens the door to a variety of highly compact optoelectronic devices.

Funding

National Natural Science Foundation of China (NSFC) (61671150, 61671147); Six Talent Peaks Project in Jiangsu Province (XCL-004).

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References

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  1. C. Sun, M. Wade, M. Georgas, S. Lin, L. Alloatti, B. Moss, R. Kumar, A. Atabaki, F. Pavanello, R. Ram, M. Popovic, and V. Stojanovic, “A 45nm SOI monolithic photonics chip-to-chip link with bit-statistics-based resonant microring thermal tuning,” in Symposium on VLSI Circuits, (2015), pp. C122–C123.
    [Crossref]
  2. L. Vivien, “Computer technology: Silicon chips lighten up,” Nature 528(7583), 483–484 (2015).
    [Crossref] [PubMed]
  3. C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y. H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
    [Crossref] [PubMed]
  4. K. Kim, J. Y. Choi, T. Kim, S. H. Cho, and H. J. Chung, “A role for graphene in silicon-based semiconductor devices,” Nature 479(7373), 338–344 (2011).
    [Crossref] [PubMed]
  5. E. J. Lee, S. Y. Choi, H. Jeong, N. H. Park, W. Yim, M. H. Kim, J.-K. Park, S. Son, S. Bae, S. J. Kim, K. Lee, Y. H. Ahn, K. J. Ahn, B. H. Hong, J.-Y. Park, F. Rotermund, and D.-I. Yeom, “Active control of all-fibre graphene devices with electrical gating,” Nat. Commun. 6(1), 6851 (2015).
    [Crossref] [PubMed]
  6. Z. Sun, A. Martinez, and F. Wang, “Optical modulators with 2D layered materials,” Nat. Photonics 10(4), 227–238 (2016).
    [Crossref]
  7. G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Özyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photonics 10(4), 244–247 (2016).
    [Crossref]
  8. M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
    [Crossref] [PubMed]
  9. M. Liu, X. Yin, and X. Zhang, “Double-Layer Graphene Optical Modulator,” Nano Lett. 12(3), 1482–1485 (2012).
    [Crossref] [PubMed]
  10. S. Ye, Z. Wang, L. Tang, Y. Zhang, R. Lu, and Y. Liu, “Electro-absorption optical modulator using dual-graphene-on-graphene configuration,” Opt. Express 22(21), 26173–26180 (2014).
    [Crossref] [PubMed]
  11. R. Hao, W. Du, H. S. Chen, X. F. Jin, L. Z. Yang, and E. P. Li, “Ultra-compact optical modulator by graphene induced electro-refraction effect,” Appl. Phys. Lett. 103(6), 061116 (2013).
    [Crossref]
  12. X. Peng, R. Hao, Z. Ye, P. Qin, W. Chen, H. Chen, X. Jin, D. Yang, and E. Li, “Highly efficient graphene-on-gap modulator by employing the hybrid plasmonic effect,” Opt. Lett. 42(9), 1736–1739 (2017).
    [Crossref] [PubMed]
  13. M. Midrio, S. Boscolo, M. Moresco, M. Romagnoli, C. De Angelis, A. Locatelli, and A. D. Capobianco, “Graphene-assisted critically-coupled optical ring modulator,” Opt. Express 20(21), 23144–23155 (2012).
    [Crossref] [PubMed]
  14. T. Pan, C. Qiu, J. Wu, X. Jiang, B. Liu, Y. Yang, H. Zhou, R. Soref, and Y. Su, “Analysis of an electro-optic modulator based on a graphene-silicon hybrid 1D photonic crystal nanobeam cavity,” Opt. Express 23(18), 23357–23364 (2015).
    [Crossref] [PubMed]
  15. M. Mohsin, D. Schall, M. Otto, B. Chmielak, S. Suckow, and D. Neumaier, “Towards the Predicted High Performance of Waveguide Integrated Electro-Refractive Phase Modulators Based on Graphene,” IEEE Photonics J. 9(1), 1–7 (2017).
    [Crossref]
  16. C. T. Phare, Y.-H. D. Lee, J. Cardenas, and M. Lipson, “Graphene electro-optic modulator with 30 GHz bandwidth,” Nat. Photonics 9(8), 511–514 (2015).
    [Crossref]
  17. Y. Ding, X. Zhu, S. Xiao, H. Hu, L. H. Frandsen, N. A. Mortensen, and K. Yvind, “Effective electro-optical modulation with high extinction ratio by a graphene-silicon microring resonator,” Nano Lett. 15(7), 4393–4400 (2015).
    [Crossref] [PubMed]
  18. C. Qiu, W. Gao, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, “Efficient modulation of 1.55 μm radiation with gated graphene on a silicon microring resonator,” Nano Lett. 14(12), 6811–6815 (2014).
    [Crossref] [PubMed]
  19. S. Das, A. Salandrino, J. Z. Wu, and R. Hui, “Near-infrared electro-optic modulator based on plasmonic graphene,” Opt. Lett. 40(7), 1516–1519 (2015).
    [Crossref] [PubMed]
  20. J. S. Shin and J. T. Kim, “Broadband silicon optical modulator using a graphene-integrated hybrid plasmonic waveguide,” Nanotechnology 26(36), 365201 (2015).
    [Crossref] [PubMed]
  21. D. Ansell, I. P. Radko, Z. Han, F. J. Rodriguez, S. I. Bozhevolnyi, and A. N. Grigorenko, “Hybrid graphene plasmonic waveguide modulators,” Nat. Commun. 6(1), 8846 (2015).
    [Crossref] [PubMed]
  22. B. H. Huang, W. B. Lu, X. B. Li, J. Wang, and Z. G. Liu, “Waveguide-coupled hybrid plasmonic modulator based on graphene,” Appl. Opt. 55(21), 5598–5602 (2016).
    [Crossref] [PubMed]
  23. Y. Ding, X. Guan, X. Zhu, H. Hu, S. I. Bozhevolnyi, L. K. Oxenløwe, N. A. Mortensen, and S. Xiao, “Efficient graphene based electro-optical modulator enabled by interfacing plasmonic slot and silicon waveguides,” arXiv:1610.05352 (2016)
  24. Z. Ma, M. H. Tahersima, S. Khan, and V. J. Sorger, “Two-Dimensional Material-Based Mode Confinement Engineering in Electro-Optic Modulators,” IEEE J. Sel. Top. Quantum Electron. 23(1), 81–88 (2017).
    [Crossref]
  25. S. X. Xia, X. Zhai, Y. Huang, J. Q. Liu, L. L. Wang, and S. C. Wen, “Multi-band perfect plasmonic absorptions using rectangular graphene gratings,” Opt. Lett. 42(15), 3052–3055 (2017).
    [Crossref] [PubMed]
  26. A. G. Brolo, “Plasmonics for future biosensors,” Nat. Photonics 6(11), 709–713 (2012).
    [Crossref]
  27. S. X. Xia, X. Zhai, Y. Huang, J. Q. Liu, L. L. Wang, and S. C. Wen, “Graphene surface plasmons with dielectric metasurfaces,” J. Lightwave Technol. 35(20), 4553–4558 (2017).
    [Crossref]
  28. M. Caldarola, P. Albella, E. Cortés, M. Rahmani, T. Roschuk, G. Grinblat, R. F. Oulton, A. V. Bragas, and S. A. Maier, “Non-plasmonic nanoantennas for surface enhanced spectroscopies with ultra-low heat conversion,” Nat. Commun. 6(1), 7915 (2015).
    [Crossref] [PubMed]
  29. X. Yin, M. Schäferling, A. K. Michel, A. Tittl, M. Wuttig, T. Taubner, and H. Giessen, “Active chiral plasmonics,” Nano Lett. 15(7), 4255–4260 (2015).
    [Crossref] [PubMed]
  30. S. X. Xia, X. Zhai, L. L. Wang, B. Sun, J. Q. Liu, and S. C. Wen, “Dynamically tunable plasmonically induced transparency in sinusoidally curved and planar graphene layers,” Opt. Express 24(16), 17886–17899 (2016).
    [Crossref] [PubMed]
  31. Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
    [Crossref] [PubMed]
  32. J. Kim, H. Son, D. J. Cho, B. Geng, W. Regan, S. Shi, K. Kim, A. Zettl, Y.-R. Shen, and F. Wang, “Electrical control of optical plasmon resonance with graphene,” Nano Lett. 12(11), 5598–5602 (2012).
    [Crossref] [PubMed]
  33. A. Majumdar, J. Kim, J. Vuckovic, and F. Wang, “Electrical control of silicon photonic crystal cavity by graphene,” Nano Lett. 13(2), 515–518 (2013).
    [Crossref] [PubMed]
  34. N. K. Emani, T. F. Chung, A. V. Kildishev, V. M. Shalaev, Y. P. Chen, and A. Boltasseva, “Electrical modulation of fano resonance in plasmonic nanostructures using graphene,” Nano Lett. 14(1), 78–82 (2014).
    [Crossref] [PubMed]
  35. Y. Yao, R. Shankar, M. A. Kats, Y. Song, J. Kong, M. Loncar, and F. Capasso, “Electrically tunable metasurface perfect absorbers for ultrathin mid-infrared optical modulators,” Nano Lett. 14(11), 6526–6532 (2014).
    [Crossref] [PubMed]
  36. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
    [Crossref]
  37. W. Chen, M. D. Thoreson, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin ultra-smooth and low-loss silver films on a germanium wetting layer,” Opt. Express 18(5), 5124–5134 (2010).
    [Crossref] [PubMed]
  38. G. Hanson, “Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene,” J. Appl. Phys. 103(6), 064302 (2008).
    [Crossref]
  39. W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6(9), 7806–7813 (2012).
    [Crossref] [PubMed]

2017 (5)

M. Mohsin, D. Schall, M. Otto, B. Chmielak, S. Suckow, and D. Neumaier, “Towards the Predicted High Performance of Waveguide Integrated Electro-Refractive Phase Modulators Based on Graphene,” IEEE Photonics J. 9(1), 1–7 (2017).
[Crossref]

X. Peng, R. Hao, Z. Ye, P. Qin, W. Chen, H. Chen, X. Jin, D. Yang, and E. Li, “Highly efficient graphene-on-gap modulator by employing the hybrid plasmonic effect,” Opt. Lett. 42(9), 1736–1739 (2017).
[Crossref] [PubMed]

Z. Ma, M. H. Tahersima, S. Khan, and V. J. Sorger, “Two-Dimensional Material-Based Mode Confinement Engineering in Electro-Optic Modulators,” IEEE J. Sel. Top. Quantum Electron. 23(1), 81–88 (2017).
[Crossref]

S. X. Xia, X. Zhai, Y. Huang, J. Q. Liu, L. L. Wang, and S. C. Wen, “Multi-band perfect plasmonic absorptions using rectangular graphene gratings,” Opt. Lett. 42(15), 3052–3055 (2017).
[Crossref] [PubMed]

S. X. Xia, X. Zhai, Y. Huang, J. Q. Liu, L. L. Wang, and S. C. Wen, “Graphene surface plasmons with dielectric metasurfaces,” J. Lightwave Technol. 35(20), 4553–4558 (2017).
[Crossref]

2016 (4)

S. X. Xia, X. Zhai, L. L. Wang, B. Sun, J. Q. Liu, and S. C. Wen, “Dynamically tunable plasmonically induced transparency in sinusoidally curved and planar graphene layers,” Opt. Express 24(16), 17886–17899 (2016).
[Crossref] [PubMed]

B. H. Huang, W. B. Lu, X. B. Li, J. Wang, and Z. G. Liu, “Waveguide-coupled hybrid plasmonic modulator based on graphene,” Appl. Opt. 55(21), 5598–5602 (2016).
[Crossref] [PubMed]

Z. Sun, A. Martinez, and F. Wang, “Optical modulators with 2D layered materials,” Nat. Photonics 10(4), 227–238 (2016).
[Crossref]

G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Özyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photonics 10(4), 244–247 (2016).
[Crossref]

2015 (11)

L. Vivien, “Computer technology: Silicon chips lighten up,” Nature 528(7583), 483–484 (2015).
[Crossref] [PubMed]

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y. H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
[Crossref] [PubMed]

E. J. Lee, S. Y. Choi, H. Jeong, N. H. Park, W. Yim, M. H. Kim, J.-K. Park, S. Son, S. Bae, S. J. Kim, K. Lee, Y. H. Ahn, K. J. Ahn, B. H. Hong, J.-Y. Park, F. Rotermund, and D.-I. Yeom, “Active control of all-fibre graphene devices with electrical gating,” Nat. Commun. 6(1), 6851 (2015).
[Crossref] [PubMed]

S. Das, A. Salandrino, J. Z. Wu, and R. Hui, “Near-infrared electro-optic modulator based on plasmonic graphene,” Opt. Lett. 40(7), 1516–1519 (2015).
[Crossref] [PubMed]

J. S. Shin and J. T. Kim, “Broadband silicon optical modulator using a graphene-integrated hybrid plasmonic waveguide,” Nanotechnology 26(36), 365201 (2015).
[Crossref] [PubMed]

D. Ansell, I. P. Radko, Z. Han, F. J. Rodriguez, S. I. Bozhevolnyi, and A. N. Grigorenko, “Hybrid graphene plasmonic waveguide modulators,” Nat. Commun. 6(1), 8846 (2015).
[Crossref] [PubMed]

C. T. Phare, Y.-H. D. Lee, J. Cardenas, and M. Lipson, “Graphene electro-optic modulator with 30 GHz bandwidth,” Nat. Photonics 9(8), 511–514 (2015).
[Crossref]

Y. Ding, X. Zhu, S. Xiao, H. Hu, L. H. Frandsen, N. A. Mortensen, and K. Yvind, “Effective electro-optical modulation with high extinction ratio by a graphene-silicon microring resonator,” Nano Lett. 15(7), 4393–4400 (2015).
[Crossref] [PubMed]

T. Pan, C. Qiu, J. Wu, X. Jiang, B. Liu, Y. Yang, H. Zhou, R. Soref, and Y. Su, “Analysis of an electro-optic modulator based on a graphene-silicon hybrid 1D photonic crystal nanobeam cavity,” Opt. Express 23(18), 23357–23364 (2015).
[Crossref] [PubMed]

M. Caldarola, P. Albella, E. Cortés, M. Rahmani, T. Roschuk, G. Grinblat, R. F. Oulton, A. V. Bragas, and S. A. Maier, “Non-plasmonic nanoantennas for surface enhanced spectroscopies with ultra-low heat conversion,” Nat. Commun. 6(1), 7915 (2015).
[Crossref] [PubMed]

X. Yin, M. Schäferling, A. K. Michel, A. Tittl, M. Wuttig, T. Taubner, and H. Giessen, “Active chiral plasmonics,” Nano Lett. 15(7), 4255–4260 (2015).
[Crossref] [PubMed]

2014 (4)

N. K. Emani, T. F. Chung, A. V. Kildishev, V. M. Shalaev, Y. P. Chen, and A. Boltasseva, “Electrical modulation of fano resonance in plasmonic nanostructures using graphene,” Nano Lett. 14(1), 78–82 (2014).
[Crossref] [PubMed]

Y. Yao, R. Shankar, M. A. Kats, Y. Song, J. Kong, M. Loncar, and F. Capasso, “Electrically tunable metasurface perfect absorbers for ultrathin mid-infrared optical modulators,” Nano Lett. 14(11), 6526–6532 (2014).
[Crossref] [PubMed]

C. Qiu, W. Gao, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, “Efficient modulation of 1.55 μm radiation with gated graphene on a silicon microring resonator,” Nano Lett. 14(12), 6811–6815 (2014).
[Crossref] [PubMed]

S. Ye, Z. Wang, L. Tang, Y. Zhang, R. Lu, and Y. Liu, “Electro-absorption optical modulator using dual-graphene-on-graphene configuration,” Opt. Express 22(21), 26173–26180 (2014).
[Crossref] [PubMed]

2013 (3)

R. Hao, W. Du, H. S. Chen, X. F. Jin, L. Z. Yang, and E. P. Li, “Ultra-compact optical modulator by graphene induced electro-refraction effect,” Appl. Phys. Lett. 103(6), 061116 (2013).
[Crossref]

A. Majumdar, J. Kim, J. Vuckovic, and F. Wang, “Electrical control of silicon photonic crystal cavity by graphene,” Nano Lett. 13(2), 515–518 (2013).
[Crossref] [PubMed]

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
[Crossref] [PubMed]

2012 (5)

J. Kim, H. Son, D. J. Cho, B. Geng, W. Regan, S. Shi, K. Kim, A. Zettl, Y.-R. Shen, and F. Wang, “Electrical control of optical plasmon resonance with graphene,” Nano Lett. 12(11), 5598–5602 (2012).
[Crossref] [PubMed]

A. G. Brolo, “Plasmonics for future biosensors,” Nat. Photonics 6(11), 709–713 (2012).
[Crossref]

W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6(9), 7806–7813 (2012).
[Crossref] [PubMed]

M. Liu, X. Yin, and X. Zhang, “Double-Layer Graphene Optical Modulator,” Nano Lett. 12(3), 1482–1485 (2012).
[Crossref] [PubMed]

M. Midrio, S. Boscolo, M. Moresco, M. Romagnoli, C. De Angelis, A. Locatelli, and A. D. Capobianco, “Graphene-assisted critically-coupled optical ring modulator,” Opt. Express 20(21), 23144–23155 (2012).
[Crossref] [PubMed]

2011 (2)

K. Kim, J. Y. Choi, T. Kim, S. H. Cho, and H. J. Chung, “A role for graphene in silicon-based semiconductor devices,” Nature 479(7373), 338–344 (2011).
[Crossref] [PubMed]

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

2010 (1)

2008 (1)

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

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Ahn, K. J.

E. J. Lee, S. Y. Choi, H. Jeong, N. H. Park, W. Yim, M. H. Kim, J.-K. Park, S. Son, S. Bae, S. J. Kim, K. Lee, Y. H. Ahn, K. J. Ahn, B. H. Hong, J.-Y. Park, F. Rotermund, and D.-I. Yeom, “Active control of all-fibre graphene devices with electrical gating,” Nat. Commun. 6(1), 6851 (2015).
[Crossref] [PubMed]

Ahn, Y. H.

E. J. Lee, S. Y. Choi, H. Jeong, N. H. Park, W. Yim, M. H. Kim, J.-K. Park, S. Son, S. Bae, S. J. Kim, K. Lee, Y. H. Ahn, K. J. Ahn, B. H. Hong, J.-Y. Park, F. Rotermund, and D.-I. Yeom, “Active control of all-fibre graphene devices with electrical gating,” Nat. Commun. 6(1), 6851 (2015).
[Crossref] [PubMed]

Ajayan, P. M.

C. Qiu, W. Gao, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, “Efficient modulation of 1.55 μm radiation with gated graphene on a silicon microring resonator,” Nano Lett. 14(12), 6811–6815 (2014).
[Crossref] [PubMed]

Albella, P.

M. Caldarola, P. Albella, E. Cortés, M. Rahmani, T. Roschuk, G. Grinblat, R. F. Oulton, A. V. Bragas, and S. A. Maier, “Non-plasmonic nanoantennas for surface enhanced spectroscopies with ultra-low heat conversion,” Nat. Commun. 6(1), 7915 (2015).
[Crossref] [PubMed]

Alloatti, L.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y. H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
[Crossref] [PubMed]

C. Sun, M. Wade, M. Georgas, S. Lin, L. Alloatti, B. Moss, R. Kumar, A. Atabaki, F. Pavanello, R. Ram, M. Popovic, and V. Stojanovic, “A 45nm SOI monolithic photonics chip-to-chip link with bit-statistics-based resonant microring thermal tuning,” in Symposium on VLSI Circuits, (2015), pp. C122–C123.
[Crossref]

Ansell, D.

D. Ansell, I. P. Radko, Z. Han, F. J. Rodriguez, S. I. Bozhevolnyi, and A. N. Grigorenko, “Hybrid graphene plasmonic waveguide modulators,” Nat. Commun. 6(1), 8846 (2015).
[Crossref] [PubMed]

Asanovic, K.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y. H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
[Crossref] [PubMed]

Atabaki, A.

C. Sun, M. Wade, M. Georgas, S. Lin, L. Alloatti, B. Moss, R. Kumar, A. Atabaki, F. Pavanello, R. Ram, M. Popovic, and V. Stojanovic, “A 45nm SOI monolithic photonics chip-to-chip link with bit-statistics-based resonant microring thermal tuning,” in Symposium on VLSI Circuits, (2015), pp. C122–C123.
[Crossref]

Atabaki, A. H.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y. H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
[Crossref] [PubMed]

Avizienis, R. R.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y. H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
[Crossref] [PubMed]

Bae, S.

E. J. Lee, S. Y. Choi, H. Jeong, N. H. Park, W. Yim, M. H. Kim, J.-K. Park, S. Son, S. Bae, S. J. Kim, K. Lee, Y. H. Ahn, K. J. Ahn, B. H. Hong, J.-Y. Park, F. Rotermund, and D.-I. Yeom, “Active control of all-fibre graphene devices with electrical gating,” Nat. Commun. 6(1), 6851 (2015).
[Crossref] [PubMed]

Basov, D. N.

G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Özyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photonics 10(4), 244–247 (2016).
[Crossref]

Boltasseva, A.

N. K. Emani, T. F. Chung, A. V. Kildishev, V. M. Shalaev, Y. P. Chen, and A. Boltasseva, “Electrical modulation of fano resonance in plasmonic nanostructures using graphene,” Nano Lett. 14(1), 78–82 (2014).
[Crossref] [PubMed]

Boscolo, S.

Bozhevolnyi, S. I.

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

Wang, J.

Wang, L.

G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Özyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photonics 10(4), 244–247 (2016).
[Crossref]

Wang, L. L.

Wang, Z.

Waterman, A. S.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y. H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
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Wu, J. Z.

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Xia, S. X.

Xiao, S.

Y. Ding, X. Zhu, S. Xiao, H. Hu, L. H. Frandsen, N. A. Mortensen, and K. Yvind, “Effective electro-optical modulation with high extinction ratio by a graphene-silicon microring resonator,” Nano Lett. 15(7), 4393–4400 (2015).
[Crossref] [PubMed]

Xu, Q.

C. Qiu, W. Gao, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, “Efficient modulation of 1.55 μm radiation with gated graphene on a silicon microring resonator,” Nano Lett. 14(12), 6811–6815 (2014).
[Crossref] [PubMed]

W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6(9), 7806–7813 (2012).
[Crossref] [PubMed]

Yang, D.

Yang, L. Z.

R. Hao, W. Du, H. S. Chen, X. F. Jin, L. Z. Yang, and E. P. Li, “Ultra-compact optical modulator by graphene induced electro-refraction effect,” Appl. Phys. Lett. 103(6), 061116 (2013).
[Crossref]

Yang, Y.

Yao, Y.

Y. Yao, R. Shankar, M. A. Kats, Y. Song, J. Kong, M. Loncar, and F. Capasso, “Electrically tunable metasurface perfect absorbers for ultrathin mid-infrared optical modulators,” Nano Lett. 14(11), 6526–6532 (2014).
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Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
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Ye, Z.

Yeom, D.-I.

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[Crossref] [PubMed]

Yin, X.

X. Yin, M. Schäferling, A. K. Michel, A. Tittl, M. Wuttig, T. Taubner, and H. Giessen, “Active chiral plasmonics,” Nano Lett. 15(7), 4255–4260 (2015).
[Crossref] [PubMed]

M. Liu, X. Yin, and X. Zhang, “Double-Layer Graphene Optical Modulator,” Nano Lett. 12(3), 1482–1485 (2012).
[Crossref] [PubMed]

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

Yu, N.

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
[Crossref] [PubMed]

Yvind, K.

Y. Ding, X. Zhu, S. Xiao, H. Hu, L. H. Frandsen, N. A. Mortensen, and K. Yvind, “Effective electro-optical modulation with high extinction ratio by a graphene-silicon microring resonator,” Nano Lett. 15(7), 4393–4400 (2015).
[Crossref] [PubMed]

Zentgraf, T.

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

Zettl, A.

J. Kim, H. Son, D. J. Cho, B. Geng, W. Regan, S. Shi, K. Kim, A. Zettl, Y.-R. Shen, and F. Wang, “Electrical control of optical plasmon resonance with graphene,” Nano Lett. 12(11), 5598–5602 (2012).
[Crossref] [PubMed]

Zhai, X.

Zhang, X.

M. Liu, X. Yin, and X. Zhang, “Double-Layer Graphene Optical Modulator,” Nano Lett. 12(3), 1482–1485 (2012).
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M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
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Zhang, Y.

Zhou, H.

Zhu, X.

Y. Ding, X. Zhu, S. Xiao, H. Hu, L. H. Frandsen, N. A. Mortensen, and K. Yvind, “Effective electro-optical modulation with high extinction ratio by a graphene-silicon microring resonator,” Nano Lett. 15(7), 4393–4400 (2015).
[Crossref] [PubMed]

ACS Nano (1)

W. Gao, J. Shu, C. Qiu, and Q. Xu, “Excitation of plasmonic waves in graphene by guided-mode resonances,” ACS Nano 6(9), 7806–7813 (2012).
[Crossref] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

R. Hao, W. Du, H. S. Chen, X. F. Jin, L. Z. Yang, and E. P. Li, “Ultra-compact optical modulator by graphene induced electro-refraction effect,” Appl. Phys. Lett. 103(6), 061116 (2013).
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X. Yin, M. Schäferling, A. K. Michel, A. Tittl, M. Wuttig, T. Taubner, and H. Giessen, “Active chiral plasmonics,” Nano Lett. 15(7), 4255–4260 (2015).
[Crossref] [PubMed]

Y. Yao, M. A. Kats, P. Genevet, N. Yu, Y. Song, J. Kong, and F. Capasso, “Broad electrical tuning of graphene-loaded plasmonic antennas,” Nano Lett. 13(3), 1257–1264 (2013).
[Crossref] [PubMed]

J. Kim, H. Son, D. J. Cho, B. Geng, W. Regan, S. Shi, K. Kim, A. Zettl, Y.-R. Shen, and F. Wang, “Electrical control of optical plasmon resonance with graphene,” Nano Lett. 12(11), 5598–5602 (2012).
[Crossref] [PubMed]

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N. K. Emani, T. F. Chung, A. V. Kildishev, V. M. Shalaev, Y. P. Chen, and A. Boltasseva, “Electrical modulation of fano resonance in plasmonic nanostructures using graphene,” Nano Lett. 14(1), 78–82 (2014).
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[Crossref] [PubMed]

Y. Ding, X. Zhu, S. Xiao, H. Hu, L. H. Frandsen, N. A. Mortensen, and K. Yvind, “Effective electro-optical modulation with high extinction ratio by a graphene-silicon microring resonator,” Nano Lett. 15(7), 4393–4400 (2015).
[Crossref] [PubMed]

C. Qiu, W. Gao, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, “Efficient modulation of 1.55 μm radiation with gated graphene on a silicon microring resonator,” Nano Lett. 14(12), 6811–6815 (2014).
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M. Liu, X. Yin, and X. Zhang, “Double-Layer Graphene Optical Modulator,” Nano Lett. 12(3), 1482–1485 (2012).
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Nanotechnology (1)

J. S. Shin and J. T. Kim, “Broadband silicon optical modulator using a graphene-integrated hybrid plasmonic waveguide,” Nanotechnology 26(36), 365201 (2015).
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G. X. Ni, L. Wang, M. D. Goldflam, M. Wagner, Z. Fei, A. S. McLeod, M. K. Liu, F. Keilmann, B. Özyilmaz, A. H. Castro Neto, J. Hone, M. M. Fogler, and D. N. Basov, “Ultrafast optical switching of infrared plasmon polaritons in high-mobility graphene,” Nat. Photonics 10(4), 244–247 (2016).
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Figures (6)

Fig. 1
Fig. 1 (a) 3D view and (b) cross-sectional view of the proposed waveguide electro-optic modulator integrated with metal patches and graphene. The outer edges of the patches along the z direction are aligned with the edge of the waveguide, where the spacing of edges is 400 nm. The gap between patches in the z direction is wgap, and the thickness of the metal patches is t. wx and wz are the widths of the patch in the x and z directions, respectively. The inset in Fig. 1(a) shows an electric field intensity cutplane aligned with the x-z plane at the middle of the metal patch thickness where t = 3 nm, wx = wz = 110 nm and wgap = 100 nm, and wavelength is 1.55 µm.
Fig. 2
Fig. 2 Transmission characteristics of the waveguides. (a) Electric field profile of the silicon waveguide in the x-z cutplane without the metal patches. The areas of the dotted boxes represent the locations where the patch array will be placed. (b) Optical transmission spectrum with t = 3 nm, wx = 110 nm, wz = 100 nm and wgap = 100 nm. The two insets show the electric field resonant intensity profiles of the metal patches in the z and x directions corresponding to the two resonant peaks of the transmission spectrum, respectively.
Fig. 3
Fig. 3 Transmission spectra of the waveguide with different patches’ sizes. The thickness of the metal patch t is 3 nm, and the gap size wgap is 100 nm. In the left of Fig. 3(a), wz is 110 nm, and wx varies from 90 to 120 nm with a 10-nm step. In the right of Fig. 3(a), wx is at 110 nm, and wz varies from 90 to 120 nm with a 10-nm step. (b) The transmission spectra with patch sizes of wx = wz = 95 nm, 100 nm, 105 nm and 110 nm, respectively. (c) The electric field distribution corresponding to the three resonance peaks of two transmission spectrum with patch sizes of wx = 110 nm, wz = 100 nm, and wx = wz = 110 nm as red circle marked in Figs. 3(a) and 3(b).
Fig. 4
Fig. 4 Electrical control of the plasmon resonance. (a) Transmission spectra (colour scale) are plotted as a function of the wavelength and chemical potential with t = 3 nm, wx = wz = 110 nm and wgap = 100 nm. (b–c) Real (εr) and imaginary (εi) parts of the graphene in-plane permittivity are calculated using the Kubo formula at temperature T = 300 K for different wavelengths in single-layer graphene. The carrier relaxation time used in the calculation is τ = 10−13 s. (d–f) The corresponding properties of resonance wavelength, intensity and peak width as a function of chemical potential in graphene.
Fig. 5
Fig. 5 The plasmon resonant wavelength as a function of chemical potential of graphene with different thicknesses, t = 3-4 nm, of the metal patches (width of wx = wz = 115 nm, and gap size of wgap = 100 nm).
Fig. 6
Fig. 6 Optical modulation based on the active graphene sheet. The transmission spectra of the device as a function of different bias voltages of graphene with wx = wz = 110 nm, t = 3 nm and wgap = 100 nm. When the bias voltage is 1.9 V, the modulator is in the states of ON, and when the bias voltage is more than 2.4 V, the modulator is in the states of OFF. So with different bias voltages, a wideband modulation can be achieved as shown in the inset.

Equations (2)

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( Δ ω / ω ) = ( Δ ε | E | 2 d r 3 / 2 ε | E | 2 d r 3 )
σ ( ω , μ c , τ , T ) = i e 2 ( ω + i τ 1 ) π 2 [ 1 ( ω + i τ 1 ) 2 0 ξ ( f d ( ξ ) ξ f d ( ξ ) ξ ) d ξ 0 f d ( ξ ) f d ( ξ ) ( ω + i τ 1 ) 2 4 ( ξ / ) 2 d ξ ]

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