Abstract

Graphene’s featureless optical absorption, ultrahigh carrier mobility, and variable optical absorption by an applied gate voltage enable a new breed of optical modulators with broad optical and electrical bandwidths. Here we report on an electro-optic modulator that integrates single-layer graphene in a sub-wavelength thick, reflective modulator structure. These modulators provide a large degree of design freedom, which allows tailoring of their optical properties to specific needs. Current devices feature an active aperture ~100 µm, and provide uniform modulation with flat frequency response from 1 Hz to >100 MHz. These novel, low insertion-loss graphene-based modulators offer solutions to a variety of high-speed amplitude modulation tasks that require optical amplitude modulation without phase distortions, a flat frequency response, or ultra-thin geometries, such as for controlling monolithic, high-repetition rate mode-locked lasers or active interferometers.

©2012 Optical Society of America

1. Introduction

Graphene is a single sheet of carbon atoms arranged in a honeycomb structure. A unique property of this two-dimensional lattice structure is that the electrons are nearly massless due to their linear dispersion relation between energy and crystal momentum [1]. Moreover, free-standing graphene absorbs electromagnetic radiation ranging from near-infrared to UV light, with a wavelength-independent quantity of: πα = 2.3%, where α is the fine structure constant [2]. More interestingly, the density of states around the Dirac point, where the conduction and valence bands in graphene meet, is close to zero. This property makes the optical absorption of graphene at low photon energies very sensitive to the occupation of electronic states near the Dirac point, which is mostly subject to finite temperature-induced broadening and/or substrate-induced doping [3]. Since the carrier-density in graphene can also be actively controlled by an external electric field in a field-effect-transistor-like structure [4], one can utilize the doping-dependent optical absorption to gain active control over the linear optical properties of graphene at mid-IR wavelengths [5, 6].

To exploit this tunable absorption in graphene for electro-optic modulation in the near-IR or visible portion of the spectrum, one needs to substantially increase the carrier density and/or the interaction between the light and the graphene. Recently, efforts have been made to evanescently couple light in a silicon waveguide to graphene [7]. Despite its high modulation speed (~1 GHz), a waveguide-type modulator limits the range of applications. In particular free-space applications that require low insertion loss, such as amplitude modulation in a high-Q laser cavity or in an active interferometer, would suffer from the inevitable coupling loss to the optical waveguide. In this work we show the fabrication and characterization of a new type of graphene-based electro-optic modulators with low insertion loss, high modulation speeds, and large active areas for free-space laser applications.

Because of the ultra-thin character of graphene, new types of electro-optic modulators can be realized using graphene as a loss-tunable layer embedded inside a multilayer structure. With the advantage of the large design freedom that multilayer coatings offer, parameters of these graphene-based modulators, such as their insertion loss and modulation depth, can be optimized to meet the requirements of the application at hand. The electro-optic modulators that we demonstrate here are, to the best of our knowledge, the first graphene-based modulators that are fabricated in a planar, reflective-type structure that can be readily deployed in lasers or active interferometers to gain direct control over their intra-cavity dynamics. This could enable active mode-locking, carrier-envelope phase control, or suppression of noise and Q-switching instabilities [8, 9]. These novel graphene devices are not only advantageous due to their compactness, but also due to their polarization insensitivity, ultra-low phase distortion, and their low drive-voltage requirements compared to established LiNbO3-based modulators. Since these devices can be made with a large active area with uniform modulation, they enable scaling for high-power applications. It should also be noted that due to the saturation of interband absorption at high peak power in graphene [10], these modulators could be used as novel hybrid mode-locking devices that allow both, passive mode-locking and active control of the laser dynamics.

2. Methods

2.1 Working principle

The interband absorption of graphene is determined by its optical conductivity [11]

σ=σ02[tanh(ω+2EF4kBT)+tanh(ω2EF4kBT)],
where σ0 = e2/4ћ is the optical conductivity of undoped graphene (i.e. with a Fermi-energy EF = 0), kB is the Boltzmann constant, e is the electron charge, ћ is the reduced Plank constant, T is the effective carrier temperature, and ω is optical frequency. The absorbed optical power in graphene is approximately proportional to its optical conductivity. A change in graphene’s Fermi level therefore changes the optical absorption at certain optical frequencies.

The charge density of electric-field-gated graphene (see Fig. 1 , left) scales linearly with the applied voltage (V) and the dielectric constant (ε), and it is inversely proportional to the thickness (d) of the dielectric (parallel-plate capacitor model). The charge density relates to the Fermi energy (EF) of graphene and further to the applied voltage by

EF|n+n0|εd|V+V0|,
where n0 is the doping concentration present in graphene due to the graphene-substrate interaction. To simplify the understanding of the voltage-dependence of the device, one could think of this doping concentration n0 as being caused by an auxiliary voltage V0. As the magnitude of the Fermi energy approaches half the photon energy ћω, the optical conductivity in graphene changes from σ0 (corresponding to the aforementioned 2.3% optical absorption) to σ0/2. For |EF| > ћω/2, the conductivity and the optical absorption approach zero (see Fig. 1, right).

 figure: Fig. 1

Fig. 1 Tuning of the optical absorption of graphene by electric field-gating. Left: Graphene on a gated dielectric with thickness d and dielectric constant ε. Right: Excitation of electrons from the valence band (blue cones) to the conduction band (red cones) through absorption of a photon. The absorption is blocked when graphene is strongly doped (either n- or p-doped; only p-doping is shown here). For a given voltage higher ε or lower d result in larger tuning of EF. ‘const’ refers to the negative value of the charge-neutrality voltage of the device (see text).

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Graphene on dielectric substrates is typically only shallowly p-doped (~100-200 meV) [3]. Therefore, fairly high voltages are required for shifting the Fermi energy beyond the desired half of the photon energy (ћω≈400 meV for telecommunications wavelengths). For example, 200 meV pre-doped graphene on a 100 nm silicon dioxide layer (ε = 3.9) requires ~55 V to reach an EF~400 meV. The use of high-k dielectrics such as Ta2O5 (ε = 22) can thus substantially decrease the required drive voltage (<10V in the example above).

2.2 Design and fabrication of graphene electro-optic modulators

Figure 2a shows the structure of a graphene electro-optic modulator. The sapphire substrate was first coated with a 20-nm titanium adhesion layer and a 100-nm silver film by thermal evaporation. A 20 nm layer of silicon nitride was coated readily after the deposition of the silver in order to prevent oxidization. The resulting silver film provides high reflectivity (~98%) for infrared light at normal incidence and also functions as a back gate electrode. Tantalum pentoxide (Ta2O5) was deposited on the silver mirror as the gate insulator by dc reactive magnetron sputtering with a tantalum target.

 figure: Fig. 2

Fig. 2 (a) Sketch of the device structure. Silver functions as the back gate and mirror. A 225 nm thick Ta2O5 layer serves as the gate insulator and the substrate for the graphene. The top contact on the graphene is formed by a ring-shaped Ti/Al electrode. Graphene outside the top contact annulus was removed by oxygen plasma to minimize the device capacitance. (b) Electric-field-square distribution (blue line) in the multilayer structure for 1.55 µm wavelength light at normal incidence. (|E|2 was normalized to 1 for the travelling incoming wave). The black curve represents the refractive index of each layer. Here, the layer thickness of SiNx is 20 nm; Ta2O5 is 225 nm, and |E|2 on graphene is 0.94, yielding a maximum loss of 5.1%, of which 2.1% are absorbed by the undoped graphene.

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The thickness of this Ta2O5 layer is one of the design degrees of freedom that can be used to tailor the optical properties of the device to the required specifications. By placing the graphene at the appropriate location in the standing wave that is formed between the incident light and the light that was reflected from the silver back-gate electrode, one can tailor the insertion loss and achievable modulation strength of the device. Hence, a careful adjustment of the thickness of the Ta2O5 layer can alter the graphene absorption from essentially zero (if the optical thickness of the Ta2O5 layer is chosen to be λ/2) to approximately 8% (for λ/4).

For any multilayer structure with embedded graphene, modified Fresnel transfer matrices can be used to calculate the insertion loss of the structure and the effective optical absorption of the graphene. The transmission and reflection coefficients at normal incidence of a planar dielectric interface (initial and final medium with index n1 and n2, respectively) with undoped graphene are t12 = 2n1/(n1 + n2 + πα) and r12 = (n2–n1 + πα)/(n2 + n1 + πα) [11]. For the whole device structure shown in Fig. 2b the relevant refractive indices are: 2.1 for the 225 nm thick Ta2O5 layer; 1.8 for the 20 nm thick SiNx layer; and n = 0.51 + 10.8i for silver at 1.55 μm wavelength. Using the Fresnel transfer-matrix method we find that the total insertion loss (including graphene absorption) of the modulator shown in Fig. 2b is 5.1% and the electric field-induced modulation depth is 2.1%; assuming the graphene could be fully bleached.

The maximum reflectivity of this simple design is limited by the reflectivity of silver mirror. If further reduction of the insertion loss is required, for example for applications inside a high-quality-factor optical cavity, one could add a top reflector formed by a stack of dielectric quarter wave layers. For instance, by adding a single layer of quarter-wave thickness (TiO2, n = 2.5) on the graphene would reduce insertion loss down to less than 3.0%, and more than half of this loss could still be actively controlled.

We used monolayer synthetic graphene of large, connected single-crystal domains with sizes ~20 µm grown by low-pressure chemical vapor deposition (CVD) on a copper foils [12]. A large sheet of graphene (several mm2) was subsequently wet transferred from the copper foil onto the Ta2O5 layer with the mechanical support of a spin-coated polymethyl methacrylate (PMMA) film. After the transfer and removal of the PMMA film the device was baked in a N2 (90%) and H2 (10%) atmosphere at ambient pressure and 200°C for an hour. This baking removed the residual PMMA and water from the wet-transfer process. The use of CVD-grown graphene enables the fabrication of graphene modulators with large active areas; something that would likely be impossible with exfoliated graphene. Even though CVD-grown graphene has domain sizes around 20 µm, and the domain boundaries substantially increase the electrical sheet resistance, we show in the following sections that the modulation from these devices exhibit good uniformity over the whole active area.

To electrically contact the graphene, we used a lift-off process to deposit a metal-annulus consisting of a 20 nm titanium wetting layer and a 200 nm aluminum conductive layer. The contact resistance between these top electrodes and the graphene was measured to be 200-500 Ohms, which is believed to limit the current speed of the device due to the resulting RC time constant. The top contacts were chosen in the depicted ring-shape (Fig. 2a and Fig. 3 , left), as this shape provides a good compromise between the low-pass effects caused by the contact and sheet resistance, yet it does not substantially add to the capacitance of the device. With this top-contact geometry, the device capacitance scales approximately linearly with the device active area, and hence, we expect that larger devices will likely exhibit a slower electrical response. To limit the device capacitance, excess graphene outside the ring electrodes were removed by oxygen plasma. Without this step the parasitic parallel capacitor that would otherwise result from this excess graphene would artificially limit the device performance. Untreated modulators were found to have much lower bandwidths due to the large capacitance of the as-transferred graphene sheet (~10 mm2).

 figure: Fig. 3

Fig. 3 (Left) Optical microscope image of the modulator. (Right) Modulation depth measured by two-dimensional scans over the active area of the graphene modulator at various driving frequencies. The modulation depth is calibrated to the incident laser power; the driving voltage was 1Vpp (square wave).

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3. Experimental results

All the following characterization was done at ambient conditions with graphene exposed to air. We characterized the modulation depth of our graphene modulators by a continuous-wave laser at 1.55 µm wavelength. The modulation effect over the whole area of the device is characterized with two linear motorized stages arranged in an orthogonal x-y configuration. The laser beam was focused onto the device with a spot size ~5 μm diameter. The reflected beam was sent into a photodiode, and the amplitude modulation was extracted with a lock-in amplifier while the stages were scanning in discrete steps (step size 2 μm). In addition to these 2D scans, we also measured the frequency response of the modulator at a fixed location inside the active area with two lock-in amplifiers (Stanford Research SR830 for measurements from 0.1 Hz to 100 kHz, and Stanford Research SR844 for measurements from 25 kHz to 200MHz; Fig. 4a ). For all these measurements the light intensity on the device was kept low (<5 kW/cm2), such that no nonlinear optical absorption could occur in the graphene sample.

 figure: Fig. 4

Fig. 4 (a) Frequency response of the graphene modulator with 225 nm Ta2O5 dielectric (blue: experimental, orange: fit). The 3dB corner was found to be 154 MHz. The fluctuations in the modulation amplitude near the frequency corner were found to be caused by RF background noise. An amplitude roll-off at frequencies lower than 1 Hz was observed and believed to be related to the hysteresis effects caused by the underlying oxide layer [13]. The driving voltage was 1Vpp (square wave) (b) Modulation depth as a function of the RMS amplitude when driven at 100 kHz (sine wave). ‘165’ and ‘225’ refers to the thickness of the Ta2O5 layer in two different devices.

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Figure 3 shows the two-dimensional scans for various modulation frequencies. The whole active area with a diameter of 100 µm shows good spatial uniformity of the modulation depth (<15% variation from the average modulation across the active aperture). The two-dimensional maps also show that the performance of the device remains the same over the whole tested frequency range from ~100 kHz up to ~50 MHz, despite the slightly increased RF background above 10 MHz. The insertion loss of the modulator was found to be ~7% (5.1% calculated), of which 2% were from the absorption of graphene. The excess loss of 1.9% likely came from imperfections in the silver mirror and from scattering at the graphene surface. Nearly half of the absorption from graphene could be modulated with only 5 Vrms (see Fig. 4b). Larger modulation depths could be achieved by larger drive voltages (up to 25 Vrms).

To verify the aforementioned design freedom we fabricated a second device with a quarter-wave layer of Ta2O5 to achieve a larger modulation depth. For that device the insertion loss was found to be 15% (13.4% calculated) with a modulation depth of 4% at 5 Vrms. In this device the modulation was an astonishing 1% per 1 Vrms at low voltages (Fig. 4b), and more than 5% at ~8.5 Vrms, which is in good agreement with the calculated value of 7% insertion loss of the graphene. This is impressive when considering that this strong modulation occurs within the single atomic layer graphene. Since the full modulation effect occurs in the one atomic layer, one can expect that this constitutes a pure amplitude modulator, i.e. an amplitude modulator with negligible parasitic phase modulation.

The frequency response of the first modulator is shown in Fig. 4. The modulator has an estimated capacitance of 7 pF and contact resistance ~200 Ohm, which corresponds to a theoretical −3dB corner of ~114 MHz. The 3dB corner was observed to be 154 MHz. We observed a roll-off of in the modulator response at frequencies below 1Hz, which we hypothesized to be caused by the substrate, as has been observed previously in graphene transistors [13]. It should be noted that these devices provide broad optical bandwidths. We measured the modulation depth of the same device at 980 nm to be 0.15% (5 Vrms). The small modulation depth is due to the small electric field at graphene and large photon energy. We also recently designed a similar modulator and demonstrated its effectiveness as an intracavity loss modulator for fiber lasers at 2 μm wavelengths [14].

4. Conclusions

We have demonstrated the effectiveness of optical modulators employing only atomic-layer thick graphene as the active medium. These devices provide high modulation depths at wavelengths around 1.55 µm, and a large, uniform area (>7850 µm2) for free-space applications. Due to their compactness and pure loss-modulation without parasitic phase modulation, these modulators might open up a pathway to novel control schemes in lasers or in active interferometers.

Acknowledgment

We thank Prof. C. Rogers and his group for the use of their RF lock-in amplifier. This research was supported in part by the NNIN at the Colorado Nanofabrication Laboratory and the National Science Foundation under Grant No. ECS-0335765 and by the Defense Advanced Research Projects Agency (DARPA) (US), Contract No. YFA N66001-11-1-4156.

References and links

1. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005). [CrossRef]   [PubMed]  

2. R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008). [CrossRef]   [PubMed]  

3. K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008). [CrossRef]   [PubMed]  

4. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004). [CrossRef]   [PubMed]  

5. F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008). [CrossRef]   [PubMed]  

6. Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4(7), 532–535 (2008). [CrossRef]  

7. 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]  

8. T. R. Schibli, U. Morgner, and F. X. Kärtner, “Control of Q-switched mode locking by active feedback,” Opt. Lett. 26(3), 148–150 (2001). [CrossRef]   [PubMed]  

9. N. Joly and S. Bielawski, “Suppression of Q-switch instabilities by feedback control in passively mode-locked lasers,” Opt. Lett. 26(10), 692–694 (2001). [CrossRef]   [PubMed]  

10. Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010). [CrossRef]   [PubMed]  

11. T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78(8), 085432 (2008). [CrossRef]  

12. X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science 324(5932), 1312–1314 (2009). [CrossRef]   [PubMed]  

13. P. Joshi, H. E. Romero, A. T. Neal, V. K. Toutam, and S. A. Tadigadapa, “Intrinsic doping and gate hysteresis in graphene field effect devices fabricated on SiO2 substrates,” J. Phys. Condens. Matter 22(33), 334214 (2010). [CrossRef]   [PubMed]  

14. I. Hartl, C.-C. Lee, C. Mohr, J. Bethge, S. Suzuki, M. E. Fermann, and T. R. Schibli, “Ultra-low phase-noise Tm-fiber frequency comb with an intra-cavity graphene electro-optic modulator,” submitted to CLEO 2012 Science and Innovations, San Jose, CA, USA.

References

  • View by:

  1. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
    [Crossref] [PubMed]
  2. R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
    [Crossref] [PubMed]
  3. K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
    [Crossref] [PubMed]
  4. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
    [Crossref] [PubMed]
  5. F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
    [Crossref] [PubMed]
  6. Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4(7), 532–535 (2008).
    [Crossref]
  7. 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]
  8. T. R. Schibli, U. Morgner, and F. X. Kärtner, “Control of Q-switched mode locking by active feedback,” Opt. Lett. 26(3), 148–150 (2001).
    [Crossref] [PubMed]
  9. N. Joly and S. Bielawski, “Suppression of Q-switch instabilities by feedback control in passively mode-locked lasers,” Opt. Lett. 26(10), 692–694 (2001).
    [Crossref] [PubMed]
  10. Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
    [Crossref] [PubMed]
  11. T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78(8), 085432 (2008).
    [Crossref]
  12. X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science 324(5932), 1312–1314 (2009).
    [Crossref] [PubMed]
  13. P. Joshi, H. E. Romero, A. T. Neal, V. K. Toutam, and S. A. Tadigadapa, “Intrinsic doping and gate hysteresis in graphene field effect devices fabricated on SiO2 substrates,” J. Phys. Condens. Matter 22(33), 334214 (2010).
    [Crossref] [PubMed]
  14. I. Hartl, C.-C. Lee, C. Mohr, J. Bethge, S. Suzuki, M. E. Fermann, and T. R. Schibli, “Ultra-low phase-noise Tm-fiber frequency comb with an intra-cavity graphene electro-optic modulator,” submitted to CLEO 2012 Science and Innovations, San Jose, CA, USA.

2011 (1)

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 (2)

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

P. Joshi, H. E. Romero, A. T. Neal, V. K. Toutam, and S. A. Tadigadapa, “Intrinsic doping and gate hysteresis in graphene field effect devices fabricated on SiO2 substrates,” J. Phys. Condens. Matter 22(33), 334214 (2010).
[Crossref] [PubMed]

2009 (1)

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science 324(5932), 1312–1314 (2009).
[Crossref] [PubMed]

2008 (5)

T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78(8), 085432 (2008).
[Crossref]

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
[Crossref] [PubMed]

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
[Crossref] [PubMed]

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4(7), 532–535 (2008).
[Crossref]

2005 (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

2004 (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

2001 (2)

An, J.

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science 324(5932), 1312–1314 (2009).
[Crossref] [PubMed]

Banerjee, S. K.

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science 324(5932), 1312–1314 (2009).
[Crossref] [PubMed]

Basko, D. M.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

Basov, D. N.

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4(7), 532–535 (2008).
[Crossref]

Bielawski, S.

Blake, P.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
[Crossref] [PubMed]

Bonaccorso, F.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

Booth, T. J.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
[Crossref] [PubMed]

Cai, W.

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science 324(5932), 1312–1314 (2009).
[Crossref] [PubMed]

Colombo, L.

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science 324(5932), 1312–1314 (2009).
[Crossref] [PubMed]

Crommie, M.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

Dubonos, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

Ferrari, A. C.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

Firsov, A. A.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

Geim, A. K.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
[Crossref] [PubMed]

T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78(8), 085432 (2008).
[Crossref]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

Geng, B.

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]

Girit, C.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

Grigorenko, A. N.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
[Crossref] [PubMed]

Grigorieva, I. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

Hao, Z.

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4(7), 532–535 (2008).
[Crossref]

Hasan, T.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

Heinz, T. F.

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
[Crossref] [PubMed]

Henriksen, E. A.

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4(7), 532–535 (2008).
[Crossref]

Jiang, D.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

Jiang, Z.

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4(7), 532–535 (2008).
[Crossref]

Joly, N.

Joshi, P.

P. Joshi, H. E. Romero, A. T. Neal, V. K. Toutam, and S. A. Tadigadapa, “Intrinsic doping and gate hysteresis in graphene field effect devices fabricated on SiO2 substrates,” J. Phys. Condens. Matter 22(33), 334214 (2010).
[Crossref] [PubMed]

Ju, L.

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]

Jung, I.

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science 324(5932), 1312–1314 (2009).
[Crossref] [PubMed]

Kärtner, F. X.

Katsnelson, M. I.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

Kim, P.

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4(7), 532–535 (2008).
[Crossref]

Kim, S.

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science 324(5932), 1312–1314 (2009).
[Crossref] [PubMed]

Li, X.

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science 324(5932), 1312–1314 (2009).
[Crossref] [PubMed]

Li, Z. Q.

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4(7), 532–535 (2008).
[Crossref]

Liu, M.

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]

Lui, C. H.

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
[Crossref] [PubMed]

Mak, K. F.

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
[Crossref] [PubMed]

Martin, M. C.

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4(7), 532–535 (2008).
[Crossref]

Misewich, J. A.

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
[Crossref] [PubMed]

Morgner, U.

Morozov, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

Nah, J.

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science 324(5932), 1312–1314 (2009).
[Crossref] [PubMed]

Nair, R. R.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
[Crossref] [PubMed]

Neal, A. T.

P. Joshi, H. E. Romero, A. T. Neal, V. K. Toutam, and S. A. Tadigadapa, “Intrinsic doping and gate hysteresis in graphene field effect devices fabricated on SiO2 substrates,” J. Phys. Condens. Matter 22(33), 334214 (2010).
[Crossref] [PubMed]

Novoselov, K. S.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

Peres, N. M. R.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
[Crossref] [PubMed]

T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78(8), 085432 (2008).
[Crossref]

Piner, R.

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science 324(5932), 1312–1314 (2009).
[Crossref] [PubMed]

Popa, D.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

Privitera, G.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

Romero, H. E.

P. Joshi, H. E. Romero, A. T. Neal, V. K. Toutam, and S. A. Tadigadapa, “Intrinsic doping and gate hysteresis in graphene field effect devices fabricated on SiO2 substrates,” J. Phys. Condens. Matter 22(33), 334214 (2010).
[Crossref] [PubMed]

Ruoff, R. S.

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science 324(5932), 1312–1314 (2009).
[Crossref] [PubMed]

Schibli, T. R.

Sfeir, M. Y.

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
[Crossref] [PubMed]

Shen, Y. R.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

Stauber, T.

T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78(8), 085432 (2008).
[Crossref]

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
[Crossref] [PubMed]

Stormer, H. L.

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4(7), 532–535 (2008).
[Crossref]

Sun, Z.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

Tadigadapa, S. A.

P. Joshi, H. E. Romero, A. T. Neal, V. K. Toutam, and S. A. Tadigadapa, “Intrinsic doping and gate hysteresis in graphene field effect devices fabricated on SiO2 substrates,” J. Phys. Condens. Matter 22(33), 334214 (2010).
[Crossref] [PubMed]

Tian, C.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

Torrisi, F.

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

Toutam, V. K.

P. Joshi, H. E. Romero, A. T. Neal, V. K. Toutam, and S. A. Tadigadapa, “Intrinsic doping and gate hysteresis in graphene field effect devices fabricated on SiO2 substrates,” J. Phys. Condens. Matter 22(33), 334214 (2010).
[Crossref] [PubMed]

Tutuc, E.

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science 324(5932), 1312–1314 (2009).
[Crossref] [PubMed]

Ulin-Avila, E.

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]

Velamakanni, A.

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science 324(5932), 1312–1314 (2009).
[Crossref] [PubMed]

Wang, F.

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]

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

Wu, Y.

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
[Crossref] [PubMed]

Yang, D.

X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, and R. S. Ruoff, “Large-area synthesis of high-quality and uniform graphene films on copper foils,” Science 324(5932), 1312–1314 (2009).
[Crossref] [PubMed]

Yin, X.

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]

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.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

Zhang, X.

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]

Zhang, Y.

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

ACS Nano (1)

Z. Sun, T. Hasan, F. Torrisi, D. Popa, G. Privitera, F. Wang, F. Bonaccorso, D. M. Basko, and A. C. Ferrari, “Graphene mode-locked ultrafast laser,” ACS Nano 4(2), 803–810 (2010).
[Crossref] [PubMed]

J. Phys. Condens. Matter (1)

P. Joshi, H. E. Romero, A. T. Neal, V. K. Toutam, and S. A. Tadigadapa, “Intrinsic doping and gate hysteresis in graphene field effect devices fabricated on SiO2 substrates,” J. Phys. Condens. Matter 22(33), 334214 (2010).
[Crossref] [PubMed]

Nat. Phys. (1)

Z. Q. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. L. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nat. Phys. 4(7), 532–535 (2008).
[Crossref]

Nature (2)

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]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene,” Nature 438(7065), 197–200 (2005).
[Crossref] [PubMed]

Opt. Lett. (2)

Phys. Rev. B (1)

T. Stauber, N. M. R. Peres, and A. K. Geim, “Optical conductivity of graphene in the visible region of the spectrum,” Phys. Rev. B 78(8), 085432 (2008).
[Crossref]

Phys. Rev. Lett. (1)

K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz, “Measurement of the optical conductivity of graphene,” Phys. Rev. Lett. 101(19), 196405 (2008).
[Crossref] [PubMed]

Science (4)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306(5696), 666–669 (2004).
[Crossref] [PubMed]

F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, and Y. R. Shen, “Gate-variable optical transitions in graphene,” Science 320(5873), 206–209 (2008).
[Crossref] [PubMed]

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
[Crossref] [PubMed]

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[Crossref] [PubMed]

Other (1)

I. Hartl, C.-C. Lee, C. Mohr, J. Bethge, S. Suzuki, M. E. Fermann, and T. R. Schibli, “Ultra-low phase-noise Tm-fiber frequency comb with an intra-cavity graphene electro-optic modulator,” submitted to CLEO 2012 Science and Innovations, San Jose, CA, USA.

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Figures (4)

Fig. 1
Fig. 1 Tuning of the optical absorption of graphene by electric field-gating. Left: Graphene on a gated dielectric with thickness d and dielectric constant ε. Right: Excitation of electrons from the valence band (blue cones) to the conduction band (red cones) through absorption of a photon. The absorption is blocked when graphene is strongly doped (either n- or p-doped; only p-doping is shown here). For a given voltage higher ε or lower d result in larger tuning of EF. ‘const’ refers to the negative value of the charge-neutrality voltage of the device (see text).
Fig. 2
Fig. 2 (a) Sketch of the device structure. Silver functions as the back gate and mirror. A 225 nm thick Ta2O5 layer serves as the gate insulator and the substrate for the graphene. The top contact on the graphene is formed by a ring-shaped Ti/Al electrode. Graphene outside the top contact annulus was removed by oxygen plasma to minimize the device capacitance. (b) Electric-field-square distribution (blue line) in the multilayer structure for 1.55 µm wavelength light at normal incidence. (|E|2 was normalized to 1 for the travelling incoming wave). The black curve represents the refractive index of each layer. Here, the layer thickness of SiNx is 20 nm; Ta2O5 is 225 nm, and |E|2 on graphene is 0.94, yielding a maximum loss of 5.1%, of which 2.1% are absorbed by the undoped graphene.
Fig. 3
Fig. 3 (Left) Optical microscope image of the modulator. (Right) Modulation depth measured by two-dimensional scans over the active area of the graphene modulator at various driving frequencies. The modulation depth is calibrated to the incident laser power; the driving voltage was 1Vpp (square wave).
Fig. 4
Fig. 4 (a) Frequency response of the graphene modulator with 225 nm Ta2O5 dielectric (blue: experimental, orange: fit). The 3dB corner was found to be 154 MHz. The fluctuations in the modulation amplitude near the frequency corner were found to be caused by RF background noise. An amplitude roll-off at frequencies lower than 1 Hz was observed and believed to be related to the hysteresis effects caused by the underlying oxide layer [13]. The driving voltage was 1Vpp (square wave) (b) Modulation depth as a function of the RMS amplitude when driven at 100 kHz (sine wave). ‘165’ and ‘225’ refers to the thickness of the Ta2O5 layer in two different devices.

Equations (2)

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σ= σ 0 2 [ tanh( ω+2 E F 4 k B T )+tanh( ω2 E F 4 k B T ) ],
E F | n+ n 0 | ε d | V+ V 0 | ,

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