Modulating the amplitude and phase of light is at the heart of many applications such as wavefront shaping1, transformation optics2,3, phased arrays4, modulators5 and sensors6. Performing this task with high efficiency and small footprint is a formidable challenge7,8. Metasurfaces5,9 and plasmonics10 are promising, but metals exhibit weak electro-optic effects. Two-dimensional materials, such as graphene, have shown great performance as modulators with small drive voltages11,12. Here, we show a graphene plasmonic phase modulator that is capable of tuning the phase between 0 and 2π in situ. The device length of 350 nm is more than 30 times shorter than the 10.6 μm free-space wavelength. The modulation is achieved by spatially controlling the plasmon phase velocity in a device where the spatial carrier density profile is tunable. We provide a scattering theory for plasmons propagating through spatial density profiles. This work constitutes a first step towards two-dimensional transformation optics3 for ultracompact modulators7 and biosensing13.
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Dickey, F. M. Laser Beam Shaping: Theory and Techniques (CRC, 2014).
Pendry, J. B., Schurig, D. & Smith, D. R. Controlling electromagnetic fields. Science 312, 1780–1782 (2006).
Vakil, A. & Engheta, N. Transformation optics using graphene. Science 332, 1291–1294 (2011).
Sun, J., Timurdogan, E., Yaacobi, A., Hosseini, E. S. & Watts, M. R. Large-scale nanophotonic phased array. Nature 493, 195–199 (2013).
Yu, N. & Capasso, F. Flat optics with designer metasurfaces. Nat. Mater. 13, 139–150 (2014).
Takeda, M., Ina, H. & Kobayashi, S. Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry. J. Opt. Soc. Am. 72, 156–160 (1982).
Reed, G. T., Mashanovich, G., Gardes, F. Y. & Thomson, D. J. Silicon optical modulators. Nat. Photon. 4, 518–526 (2010).
Liu, K., Ye, C. R., Khan, S. & Sorger, V. J. Review and perspective on ultrafast wavelength-size electro-optic modulators. Laser Photon. Rev. 9, 172–194 (2015).
Kildishev, A. V., Boltasseva, A. & Shalaev, V. M. Planar photonics with metasurfaces. Science 339, 1232009 (2013).
Dionne, J., Diest, K., Sweatlock, L. & Atwater, H. PlasMOStor: a metal-oxide-Si field effect plasmonic modulator. Nano Lett. 9, 897–902 (2009).
Mohsin, M. et al. Experimental verification of electro-refractive phase modulation in graphene. Sci. Rep. 5, 10967 (2015).
Sun, Z., Martinez, A. & Wang, F. Optical modulators with 2D layered materials. Nat. Photon. 10, 227–238 (2016).
Rodrigo, D. et al. Mid-infrared plasmonic biosensing with graphene. Science 349, 165–168 (2015).
Fei, Z. et al. Gate-tuning of graphene plasmons revealed by infrared nano-imaging. Nature 487, 82–85 (2012).
Chen, J. et al. Optical nano-imaging of gate-tunable graphene plasmons. Nature 487, 77–81 (2012).
Woessner, A. et al. Highly confined low-loss plasmons in graphene–boron nitride heterostructures. Nat. Mater. 14, 421–425 (2015).
Wang, G., Liu, X., Lu, H. & Zeng, C. Graphene plasmonic lens for manipulating energy flow. Sci. Rep. 4, 1–7 (2014).
Fei, Z. et al. Electronic and plasmonic phenomena at graphene grain boundaries. Nat. Nanotech. 8, 821–825 (2013).
Chen, J. et al. Strong plasmon reflection at nanometer-size gaps in monolayer graphene on SiC. Nano Lett. 13, 6210–6215 (2013).
Alonso-González, P. et al. Controlling graphene plasmons with resonant metal antennas and spatial conductivity patterns. Science 344, 1369–1373 (2014).
Phillips, P. L., Knight, J. C., Pottage, J. M., Kakarantzas, G. & Russell, P. S. J. Direct measurement of optical phase in the near field. Appl. Phys. Lett. 76, 541–543 (2000).
Balistreri, M. L. M., Korterik, J. P., Kuipers, L. & Van Hulst, N. F. Local observations of phase singularities in optical fields in waveguide structures. Phys. Rev. Lett. 85, 294–297 (2000).
Li, Z. et al. Plasmonic metasurfaces to steer infrared light. Sci. Rep. 5, 12423 (2015).
Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614–617 (2013).
Huber, A., Ocelic, N., Kazantsev, D. & Hillenbrand, R. Near-field imaging of mid-infrared surface phonon polariton propagation. Appl. Phys. Lett. 87, 16–18 (2005).
Born, M. & Wolf, E. Principles of Optics (Cambridge Univ. Press, 1999).
Liu, M.-H. Theory of carrier density in multigated doped graphene sheets with quantum correction. Phys. Rev. B 87, 125427 (2013).
Polini, M. et al. Plasmons and the spectral function of graphene. Phys. Rev. B 77, 081411 (2008).
Torre, I., Katsnelson, M. I., Diaspro, A., Pellegrini, V. & Polini, M. Lippmann-Schwinger theory for two-dimensional plasmon scattering. Preprint at http://arXiv.org/abs/1702.04925 (2017).
Garcia-Pomar, J. L., Nikitin, A. Y. & Martin-Moreno, L. Scattering of graphene plasmons by defects in the graphene sheet. ACS Nano 7, 4988–4994 (2013).
Haffner, C. et al. All-plasmonic Mach–Zehnder modulator enabling optical high-speed communication at the microscale. Nat. Photon. 9, 525–528 (2015).
Green, W. M., Rooks, M. J., Sekaric, L. & Vlasov, Y. A. Ultra-compact, low RF power, 10 Gb/s silicon Mach-Zehnder modulator. Opt. Express 15, 17106–17113 (2007).
Hosseini, A. et al. Large optical spectral range dispersion engineered silicon-based photonic crystal waveguide modulator. Opt. Express 20, 12318–12325 (2012).
Wang, Z. et al. Experimental demonstration of graphene plasmons working close to the near-infrared window. Opt. Lett. 41, 5345–5348 (2016).
Gómez-Díaz, J. S. & Perruisseau-Carrier, J. Graphene-based plasmonic switches at near infrared frequencies. Opt. Express 21, 15490–15504 (2013).
We thank A. J. Huber, K.-J. Tielrooij, I. Epstein and W. Heni for fruitful discussions, and D. Davydovskaya and G. Navickaite for assistance in the clean room. Open source software was used (www.matplotlib.org, www.python.org, www.inkscape.org). F.H.L.K. acknowledges financial support from the Spanish Ministry of Economy and Competitiveness, through the ‘Severo Ochoa’ Programme for Centres of Excellence in R&D (SEV-2015-0522), support by Fundacio Cellex Barcelona, the ERC starting grant (307806, CarbonLight), the Government of Catalonia through the SGR grant (2014-SGR-1535), the Mineco grants Ramón y Cajal (RYC-2012-12281) and Plan Nacional (FIS2013-47161-P), and project GRASP (FP7-ICT-2013-613024-GRASP). F.H.L.K. and R.H. acknowledge support by the EC under Graphene Flagship (contract no. CNECT-ICT-696656). Y.G. and J.H. acknowledge support from the US Office of Naval Research N00014-13-1-0662. M.P. is extremely grateful for the financial support granted by the ICFO during a visit in August 2016 and acknowledges Fondazione Istituto Italiano di Tecnologia. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan and JSPS KAKENHI grant numbers JP26248061, JP15K21722 and JP25106006.
R.H. is co-founder of Neaspec GmbH, a company producing scattering-type scanning near-field optical microscope systems such as the ones used in this study. All other authors declare no competing financial interests.
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Woessner, A., Gao, Y., Torre, I. et al. Electrical 2π phase control of infrared light in a 350-nm footprint using graphene plasmons. Nature Photon 11, 421–424 (2017). https://doi.org/10.1038/nphoton.2017.98
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