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.
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.