Electrical 2π phase control of infrared light in a 350-nm footprint using graphene plasmons

Modulating the amplitude and phase of light is at the heart of many applications such as wavefront shaping(1), transformation optics(2,3), phased arrays(4), modulators(5) and sensors(6). Performing this task with high efficiency and small footprint is a formidable challenge(7,8). Metasurfaces(5,9) and plasmonics(10) are promising, but metals exhibit weak electro-optic effects. Two-dimensional materials, such as graphene, have shown great performance as modulators with small drive voltages(11,12). Here, we show a graphene plasmonic phase modulator that is capable of tuning the phase between 0 and 2 pi in situ. The device length of 350 nm is more than 30 times shorter than the 10.6 mu m 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 optics(3) for ultracompact modulators(7) and biosensing(13).