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

Modulating the amplitude and phase of light is at the heart of many applications such as wavefront shaping, transformation optics, phased arrays, modulators and sensors. Performing this task with high efficiency and small footprint is a formidable challenge. Metasurfaces and plasmonics 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. Here we show a graphene plasmonic phase modulator which is capable of tuning the phase between 0 and 2{\pi} in situ. With a footprint of 350nm it is more than 30 times smaller 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 for ultra-compact modulators and biosensing.