Modulating the amplitude and phase of light is at the heart of many applications such as wavefront shaping¹, transformation optics^2,3, phased arrays⁴, modulators⁵ and sensors⁶. Performing this task with high efficiency and small footprint is a formidable challenge^7,8. Metasurfaces^5,9 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 voltages^11,12. 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.

调制光的振幅和相位是许多应用程序的核心，例如波前成形¹，转换光学器件^2,3，相控阵⁴，调制器⁵和传感器⁶。以高效率和小占用空间执行此任务是一个艰巨的挑战^7,8。超表面^5，9和等离激元¹⁰是有希望的，但是金属显示出弱的电光效应。二维材料（例如石墨烯）作为具有较小驱动电压^11,12的调制器已显示出出色的性能。在这里，我们展示了一种石墨烯等离激元相位调制器，该调制器能够在0至2π之间原位调整相位。350 nm的器件长度比10.6μm自由空间波长短30倍以上。通过在空间载流子密度分布可调的设备中，通过空间控制等离激元相速度来实现调制。我们为通过空间密度分布传播的等离激元提供了散射理论。这项工作构成了面向超紧凑型调制器⁷和生物传感¹³的二维转换光学器件^3的第一步。