Phase modulation of light is the core of many optoelectronic applications, such as electro-optic switch, sensors and modulators. Graphene Surface plasmon polaritons (SPPs) exhibit unique properties in phase modulation including dynamic tunability, a small driving voltage and small device size. In this paper, the novel phase modulation capability of graphene SPPs in mid-infrared are confirmed through theory and simulation. The results show that graphene SPPs can realize continuous tuning of the phase shift at multiple wavelengths in mid-infrared, covering the phase range from 0 • to 360 • . Based on these results, a sandwich waveguide structure of dielectric-graphene-dielectric with a device length of 800 nm is proposed, which shows up to 381 • phase modulation range at an operating wavelength of 6.55 µm, given a 1 V driving voltage. In addition, the structure size is much shorter than the wavelength in mid-infrared and can realize sub-wavelength operation. This work paves the way to develop graphene-based tunable devices for mid-infrared wave-front control.Nanomaterials 2020, 10, 576 2 of 10 optical devices such as modulators, polarizers, sensors, etc. Due to their tunability and small size, these graphene-based devices have advantages over traditional devices. In addition, graphene has been proven to support SPPs from a mid-infrared band to THz and SPPs bound to the surface of doped graphene, which exhibit a number of favorable properties [16,17]. The ability to fabricate large-sized, high-crystalline samples enables the lifetime of SPPs to reach hundreds of optical cycles, making graphene a potential alternative for precious metal SPPs [12].The phase modulation of light is at the core of many applications and much research [18]. Phase modulation in mid-infrared can be applied to the design of a phased array radar, atmospheric communication equipment, mid-infrared detector, etc. [19,20]. It is a huge challenge to accomplish the design of these devices efficiently with a small device size [21]. However, traditional phase modulators in mid-infrared are mainly based on waveguides employing electro-optic materials such as GaAs and LiNbO 3 , which have large device sizes and require high external driving voltages [22,23]. Besides, these phase modulators suffer relatively large power dissipation and weak tunability, which greatly limits their application in light manipulation equipment. In this context, graphene SPPs shows great potential in mid-infrared phase modulation, which exhibits unique properties as a phase modulation platform with dynamic tunability, small footprint and small drive voltage [21]. The carrier concentration of graphene can be tuned over a wide range by electrostatic gate [24,25]. However, at present, the study of mid-infrared phase modulation based on graphene is mostly confined to the regulation function of graphene, and the application of graphene SPPs in mid-infrared phase modulation has not been studied systematically. This paper theoretically demonstrates the phase modulation of mid-infrare...