# Tunable Plasmonic Talbot Effect Based on Graphene Monolayer
## 1 Introduction  
The Talbot effect [1], a superposition phenomenon of multi-slit interference and single-slit diffraction, was interpreted by [PERSON] according to the Fresnel diffraction theory [2]. When a plane wave illuminates a periodic structure, imitative images of structure should appear at a periodic distance behind the structure. The self-imaging effect has attracted more attention from researchers. Excitingly, due to the excellent properties of optical imaging, Talbot effect is widely employed in lithography [3], optical metrology and laser resonators [4]. More recently, [PERSON] et al. have reported the plasmonic Talbot effect on metals [5]. The plasmonic Talbot effect occurs when surface plasmon waves are incident which is produced by the powerful interaction between the free electron oscillations and the electromagnetic field at the metal-dielectric interface. As new branch of self-imaging effect, the plasmonic Talbot effect breaks the diffraction limit [6; 7; 8; 9; 10; 11] due to the excellent electromagnetic field confinement ability of plasmon [12; 13; 14; 15; 16]. However, in noble metals, huge ohmic loss prevents the plasmon from long distance propagation, and more seriously, it is difficult to tune the operating wavelength of the whole device once the geometric structure is determined [17; 18; 19; 20; 21]. All the drawbacks limit the implication of the conventional metal-based plasmonic Talbot effect.  
To have a deeper study, some researchers shift their focus to the plasmonic Talbot effect in graphene. Graphene is a two-dimensional structure that supports surface plasmon in the infrared and terahertz wavelength range [22; 23; 24; 25]. Besides the high confinement and low loss nature, the conspicuous feature of graphene materials is that the chemical potential can be adjusted by chemical doping or the external gate voltage. Thus, the surface conductivity of graphene can be flexibly regulated by controlling the chemical potential [14; 26]. When the surface conductivity of graphene is changed, the graphene is equipped with the property of noble metals that can excite and propagate surface plasmon polaritons(SPPs). What is more, compared to noble metals, the SPPs supported by graphene possess lower loss and stronger field confinement. Recently, [PERSON] et al. demonstrated the plasmonic Talbot effect in monolayer graphene sheet arrays when surface plasmon polaritons between graphene experience weak coupling [19]. This investigation also finds that the Talbot effect distance can be regulated by some parameters of graphene. The graphene-based Talbot effect has potential applications in a sub-wavelength adjustable device [27].  
In this work, the plasmonic Talbot effect based on monolayer graphene is investigated theoretically in the terahertz frequency range and the initial period D is 160 nm. The Talbot effect distance is studied by varying the chemical potential, incident wavelength and period. Additionally, full width at half maximum (FWHM) of the Talbot image is explored as a function of incident wavelength and chemical potential of the graphene sheet. Our proposed structure might have significant applications in graphene-based nanometer imaging devices, and open a new implication for the Talbot effect in sub-wavelength imaging.