Graphene-combined devices enable a convenient and robust way for terahertz(THz) wave manipulation due to its plasmonic behavior and tunability via electrical biasing [1, 2]. Here we propose a type of graphene metasurfaces consisting of rectangular graphene patches for efficient THz wave manipulation. The metasurfaces can convert both linear and circular incident wave to its cross-polarized component with perfect polarization conversion. Moreover, the phase of the cross-polarized wave can be tuned in a wide range over 180° via electrical biasing, so we can develop several functional devices such as a switchable anomalous deflection device and a tunable dual-polarity focusing mirror.

The basic structure is composed of a graphene patch with size L₁ = 23 μm and L₂ = 18 μm  on a metal ground, with a 20 μm-thick silica spacer inserted in between, demonstrated in Fig. 1(a). The size of each unit cell is P_x = P_y = 40 μm and the chemical potential μ_c is 0.5 eV. The plasmonic resonance modes along both sides  L₁ and L₂ are coupled with the dielectric cavity, leading to a halfwave-plate behavior, shown in Fig. 1(b). When illuminated by an x-polarized incident wave, both resonance modes can be excited, leading to a polarization conversion ratio ( PCR = R_xy/(R_xx+R_xy)) higher than 99% in a range from 217 μm  to 237 μm. The same principle applies to circular incidence, thereby leading to a straightforward design of high-efficiency metasurfaces based on Pancharatnam–Berry phase, see in Fig. 2(a). The efficiency is higher than previous work using graphene cut-wires [3] or nano-crosses [4].

 The cross-polarization response of a unit cell versus μ_c is shown in Fig. 2(b), with incidence wavelength λ = 230 μm. Varying μ_c from 0.21eV to 0.68eV can result in a phase change of 180° while keeping the normalized amplitude larger than 0.6. Taking mirror image of the structure, an additional 180° phase shift is added, leading to a full 360° phase modulation. Utilizing these mirror-imaged unit cells, we can design a switchable beam deflection device whose reflection angle can be tuned from −46° to 0° and 46° simply by changing μ_c of each patch, as shown in Fig. 3. Another functional metasurface demonstration is a tunable focusing mirror whose focal spot can be tuned in both longitudinal and transversal direction. Besides, it can also be switched from a concave mirror to a convex one, shown in Fig. 4. It is worth emphasizing that these devices work under both linear and circular incidences.

In conclusion, we have proposed a type of graphene metasurfaces which can convert incident wave to its orthogonal counterpart with nearly 100% PCR. Moreover, the response of each unit cell can be tuned individually, leading to a dynamic manipulation of the wavefront. The proposed metasurfaces may have great potential in various THz applications.