## 2 Design Principle and Simulation Method  
To illustrate the design principle of our approach, Figure 1 schematically shows a unit cell of the proposed anisotropic metasurface, which is composed of a square metal ring with a cross resonator, a dielectric substrate, and a back metal-ground. The square metal ring is used to modulate the phase response of the unit cell to cover a wide range. The metal cross resonator is designed to control the phase of \(x\)- and \(y\)-polarized reflections independently by varying the geometric sizes of the transverse and vertical rods, respectively. The dielectric substrate sustains the metal ring and the cross resonator. The metal-ground is used to effectively reflect microwave back to free space. The top and bottom panels of Figure 1a are the perspective views of the unit cell from the front and back, respectively. Figure 1b shows the detailed front view of a unit cell with geometrical parameters. A numerical simulation is performed by using CST Microwave Studio (2015, CST China Ltd., Shanghai, China). The period boundary condition and the absorbing boundary condition are set in the \(x/y\) and \(z\) directions to save memory, and to reduce simulation time, respectively. The unit cell is illuminated by a plane wave propagating along the backward direction (from \(+z\) to \(-z\)) with \(x\)- and \(y\)-polarization. To acquire a wide phase coverage (at least 280\({}^{\circ}\)), the geometrical parameters are optimized, and ultimately listed as follows: \(p=7\) mm, \(\mathrm{w}=1.2\) mm, \(\  
of 15 GHz. The dielectric substrate is set as FR4, with a relative permittivity of 4.3 and a loss tangent of 0.001 [31]. The metal is approximately set as a perfect electric conductor (PEC) for simulation convenience. The incident microwave source is a plane wave propagating along the \(z\)-axis with \(x/y\) polarization. To demonstrate the anisotropic response of the unit cell for different polarized incident microwaves, Figure 2 shows the reflective coefficient S\({}_{11}\) of the proposed metasurface at a frequency of 15 GHz as a function of dx and dy. Figure 2a,b shows the amplitude and phase of S\({}_{11}\) under \(x\)-polarized incidence, with dx and dy varying from 4 mm to 6.5 mm, respectively. The results indicate a large amplitude over 0.98, and a phase shift of about 320\({}^{\circ}\) with varying dx, while S\({}_{11}\) is independent on dy. Figure 2c,d shows the amplitude and phase of S\({}_{11}\) under \(y\)-polarized incidence, with dx and dy varying from 4 mm to 6.5 mm, respectively. It is shown that the dependence of S\({}_{11}\) under \(y\)-polarized incidence on dx and dy is similar to that of under \(x\)-polarized on dy and dx, respectively, due to the symmetry of the proposed metasurface. Overall, the local phase for \(x\)- and \(y\)-polarized microwaves can be independently tailored by controlling the geometrical parameters, which is called the double-phase modulating mechanism. As mentioned above, the square metal ring could increase the coverage of the phase response of the unit cell. To demonstrate, the amplitude and phase of reflective coefficient S\({}_{11}\) for the unit cell with and without the square ring are compared in Figure 3. Here, dy is fixed 4.5 mm and dx is varying from 4 mm to 6.5 mm. Figure 3a,c shows that the reflective amplitude is always over 0.98 with and without the square ring, respectively, indicating the proposed structure is high efficiently. Figure 3b shows that the phase shift of S\({}_{11}\) for the proposed structure under \(x\)-polarized incidence covers a broad angle range of 320\({}^{\circ}\) (from \(-45^{\circ}\) to \(-365^{\circ}\)). In contrast, Figure 3d shows that the phase shift of S\({}_{11}\) for the  
Figure 2: Simulated reflective coefficient S\({}_{11}\) of the unit cell. The (**a**) amplitude and (**b**) phase of S\({}_{11}\) under \(x\)-polarized incidence as functions of dx and dy. The (**c**) amplitude and (**d**) phase of S\({}_{11}\) under \(y\)-polarized incidence as functions of dx and dy.