## 2 Reflectarray Design and Structure  
To meet the requirements of dual-frequency and dual-polarization, cross-dipole elements were used for the present research. As shown in Figure 2a, for each cross-dipole  
Figure 1: (**a**) Configuration of traditional reflectarray. (**b**) Reflection phase response for different substrates. element, the horizontal dipole (\(x\)-direction) deals with the required reflection phase shift for the horizontally polarized incident wave at 12 GHz. The vertical dipole (\(y\)-direction) was designed for the vertical polarization at 16 GHz. The schematic diagram of the FSS sandwiched reflectarray is illustrated in Figure 2. Double substrates were used as shown in Figure 2b. The metal ground plane was the bottom of the first substrate (substrate 1, single metal). The top layer of the second substrate (substrate 2) was the reflectarray element layer. \(7\times 11\) elements with a size of 70 \(\times\) 110 mm\({}^{2}\) were designed. The FSS layer was etched on the other side of substrate 2 with structure of loops linked by stripe lines. As shown in Figure 2b, the FSS layer was sandwiched between the reflectarray element layer and the metal layer. The thicknesses of two substrates were \(h_{1}=0.8\) mm, \(h_{2}=1.6\) mm, respectively. The permittivity was selected as 2.5 for both substrates. To analyze the reflection phase characteristics of the unit cell, an infinite periodic model was performed using HFSS simulation with normal incidence. The periodic boundary condition (PBC) was set around the model and Floquet's ports were used, as shown in Figure 3a. Figure 3: (**a**) Reflection phase methodology. (**b**) Relation between dipole length and reflection phase at 12 GHz. (**c**) Relation between dipole length and reflection phase at 16 GHz. Figure 2: Schematic diagram and side view of the FSS sandwiched reflectarray. In a lower operating frequency (12 GHz), as can be seen in Figure 3b, if there is only a metal ground plane with a distance of 1.6 mm (\(H\) = 1.6 mm) from the reflectarray element layer (RA layer), the curve of the reflection phase shows a rapid variation around the resonance and a slow variation off resonance. When the metal ground is set to the distance of 2.4 mm (\(H\) = 2.4 mm), a smoother phase variation phase range can be obtained. However, the distance of 2.4 mm is too thick for 16 GHz, as depicted in Figure 3c. For the case of \(H\) = 2.4 mm without FSS, the phase variation is smooth but phase range is limited to less than 280\({}^{\circ}\), which is not enough for the design. When the FSS layer is inserted, the reflectarray has a frequency selected reflection ground. Thus, for the lower operating frequency (12 GHz), the FSS layer is invisible and the reflection plane acts as the metal ground of substrate 1. For the other working frequency (16 GHz), the inserted FSS is a PEC-like layer, from which the incidence field can be directly reflected. From Figure 3c, it can be observed that smooth phase ranges (more than 300 degree) are obtained at both the lower and upper frequency by using the FSS sandwiched structure. At 16 GHz, a wider phase range can be obtained with inserted FSS. If the metal ground plane is replaced by FSS for \(H\) = 1.6 mm, a similar phase response can be obtained. For the case of \(H\) = 2.4 mm, FSS and the ground plane comprise a whole reflection structure. Due to the interaction between them, the FSS layer must be properly optimized. The final optimized FSS element has an inner loop length of 4.5 mm. As shown in Figure 3c, a more linear performance is obtained with the inserted FSS layer at the upper operating frequency. The FSS element geometry is sketched in Figure 4; the adjacent loop elements are connected with a strip line. The size and shape of the FSS were optimized for a perfect transparent layer at the lower working frequency and a perfect reflection layer at the upper working frequency. As demonstrated in Figure 4b, the \(-\)5 dB S11 band is less than 1.8 GHz at 16 GHz and the reflecting amplitude is less than \(-\)20 dB at 12 GHz.