## 5 Passive Dual-Band Phase-Gradient Metasurfaces
### Composite Metal-Dielectric Unit Cells  
Composite (metal-dielectric) unit cells are made up of both metal and dielectric material. A detailed analysis of the choice of resonating element for such unit cells was presented in [93]. Multilayer printed unit cells can be used to design the metasurfaces. For implementing metasurface, only those cells that offer high transmission magnitude, ideally less than -1 dB, are selected. However, when the complete phase range is impossible using only -1 dB cells, a few cells with up to -3 dB transmission magnitude can also be selected. According to the detailed analysis of metasurfaces conducted in [94], the transmission phase of any single layer (one conductor layer placed over a dielectric substrate) surface is a function of substrate electrical thickness \(\beta h_{d}\), where \(\beta\) is the phase constant (\(\beta=\frac{2\tau\sqrt{e_{r}}}{\lambda_{0}}\)) and \(h_{d}\) is the height of the substrate. With a single-layer unit cell, the maximum phase range that can be achieved regardless of the implemented metallic element shape is \(54^{\circ}\) with a transmission coefficient magnitude within \(-1\) dB and \(90^{\circ}\) with a transmission coefficient magnitude greater than \(-3\) dB. To increase the phase range, the number of layers must be increased. Wide-band dual resonant double square ring unit cells are presented in [95]. The unit cell structure has four metal-dielectric layers separated by an air gap. Adding the inner rings increases the achievable phase range and improves the 1 dB gain bandwidth by 7.5%. For any selected unit cell geometry, the phase range of a multi-layer unit cell structure depends on the substrate material, the number of layers, and the spacing between the layers. A minimum three-layer structure with two dielectric layers and three metal layers is required to provide a phase range of \(360^{\circ}\), also at the cost of a reduced transmission coefficient magnitude of \(-3\) dB. Increasing the number of layers increases the phase range with a transmission coefficient magnitude closer to 0 and more significant than \(-1\) dB. It is also deduced that the electrical thickness of a substrate \(\beta h_{d}\) should be at least 90 degrees at the resonant frequency to achieve the maximum transmission phase range. The complete analysis of two-, three-, and four-layer FSSs is given for different relative permittivity values inimproves [94]. It is concluded that the height of the dielectric layer should be selected according to the required phase range and the dielectric permittivity. If \(\beta h_{d}\) decreases below 90 degrees, the phase range is reduced to 120 degrees. If \(\beta h_{d}\) increases above 90 degrees, the transmission phase range is reduced to 240 degrees. For a three-layer FSS, with an increase in relative permittivity, the phase range increases. For \(e_{r}=4.7\) and \(|S_{21}|\geq-3\) dB, a transmission phase range of 360 degrees can be achieved with a four-layer unit cell with a reasonable transmission magnitude of \(|S_{21}|\geq-1\) dB. The analysis included conducting experiments with different shapes of unit elements. The main challenge in building a thin and lightweight metasurface is to achieve a complete 360-degree phase range while minimizing the number of layers. This optimization is essential to reduce the design expense. To design a dual-band beam steering system, the unit cell should be able to resonate in two different frequency bands. Many structures reported in the literature focus solely on the dual-band metasurface design without addressing the beam steering aspect. Designing a dual-band unit cell for a dual-band phase gradient metasurface is more challenging than designing a single-band PGM, primarily due to the need for independent \(360^{\circ}\) phase range coverage required at the dual frequency bands, which is often achieved by varying the dimensions/rotation angle of the resonant elements of the cell.