## 5 Passive Dual-Band Phase-Gradient Metasurfaces
### Composite Metal-Dielectric Unit Cells
Most cells reported in the literature are selected based on identifying phase pairs that simultaneously provide the required phase for both frequencies while maintaining a high transmission magnitude. However, this process is time-consuming, involvingrigorous parameter sweep simulations, in which cell parameters are varied to analyze the phase response at both frequencies. This generates data sets with the maximum possible phase combinations for two frequencies with a high transmission coefficient magnitude. The highly transmitting cells are then selected from these generated data sets depending on the required phase profile of the metasurface. Such dual-band PGMs are reported in [32; 61; 69; 96; 97], where the phase shift through the cell is tuned either by varying the length or width of the geometric shape within the cell or by rotating the shape itself at various angles within the cell. In [32], phase tuning is achieved using phase delay (PD) unit cells, and a generic methodology to reduce the complexity of dual-band metasurface is presented. This work is an extension of the earlier work in [84; 98]. According to [32], the cells corresponding to the frequencies \(f_{1}\) and \(f_{2}\) can be designed using square loops corresponding to the lower frequency and square patches corresponding to the higher frequency. Ref. [32] further suggested that if the frequency in the two bands is selected to maximize the greatest common divider between them, it will result in fewer non-repeated cells to achieve 360\({}^{\circ}\) independent phase wrapping at the dual frequency bands. In the given analysis, the cell period is \(\lambda/4\times\lambda/4\) for the lower-frequency band and \(\lambda/3\times\lambda/3\) at the higher-frequency band. The reported unit cell is a seven-layer structure, and cell sizes are optimized to obtain the specific dimensions, giving required phases with high transmission coefficient magnitudes for both bands. Along with the time-consuming cell selection process discussed previously, another design limitation is utilizing seven metal and six dielectric layers, leading to a thicker metasurface. These layers are also bonded together, increasing the overall cost and complexity of the design and fabrication process. A comparison of the response of PD and phase rotation (PR) unit cells in terms of the scattering parameters of the surface is also discussed in [99]. The paper compares the working principles of PD and PR cells, their effect on the polarization of incident waves, and their design complexity. In another study, a dual-band cell is introduced with circular polarization, operating at frequencies of 20 GHz and 30 GHz [68]. The unit cells designed for each frequency allowed independent phase variation at the respective bands, achieved by adjusting distinct cell parameters separately. To achieve this, the resonating element for the higher frequency band is strategically positioned at the corners of each cell. This placement ensures that when the cells are arranged in a periodic lattice, they formed complete resonating elements. In contrast, the resonating element is placed in the center of each cell for the lower-frequency band. This approach of interleaving the resonating elements specific to different frequency bands reduced the computational time required compared to previous techniques that aimed to identify common phase pairs. The overall structure of the proposed design consists of three layers, comprising three metal and three dielectric layers, with dual-polarized slot elements. Beam steering is achieved by translational sliding of the TA relative to the feeder. The proposed unit cell design is also converted to an all-metallic structure, eliminating the requirement of expensive laminates and making the cell suitable for high-temperature applications. The same approach of strategically positioning the resonant elements within the unit cell to achieve independent frequency tuning at the dual frequency bands is also utilized in [33; 60; 63]. Interleaved cells, however, acquire more space.