# Two-Dimensional Beam Steering Based on Compact Programmable Coding Metasurface
## 2 Design and Simulation  
The profile of the programmable coding metasurface is shown in Figure 1. It consists of 16 rows and 16 columns of meta-atoms, and each atom contains three layers of metal and two layers of dielectric. The structure of each atom is demonstrated in Figure 2: there are two rectangular metal patches on the top metal layer, and a PIN diode is loaded between the two patches. The middle metal layer is severed as the ground, and a fan-shaped bias line on the bottom metal layer is designed to reduce the influence of DC bias on RF performance. The three metal layers are all copper with a thickness of 0.035 mm. The two dielectric layers are both Rogers RO4003C (\(\epsilon\) = 3.55), and the upper layer's thickness is 1 mm while that of the lower layer is 0.5 mm. The PIN diode MACOM MADP-000907-14020 is selected due to its low insertion loss in the working frequency range. With different digital signals from digital control system applied to the PIN diode, the diode can be switched between \"on\" and \"off\" states. The topology of the digital control circuit is shown in the Appendix A. The equivalent circuit of the PIN diode in \"on\" and \"off\" states is shown in the left of Figure 2b, and the corresponding parameters are as follows: L = 0.05 nH, R\({}_{\text{on}}\) = 4.2 \(\Omega\), R\({}_{\text{off}}\) = 300 k\(\Omega\), C\({}_{\text{off}}\) = 42 fF, according to the S-parameter file. Figure 1: 3D schematic diagram of the proposed programmable coding metasurface with different beam manipulation functions. The digital control system provides the digital signals to control state of each meta-atom, and the beam and the corresponding coding pattern are shown in the right. When a bias voltage is applied to the PIN diode, the diode switches between on and off depending on the voltage. When the meta-atom is irradiated with an x-polarized wave, the reflected wave will also be changed as the diode switches. The digital signal flows as shown by the blue arrows in Figure 2c: The left patch connects to the digital control board through a via hole, while the right patch connects to the ground through another via hole. The digital signal from the bottom metal passes through the left via hole to the left patch, flows to the right patch after the PIN diode, and finally connects to the ground by the right via hole. For the 1-bit metasurface, the phase difference of the two states should be optimized to 180\({}^{\circ}\). The optimized structural parameters are as follows: w = 4 mm, p\({}_{\text{x1}}\) = 1.1 mm, p\({}_{\text{y1}}\) = 1.4 mm, p\({}_{\text{x2}}\) = 1.3 mm, p\({}_{\text{y2}}\) = 1.7 mm. Figure 3 shows the simulated reflection amplitude and phase of the designed meta-atoms under an x-polarized incident wave, which is simulated by CST Microwave Studio software with a periodic boundary. When the PIN diode is switched from the \"on\" state to the \"off\" state, the phase of the reflected wave is changed from \(-66.4^{\circ}\) to \(112.7^{\circ}\) at 27.75 GHz, which means the difference between the two states is 179.1\({}^{\circ}\). In addition, the amplitude of the reflected wave is almost constant in the operating frequency band. The simulated results show that the proposed metasurface meta-atom satisfies the requirement of \"0\" and \"1\" meta-atoms for a 1-bit digital coding metasurface. Figure 2: The 3D schematic diagram (**a**), top view (**b**), side view (**c**), and bottom view (**d**) of the meta-atom, where w = 4 mm, p\({}_{\text{x1}}\) = 1.1 mm, p\({}_{\text{y1}}\) = 1.4 mm, p\({}_{\text{x2}}\) = 1.3 mm, p\({}_{\text{y2}}\) = 1.7 mm, h\({}_{\text{h}}\) = 1 mm, h\({}_{\text{2}}\) = 0.5 mm. The left of (**b**) is the equivalent circuit of the PIN diode in “on” and “off” states. The blue arrows in (**c**) are the flow of the digital signal. To verify the beam-modulating performance of the designed digital coding metasurface, we performed full-wave simulations of the metasurface with the radiation from a pyramidal horn antenna, which can emit a spherical wave.