4.2.2. Adaptive Beam Steering with Optimal Phase Control

To validate the effectiveness of the optimal phase control scheme, firstly, we present the optimal quantized phase distribution and the corresponding beam pattern which is compared to the one from the beam synthesis scheme in Figure 13. It can be observed from Figure 13b that a better beam pattern with a higher transmission coefficient is achieved with optimal phase distribution in comparison with the one of a beam synthesis scheme.

**Figure 13.** Optimal phase control scheme results: (**a**) optimal quantized phase distribution for steering beam at (30◦, 0◦); (**b**) comparison of beam pattern between optimal phase control (Optimal) and the beam synthesis (BS) schemes.

Furthermore, we measured and compared the efficiency of power transfer between the optimal phase and random phase control schemes in Figure 14a. We also compared the optimal phase control and the beam synthesis schemes in Figure 14b. As can be seen from Figure 14, the proposed scheme demonstrates much higher efficiency in comparison with the random phase control scheme. At the same time, it is clear that the optimal one outperforms the beam synthesis scheme as indicated in Figure 14b. While around 4% efficiency is observed in the optimal phase control scheme at 50 cm with the steering angle of 30◦, only around 3% efficiency is achieved in beam synthesis scheme. By extending the size of the coding metasurface, higher power transfer efficiency will be achieved.

The above results were acquired considering only line of sight transmission. However, in actual WPT scenarios, obstacles such as humans and animals might be exposed between the transmitter (Tx) and the receiver (Rx). Hence, this would have a severe effect on power transmission efficiency. To comprehend this problem, we investigated the power transfer efficiency as a human hand and body inserted between Tx and Rx, and the results are indicated in Figure 15. It is evident that the efficiency declines almost 1% with hand blocking and almost drops to 0% with human body blockage.

Actually, we can redo the training to get the optimal phase to enhance the efficiency when the human phantom is inserted. We did re-training with a human body exposed in some positions and compared with the results without re-training as presented in the Table 2. It is clear that remarkable improvement can be achieved by re-training the programmable metasurface when humans are exposed between Tx and Rx.

Table 3 shows the comparison of the proposed system with the previous works. With a fixed beam and large dimensions, the reflect array in [26] provides a higher efficiency compared to the phased array in [27] and our work. This results not only from the large size of the surface but also from the almost ideal phase distribution used in focusing to a fixed position in this work. This shows the potential of using a metasurface in WPT. The phased array in [27] outperforms our work in transfer distance operating in the lower frequency, which suffers lower loss from transmission path but leads to a physically large system. The performance of our proposed programmable metasurface can be enhanced with a larger size of the metasurface.

**Figure 14.** Power transmission efficiency comparison: (**a**) optimal phase control and random phase control schemes with the steering angle at (30◦, 0◦); (**b**) optimal phase control (optimal) and beam synthesis (BS) schemes at different distances.

**Figure 15.** Performance comparison between no block, block with a human body and hand (Rx is 100 cm away from the metasurface (Tx)): (**a**) transmission coefficient; (**b**) efficiency.

**Table 2.** Transmission coefficient enhancement as re-training with human body exposure.


