## 3 Performance in Wireless Power Transmission  
The wireless power transmission performance capabilities of the proposed RDA with the EBGs are investigated. The simulation model, as shown in Figure 9, was performed using CST Microwave Studio. The receiver antenna is a single CP Koch-shaped patch antenna operating at 5.2 GHz and is located along the \(+z\)-direction. Here, 5 \(\times\) 5 Koch-shaped patch arrays with and without EBGs are used as wireless power transmitters, transmitting a total power of 50 W. The power transmitter and receiver are enclosed by a concrete box filled with air to approximate a practical indoor environment. The concrete box has overall dimensions of 2 \(\times\) 1.2 \(\times\) 1.2 m\({}^{3}\). Approximately 400 million mesh cells are used for each simulation of the wireless power transmission. All simulations are run on a computer with an Intel Core i7-5960X 3.0 GHz CPU and 128 GB of RAM integrated with two NVIDIA Quadro P6000 GPUs. The average runtime is approximately four hours for each simulation. The wireless power transmission procedure involves two steps. In the first step, only the receiver antenna was excited, and the transmission coefficient phase from the receiver antenna to each of the antenna elements of the power transmitter were recorded. The phase profile was then analyzed through phase conjugation at each antenna element. In the second step, all of the antenna elements of the power transmitter were simultaneously excited with the conjugate-phase profile, forming a wireless power beam back in the reverse direction to the power receiver. The wireless power transmission performance is evaluated by analyzing the amount of received power at the receiver. To realize a far-field retrodirective scenario, the distance between the power transmitter and the power receiver is set to 1 m. Received power of 0.2685 W was harvested by the receiver when the power was transmitted by the RDA with the EBGs. Meanwhile, when the power was transmitted by the RDA without the EBGs, only 0.2412 W of power was received. Therefore, an improvement of 11.32% is achieved using the RDA with the EBGs. For a further investigation, three 10 \(\times\) 10 arrays, in this case two RDAs without the EBGs having an inter-element spacing of 0.5\(\lambda\) and 0.4\(\lambda\) and one RDA with the EBGs having an inter-element spacing of 0.4\(\lambda\), are used as the wireless power transmitters. The total transmitted power is 50 W. The distance between the transmitter and receiver is kept at 1 m so that a near-field retrodirective scenario is realized. The simulated results of the received powers are summarized in Table 1. For the case without EBGs, 1.339 W of power was received when using the RDA with an inter-element spacing of 0.5\(\lambda\), whereas when the inter-element spacing is reduced to 0.4\(\lambda\), the received power was only 0.827 W, representing a significant decrease. This reduction in the received power was mainly caused by the reduced gain which resulted when the inter-element spacing was decreased from 0.5 to 0.4\(\lambda\). However, with an inter-element spacing as small as 0.4\(\lambda\), the gain enhancement can be achieved by suppressing the mutual coupling effects, hence improving the received power. By using the EBGs to reduce mutual  
Figure 8: Simulated radiation patterns of the 5 \(\times\) 5 CP RDA arrays with EBGs (solid line curve) and without EBGs (dashed line curve) at 5.2 GHz: (**a**) \(xz\)-plane and (**b**) \(yz\)-plane. coupling, 0.930 W of power could be harvested, showing an improvement of 12.45% compared to the CP RDA without the EBGs. Finally, the wireless power transmission performance capabilities when the power receiver moves along the \(x\)- and \(y\)-directions were investigated.