# Electromagnetic Power Harvester Using Wide-Angle and Polarization-Insensitive Metasurfaces
## 2 Design of the MS Energy Harvester
The open-ended surface currents distribution that was generated by various incident waves from the split-ring resonant lead to single-port collection with angle and polarization sensitive performance on a split-ring structure. So, the proposed square-ring MS structure can harvesting wide-angle, polarization-insensitive incident waves by optimizing the position of the harvesting point, and maintain high efficiency when compared to the structure described in the reference [6; 10; 11; 12] only collects single-polarized incident waves. By changing the value of each parameter of the MS structure (\(L\), \(W\), \(P\), \(\varepsilon_{r}\), \(t\)), we can flexibly change the working frequency band, matching the load (R) value, to achieve the performance of effective energy harvesting. The square-ring MS structure is proposed to replace the traditional antenna as the front of the rectifier in the energy-harvesting system. It is worth pointing out that the proposed MS structure can effectively captures the ambient radiofrequency energy and then concentrated on the load resistance, which can be replaced by the rectifier circuit in the later work. The power harvesting efficiency of the MS collector can be computed by  
\[\eta=\frac{P_{L}}{P_{r}}\times 100\% \tag{1}\]  
where \(P_{L}\) is the power collected by the load, and the \(P_{r}\) is the received total power incident on the cross-sectional area (A) of the whole MS structure, which can be computed using the surface integral of a Poynting vector on A. The simulation results of the reflection coefficient S\({}_{11}\) and power harvesting efficiency are shown in Figure 4. It can be seen that the impedance matching is good at the working frequency of 2.5 GHz. That is to say, the MS structure has the ability of capturing the electromagnetic wave energy. By calculating the receiving power in the lumped port, we can see that the MS harvester can collect the energy more than 90% from the incident power at 2.5 GHz. The captured electromagnetic energy by the square-ring MS can be transferred into the matching load through vias effectively. Figure 5 is the surface current distribution on the square ring and the back ground of the MS structure at 2.5 GHz. It can be seen that the surface current flows along the small ring, and the energy is eventually harvested to the port of the resistive load. Figure 4: Reflection coefficient \(S_{11}\) and power harvesting efficiency using square-ring MS structure. The incident angle and polarization stability of MS structure should be considered from the two cases of transverse electric (TE) and transverse magnetic (TM) oblique incidences. The TE-polarized oblique incidence refers to the change of electromagnetic wave incident angles to ensure the electric field vector is always parallel with the surface of MS structure, while the TM-polarized oblique incidence refers to the change of the electromagnetic wave incident angles to ensure that the magnetic field vector is always parallel with the surface of MS structure. Figure 6a shows the power harvesting efficiency characteristics at oblique incidence with TE polarization in the resonant bands. When the harvester tilted with angle \(\theta=0^{\circ}\) and \(15^{\circ}\), the maximum harvesting efficiency achieved was 90.5% at 2.5 GHz and 90.4% at 2.52 GHz. For angle \(\theta=30^{\circ}\) and \(45^{\circ}\), collection efficiency of 89.8% at 2.56 GHz and 88.4% at 2.62 GHz. The last tilted angle is \(\theta=60^{\circ}\) and a collection efficiency of 85.2% is achieved at 2.67 GHz. For TM polarization, as shown in Figure 6b, the energy collection efficiency is 90% (when \(\theta=0^{\circ}\) at 2.5 GHz), and the maximum efficiency is 91.4% (when \(\theta=45^{\circ}\) at 2.62 GHz). When the oblique incidence \(\theta\) are \(15^{\circ}\), \(30^{\circ}\), and \(60^{\circ}\), the harvesting efficiency are 91.1% at 2.52 GHz, 91% at 2.56 GHz, and 91.2% at 2.67 GHz. The rate of change of efficiency is very small.