High Aperture E ﬃ ciency Array Antenna for Wireless Power Transfer Applications

: We propose a novel array antenna with high aperture e ﬃ ciency by employing an array element operating in a high-order mode to improve the transmission e ﬃ ciency of wireless power transmission applications. The proposed array element, operating at a frequency of 5.8 GHz, consists of a square patch with four metallic shorting pins, an extended cavity, and a high dielectric superstrate. The four metallic shorting pins derive the high-order operation, which can enhance the bore-sight gain, resulting in the high aperture e ﬃ ciency of the array. The extended cavity structure can help further improvement the aperture e ﬃ ciency and minimize the mutual coupling strength between adjacent elements. The proposed antenna element is extended to 2 × 2 and 4 × 4 arrays, resulting in aperture e ﬃ ciencies of 74.2% and 80.5%, respectively. For the 2 × 2 array, maximum measured gains of 19.9 dBi in the zx -plane and 18.8 dBi in the zy -plane are observed. For the 4 × 4 array, the maximum measured gains of 24.3 dBi in the zx -plane and 24.5 dBi in the zy -plane are obtained in a full-anechoic chamber. Finally, the transmission e ﬃ ciency of 6% with a distance of 0.8 m between the transmitter (Tx) and the receiver (Rx) is measured when setting up the wireless power transfer system, which consists of the Tx with the proposed 4 × 4 array and the Rx with a single element. The variance value is then calculated from the E -ﬁeld distributions when an input power of 1 W is used. The variance of the proposed array is 163.6, is 334.9 lower than the variance of 498.5 without the extended cavity structure. The results demonstrate that the extended cavity structure can lead to more uniform E-ﬁeld distributions, which can improve aperture e ﬃ ciency.


Introduction
Wireless power transmission techniques have been extensively adopted to supply electric power for household appliances, smartphones, and other electronic devices [1][2][3][4][5][6][7]. They can be classified into three categories: magnetic induction, magnetic resonance, and electromagnetic radiation methods [8]. In particular, the electromagnetic radiation method has the advantage of transmitting power to multiple receivers over relatively long distances when the array antenna is used as a transmitter. However, as the transmission distance increases, the propagation loss in free-space increases drastically, and thus the overall transmission efficiency is significantly degraded. Extensive previous studies, such as the focal point adjustment [9][10][11][12], optimization of the phase and amplitude for microstrip patches by network feed control [13][14][15], and efficient rectenna design by combining patch antennas and rectifier circuits [16][17][18][19][20], have been carried out to improve the transmission efficiency of wireless power transmission. However, studies to improve transmission efficiency in consideration of antenna gain and aperture efficiency from an array antenna perspective have not yet been sufficiently conducted.
In this paper, we propose an array antenna with high aperture efficiency by employing an array element operating in a high-order mode to improve the transmission efficiency for wireless power transmission applications. The proposed array element consists of a square patch with four metallic shorting pins, an extended cavity, and a high dielectric superstrate. As indicated in [21,22], the stacked patches are often used to improve the bandwidth characteristic of planar antennas. Although broadband can be achieved, the stacked patches are not effective in increasing the gain characteristics. After investigating various antenna design approaches, we found that the cavity structure along with the patch is significantly effective in improving the bore-sight gain, although it requires additional manufacturing costs. The four metallic shorting pins derive the high-order operation by varying the near-field distributions in the radiating patch [23][24][25][26]. This high-order operation can enhance the bore-sight gain of the antenna element without increasing the antenna aperture size, resulting in the high aperture efficiency of the array. In a previous study, this high-order mode with a fractal structure was used to increase the bore-sight and reduce the number of array elements [27]. In this work, on the other hand, the high-order mode is derived by employing the metallic shorting pins. The dielectric superstrate is placed above the patch, which is derived from the Fabry-Perot theory, to further enhance the bore-sight gain. The extended cavity structure can increase the aperture efficiency by decreasing the mutual coupling strength between adjacent elements and reducing the back radiation. The proposed element is extended to 2 × 2 and 4 × 4 arrays, and the optimal distances between elements for high aperture efficiency are examined. To verify the performance enhancement of the proposed array, aperture efficiency according to the array distance and transmission efficiency is analyzed. The radiation characteristics of the fabricated array are then measured in a full-anechoic chamber. The results demonstrate that the proposed array is suitable for achieving high aperture efficiency with enhanced transmission efficiency for wireless power transfer applications. Figure 1 shows the geometry of the proposed antenna element that consists of a square patch with four metallic shorting pins, an extended cavity, and a high dielectric superstrate (ε r = 10, tanδ = 0.004). The square patch of the side length w 1 is printed on the Duroid substrate (ε r = 2.2, tanδ = 0.0009), with side length w 2 and thickness h t . The metallic shorting pins are placed on four corners of the square patch that are connected electrically between the patch and the ground plane. These four pins enable the high-order operation by changing the pin locations ([p x1 , p y1 ], [p x2 , p y2 ], [p x3 , p y3 ], [p x4 , p y4 ]) and diameter d, which can vary near-field distributions on the patch, resulting in an enhanced bore-sight gain. The high dielectric superstrate is then placed above the patch with a height h, which is derived from the Fabry-Perot theory, to further enhance the bore-sight gain. The extended cavity structure with a height h c resides above the ground plane and surrounds the entire lateral surface of the Duroid substrate. This structure can improve the aperture efficiency and help decrease the mutual coupling strength between adjacent elements by reducing the leakage field from the antenna substrate. The antenna is fed directly by the 50 Ω SMA connector from the cavity bottom to the patch, and the feeding point is denoted as (f x , f y ). The proposed antenna is optimized using the FEKO EM simulation software [28], and the detailed antenna parameters are listed in Table 1. In the simulation, the antenna structure is modelled using piecewise triangular meshes of 1/25 wavelength, and to speed up the simulation, the multilevel fast multipole method (MLFMM) is utilized in the software. We used the computer with an Intel(R) Core (TM) i7-8700 K CPU @ 3.70 GHz and RAM of 32.0 GB. For a single antenna element, it takes 86 seconds per each frequency point, and for the 2 × 2 array, it takes 8.5 min per each frequency point.      Figure 2 presents the photographs of the fabricated antenna on the Duroid substrate with the extended cavity structure and the high dielectric superstrate. The extended cavity is made by folding copper plates and welding the folded parts, as shown in Figure 2a. The radiating patch is printed on the Duroid substrate by etching technique, and the four locations for the shorting pins are perforated Energies 2020, 13, 2241 4 of 15 through the substrate. The thick high dielectric superstrate is made by stacking four layers of a high dielectric board (CER-10, Taconic). The 50 Ω SMA connector is placed at the bottom of the extended cavity structure to provide direct feeding with the patch. The metallic shorting pins are made by soldering the perforated holes from the patch to the cavity and filling them completely with lead, as shown in Figure 2b. A 23-mm-thick Styrofoam is used between the patch and the superstrate to place the high dielectric superstrate above the patch radiator, and the antenna is installed inside a covering case to protect it from any external damage as shown in Figure 2c. Figure 2d exhibits the fully assembled antenna element.

Proposed Antenna Structure and Fabrication
Energies 2020, 13, x FOR PEER REVIEW 4 of 15 copper plates and welding the folded parts, as shown in Figure 2a. The radiating patch is printed on the Duroid substrate by etching technique, and the four locations for the shorting pins are perforated through the substrate. The thick high dielectric superstrate is made by stacking four layers of a high dielectric board (CER-10, Taconic). The 50  SMA connector is placed at the bottom of the extended cavity structure to provide direct feeding with the patch. The metallic shorting pins are made by soldering the perforated holes from the patch to the cavity and filling them completely with lead, as shown in Figure 2b. A 23-mm-thick Styrofoam is used between the patch and the superstrate to place the high dielectric superstrate above the patch radiator, and the antenna is installed inside a covering case to protect it from any external damage as shown in Figure 2c. Figure 2d exhibits the fully assembled antenna element.  Figure 3 shows the current distributions on the patch antenna surface with and without shorting pins, which is simulated using the FEKO EM simulation software [28]. The patch antenna without shorting pins operates in the TM010 mode, while the patch with shorting pins can change the current distributions to a high-order mode of TM030. Figure 4 shows the 2-D radiation patterns with and without the shorting pins. The simulated bore-sight gains with and without shorting pins are 10.7 dBi and 7.9 dBi, respectively. These results show that the patch antenna with metallic shorting pins can improve bore-sight gain by about 2.8 dB using the high-order mode operation.  Figure 3 shows the current distributions on the patch antenna surface with and without shorting pins, which is simulated using the FEKO EM simulation software [28]. The patch antenna without shorting pins operates in the TM 010 mode, while the patch with shorting pins can change the current distributions to a high-order mode of TM 030 . Figure 4 shows the 2-D radiation patterns with and without the shorting pins. The simulated bore-sight gains with and without shorting pins are 10.7 dBi and 7.9 dBi, respectively. These results show that the patch antenna with metallic shorting pins can improve bore-sight gain by about 2.8 dB using the high-order mode operation.

Simulation and Measurement
The phase angle n is calculated by the phase variation from the PEC surface to the superstrate, and also by the path differences of the multiple reflections, as shown in Equation (2) where is the wavelength of the target frequency. The power pattern S can be defined as follows: The phase angle n is calculated by the phase variation from the PEC surface to the superstrate, and also by the path differences of the multiple reflections, as shown in Equation (2) where is the wavelength of the target frequency. The power pattern S can be defined as follows:  Figure 5 illustrates the Fabry-Perot structure consisting of a perfect electric conductor (PEC) surface and a superstrate placed at a height h. The complex reflection coefficients of the PEC surface and the superstrate are e jϕ 1 and pe jϕ 2 , where p is the amplitude, and ϕ 1 , ϕ 2 are the reflection phases. The superstrate is a partially reflective surface, and we assume there is no transmission loss. The excited electromagnetic waves by a source are partially reflected by the superstrate and partially transmitted through the superstrate. The electric field intensities outside the Fabry-Perot structure are then obtained by the vector sum of multiple rays, as expressed in Equation (1) The phase angle θ n is calculated by the phase variation from the PEC surface to the superstrate, and also by the path differences of the multiple reflections, as shown in Equation (2), Energies 2020, 13, 2241 where λ is the wavelength of the target frequency. The power pattern S can be defined as follows: where f (α) is the function of the antenna pattern in the direction α. Therefore, h can be written as and we found that h is 23 mm in our geometry at 5.8 GHz. Figure 6 shows the 2-D radiation patterns with and without the superstrate. The simulated bore-sight gain with the superstrate is 13.8 dBi, whereas it is 10.7 dBi without the superstrate. These results show that the superstrate can improve the bore-sight gain by 3.1 dB using Fabry-Perot theory.
where ( ) is the function of the antenna pattern in the direction . Therefore, h can be written as and we found that h is 23 mm in our geometry at 5.8 GHz. Figure 6 shows the 2-D radiation patterns with and without the superstrate. The simulated boresight gain with the superstrate is 13.8 dBi, whereas it is 10.7 dBi without the superstrate. These results show that the superstrate can improve the bore-sight gain by 3.1 dB using Fabry-Perot theory.
where ( ) is the function of the antenna pattern in the direction . Therefore, h can be written as 12 , 42 and we found that h is 23 mm in our geometry at 5.8 GHz. Figure 6 shows the 2-D radiation patterns with and without the superstrate. The simulated boresight gain with the superstrate is 13.8 dBi, whereas it is 10.7 dBi without the superstrate. These results show that the superstrate can improve the bore-sight gain by 3.1 dB using Fabry-Perot theory.     Figure 8. This result indicates that the gain is improved 6.6 dB over the patch antenna without shorting pins. There is some Energies 2020, 13, 2241 7 of 15 discrepancy between simulation and measurement, which is due to slight variations in the effective dielectric constant and manufacturing errors of the thick superstrate. Figure 9 shows the 2-D radiation patterns of the antenna in the zxand zy-planes. For accurate measurement, the antenna is mounted on a Styrofoam with a 3-axis positioner in a full anechoic chamber. The measured half-power beamwidths at 5.8 GHz are 30 • in the zx-plane and 35 • in the zy-plane.
Energies 2020, 13, x FOR PEER REVIEW 7 of 15 GHz. The measured and simulated bore-sight gains are 15.2 dBi and 14.5 dBi at 5.8 GHz, respectively, and they are greater than 8 dBi over the entire range of 5.4-6 GHz, as shown in Figure 8. This result indicates that the gain is improved 6.6 dB over the patch antenna without shorting pins. There is some discrepancy between simulation and measurement, which is due to slight variations in the effective dielectric constant and manufacturing errors of the thick superstrate. Figure 9 shows the 2-D radiation patterns of the antenna in the zx-and zy-planes. For accurate measurement, the antenna is mounted on a Styrofoam with a 3-axis positioner in a full anechoic chamber. The measured half-power beamwidths at 5.8 GHz are 30° in the zx-plane and 35° in the zyplane.  GHz. The measured and simulated bore-sight gains are 15.2 dBi and 14.5 dBi at 5.8 GHz, respectively, and they are greater than 8 dBi over the entire range of 5.4-6 GHz, as shown in Figure 8. This result indicates that the gain is improved 6.6 dB over the patch antenna without shorting pins. There is some discrepancy between simulation and measurement, which is due to slight variations in the effective dielectric constant and manufacturing errors of the thick superstrate. Figure 9 shows the 2-D radiation patterns of the antenna in the zx-and zy-planes. For accurate measurement, the antenna is mounted on a Styrofoam with a 3-axis positioner in a full anechoic chamber. The measured half-power beamwidths at 5.8 GHz are 30° in the zx-plane and 35° in the zyplane.  GHz. The measured and simulated bore-sight gains are 15.2 dBi and 14.5 dBi at 5.8 GHz, respectively, and they are greater than 8 dBi over the entire range of 5.4-6 GHz, as shown in Figure 8. This result indicates that the gain is improved 6.6 dB over the patch antenna without shorting pins. There is some discrepancy between simulation and measurement, which is due to slight variations in the effective dielectric constant and manufacturing errors of the thick superstrate. Figure 9 shows the 2-D radiation patterns of the antenna in the zx-and zy-planes. For accurate measurement, the antenna is mounted on a Styrofoam with a 3-axis positioner in a full anechoic chamber. The measured half-power beamwidths at 5.8 GHz are 30° in the zx-plane and 35° in the zyplane.

2  2 Array Extension
The proposed antenna is then extended to a 2  2 array, as shown in Figure 10a. We used the 4way power dividers as the feeding network, as shown in Figure 10b. These dividers were used for the feeding network of the 2 x 2 array as well as the 4 x 4 array. To maximize the performance of the array for wireless power transmission applications, an optimal design of the array is carried out to maximize the array aperture efficiency. The aperture efficiency of the array can be written as where Aem is the effective maximum area of the array, and Aphysical is the physical area (A2 2 ) of the array aperture. The effective maximum area Aem can be written as 2 . 4 em AG    (6) where  and G represent the wavelength and the antenna gain, respectively. Figure 10c shows the aperture efficiency according to the distance d2 between adjacent elements at 5.8 GHz. The solid line and dashed line indicate the aperture efficiencies with and without the extended cavity structure, respectively. The maximum aperture efficiencies with and without the cavity structure are 74.2% (d2 = 7.5 mm) and 61.2% (d2 = 2.5 mm), respectively. Additionally, the maximum aperture efficiency of the array without shorting pins is 22.05% (d2 = 0 mm). To analyze the effectiveness of the proposed extended cavity structure, we observe the E-field distributions (Ey) on the 2  2 array surface (−75 mm  x, y  75 mm) at z = 57.6 mm with and without the cavity, as shown in Figure 11. The variance value is then calculated from the E-field distributions when an input power of 1 W is used. The variance of the proposed array is 163.6, which is 334.9 lower than the variance of 498.5 without the extended cavity structure. The results demonstrate that the extended cavity structure can lead to more uniform E-field distributions, which can improve aperture efficiency.

2 × 2 Array Extension
The proposed antenna is then extended to a 2 × 2 array, as shown in Figure 10a. We used the 4-way power dividers as the feeding network, as shown in Figure 10b. These dividers were used for the feeding network of the 2 × 2 array as well as the 4 × 4 array. To maximize the performance of the array for wireless power transmission applications, an optimal design of the array is carried out to maximize the array aperture efficiency. The aperture efficiency η of the array can be written as where A em is the effective maximum area of the array, and A physical is the physical area (A 2 2 ) of the array aperture. The effective maximum area A em can be written as where λ and G represent the wavelength and the antenna gain, respectively. Figure 10c shows the aperture efficiency according to the distance d 2 between adjacent elements at 5.8 GHz. The solid line and dashed line indicate the aperture efficiencies with and without the extended cavity structure, respectively. The maximum aperture efficiencies with and without the cavity structure are 74.2% (d 2 = 7.5 mm) and 61.2% (d 2 = 2.5 mm), respectively. Additionally, the maximum aperture efficiency of the array without shorting pins is 22.05% (d 2 = 0 mm). To analyze the effectiveness of the proposed extended cavity structure, we observe the E-field distributions (E y ) on the 2 × 2 array surface (−75 mm ≤ x, y ≤ 75 mm) at z = 57.6 mm with and without the cavity, as shown in Figure 11. The variance value is then calculated from the E-field distributions when an input power of 1 W is used. The variance of the proposed array is 163.6, which is 334.9 lower than the variance of 498.5 without the extended cavity structure. The results demonstrate that the extended cavity structure can lead to more uniform E-field distributions, which can improve aperture efficiency.   Subsequently, we analyze the effect of the extended cavity structure on the beam characteristics of the array. For this purpose, the bore-sight gains of the active element pattern according to d 2 are examined, as shown in Figure 12a. The maximum bore-sight gain of 14.1 dBi (d 2 = 15 mm) is observed for the proposed antenna with the cavity structure, whereas the maximum bore-sight gain of 12.7 dBi (d 2 = 2.5 mm) is observed without the cavity structure. Figure 12b shows the error in the bore-sight beam direction depending on d 2 , where the ideal beam direction is θ = 0 • in the active element pattern. Herein, the proposed antenna has an asymmetric feeding structure, which causes deviations in the bore-sight beam direction. The proposed array antenna has a lower than 1.2 • of the average errors when varying d 2 from 0 mm to 20 mm, which is much less than the average error of 9.1 • without the cavity structure. To further validate the effect of the extended cavity structure, we examine the average mutual couplings (|S 21 |, |S 31 |, and |S 41 |) of the 2 × 2 array according to d 2 , as shown in Figure 12c. We also measure the coupling using network analyzer (HP3753D). Port 1 of the network analyzer is connected to the upper left antenna in the array, and Port 2 is connected to the other three antennas one at a time. Except for the two measuring antennas, the other antennas are terminated by 50 Ω. The measured average mutual coupling between antennas is −32 dB, and the simulation value is −34 dB when d 2 = 7.5 mm. The proposed array antenna with the cavity structure again shows a lower mutual coupling than the array without the cavity structure. These results demonstrate that the extended cavity structure can minimize the mutual coupling strength between adjacent elements, resulting in an increased bore-sight gain with a low error in the bore-sight beam direction.
Energies 2020, 13, x FOR PEER REVIEW 10 of 15 examined, as shown in Figure 12a. The maximum bore-sight gain of 14.1 dBi (d2 = 15 mm) is observed for the proposed antenna with the cavity structure, whereas the maximum bore-sight gain of 12.7 dBi (d2 = 2.5 mm) is observed without the cavity structure. Figure 12b shows the error in the bore-sight beam direction depending on d2, where the ideal beam direction is  = 0° in the active element pattern.
Herein, the proposed antenna has an asymmetric feeding structure, which causes deviations in the bore-sight beam direction. The proposed array antenna has a lower than 1.2° of the average errors when varying d2 from 0 mm to 20 mm, which is much less than the average error of 9.1° without the cavity structure. To further validate the effect of the extended cavity structure, we examine the average mutual couplings (|S21|, |S31|, and |S41|) of the 2  2 array according to d2, as shown in Figure  12c. We also measure the coupling using network analyzer (HP3753D). Port 1 of the network analyzer is connected to the upper left antenna in the array, and Port 2 is connected to the other three antennas one at a time. Except for the two measuring antennas, the other antennas are terminated by 50 . The measured average mutual coupling between antennas is -32 dB, and the simulation value is −34 dB when d2 = 7.5 mm. The proposed array antenna with the cavity structure again shows a lower mutual coupling than the array without the cavity structure. These results demonstrate that the extended cavity structure can minimize the mutual coupling strength between adjacent elements, resulting in an increased bore-sight gain with a low error in the bore-sight beam direction.   Figure 13 shows the simulated and measured radiation patterns of the proposed 2 × 2 array, which is fed by a 4-way power divider. The maximum measured gains are 19.9 dBi in the zx-plane and 18.8 dBi in the zy-plane. The simulated maximum gain is 20.0 dBi in both the zxand zy-planes. The measured and simulated half-power beamwidths are 14.4 • and 14.1 • in the zx-plane, while 15 • and 14.5 • in the zy-plane. In the zy-plane, the simulated radiation pattern is not symmetrical with respect to 0 • , and this is due to the asymmetric feeding structure of the array antenna.
Energies 2020, 13, x FOR PEER REVIEW 11 of 15 Figure 13 shows the simulated and measured radiation patterns of the proposed 2  2 array, which is fed by a 4-way power divider. The maximum measured gains are 19.9 dBi in the zx-plane and 18.8 dBi in the zy-plane. The simulated maximum gain is 20.0 dBi in both the zx-and zy-planes. The measured and simulated half-power beamwidths are 14.4° and 14.1° in the zx-plane, while 15° and 14.5° in the zy-plane. In the zy-plane, the simulated radiation pattern is not symmetrical with respect to 0°, and this is due to the asymmetric feeding structure of the array antenna.

4  4 Array Extension
To achieve higher gain characteristics, we extend the proposed antenna to a 4  4 array, as shown in Figure 14a. Figure 14b shows the aperture efficiency according to the distance d4, and the maximum aperture efficiency of 80.5% is achieved when d4 is 0 mm. Figure 15a

4 × 4 Array Extension
To achieve higher gain characteristics, we extend the proposed antenna to a 4 × 4 array, as shown in Figure 14a. Figure 14b shows the aperture efficiency according to the distance d 4 , and the maximum aperture efficiency of 80.5% is achieved when d 4 is 0 mm. Figure 15a Figure 13 shows the simulated and measured radiation patterns of the proposed 2  2 array, which is fed by a 4-way power divider. The maximum measured gains are 19.9 dBi in the zx-plane and 18.8 dBi in the zy-plane. The simulated maximum gain is 20.0 dBi in both the zx-and zy-planes. The measured and simulated half-power beamwidths are 14.4° and 14.1° in the zx-plane, while 15° and 14.5° in the zy-plane. In the zy-plane, the simulated radiation pattern is not symmetrical with respect to 0°, and this is due to the asymmetric feeding structure of the array antenna.

4  4 Array Extension
To achieve higher gain characteristics, we extend the proposed antenna to a 4  4 array, as shown in Figure 14a. Figure 14b shows the aperture efficiency according to the distance d4, and the maximum aperture efficiency of 80.5% is achieved when d4 is 0 mm. Figure 15a  To investigate the efficiency of wireless power transfer between antennas in free space, we set up the system consisting of the transmitter (Tx) with the proposed 4  4 array and the receiver (Rx) with a single element. Instead of using a probe, we use the identical single element for the Rx. Since the power transmission is for indoor environment, the distance in the transmission efficiency measurement is less than 2 m, that is in the near-radiating zone, as shown in Figure 16a. We calculate the transmission efficiency using formula as written (Equation (7)). The measured and simulated To investigate the efficiency of wireless power transfer between antennas in free space, we set up the system consisting of the transmitter (Tx) with the proposed 4 × 4 array and the receiver (Rx) with a single element. Instead of using a probe, we use the identical single element for the Rx. Since the power transmission is for indoor environment, the distance in the transmission efficiency measurement is less than 2 m, that is in the near-radiating zone, as shown in Figure 16a. We calculate Energies 2020, 13, 2241 13 of 15 the transmission efficiency using formula as written (Equation (7)). The measured and simulated maximum transmission efficiencies are 6% and 7%, respectively, when the distance between Rx to Tx is 0.8 m. We also compare the properties between the proposed antenna and three reference previous research. In this comparison, we examine the operating frequency, aperture size, and the transmission efficiency. The detailed explanations are given in Table 2.
Energies 2020, 13, x FOR PEER REVIEW 13 of 15 maximum transmission efficiencies are 6% and 7%, respectively, when the distance between Rx to Tx is 0.8 m. We also compare the properties between the proposed antenna and three reference previous research. In this comparison, we examine the operating frequency, aperture size, and the transmission efficiency. The detailed explanations are given in Table 2.

Conclusions
An array antenna with a high aperture efficiency was proposed by employing an array element operating in a high-order mode to improve the transmission efficiency for wireless power transmission applications. The proposed array element consisted of a square patch with four metallic shorting pins, an extended cavity, and a high dielectric superstrate. The proposed array element characteristics, such as the reflection coefficient, bore-sight gain, and radiation patterns, of the proposed antenna were measured, and the average reflection coefficient was 15.0 dB with a bandwidth of 400 MHz (5.6 GHz to 6 GHz, |Γ| < −10 dB). The bore-sight gains were 15.2 dBi, and the measured half-power beamwidths were 30° in the zx-plane and 35° in the zy-plane. The proposed antenna element was extended to 2  2 and 4  4 arrays, resulting in aperture efficiencies of 74.2% and 80.5%, respectively. The maximum measured gains of 19.9 dBi in the zx-plane and 18.8 dBi in the zy-plane for the 2 × 2 array and 24.3 dBi in the zx-plane and 24.5 dBi in the zy-plane for the 4 × 4 array are observed in a full-anechoic chamber. The transmission efficiency of 6% with a distance of 0.8 m between the Rx and the Tx was measured when setting up the wireless power transfer system consisting of the Tx with the proposed 4  4 array and the Rx with a single element.

Conclusions
An array antenna with a high aperture efficiency was proposed by employing an array element operating in a high-order mode to improve the transmission efficiency for wireless power transmission applications. The proposed array element consisted of a square patch with four metallic shorting pins, an extended cavity, and a high dielectric superstrate. The proposed array element characteristics, such as the reflection coefficient, bore-sight gain, and radiation patterns, of the proposed antenna were measured, and the average reflection coefficient was −15.0 dB with a bandwidth of 400 MHz (5.6 GHz to 6 GHz, |Γ| < −10 dB). The bore-sight gains were 15.2 dBi, and the measured half-power beamwidths were 30 • in the zx-plane and 35 • in the zy-plane. The proposed antenna element was extended to 2 × 2 and 4 × 4 arrays, resulting in aperture efficiencies of 74.2% and 80.5%, respectively. The maximum measured gains of 19.9 dBi in the zx-plane and 18.8 dBi in the zy-plane for the 2 × 2 array and 24.3 dBi in the zx-plane and 24.5 dBi in the zy-plane for the 4 × 4 array are observed in a full-anechoic chamber. The transmission efficiency of 6% with a distance of 0.8 m between the Rx and the Tx was measured when setting up the wireless power transfer system consisting of the Tx with the proposed 4 × 4 array and the Rx with a single element.