## 1 Introduction  
Recently, wireless power transfer systems (WPTSs) have gained more attention in various applications owing to their advantages of convenience and safe user experience. On the basis of their required operating distance and amount of power, they can be classified into radiative and non-radiative types [1; 2; 3; 4; 5; 6; 7; 8]. A radiative WPTS is based on a range of microwave frequencies and laser techniques and is widely used in high-power and far-field applications. On the other hand, a non-radiative WPTS uses near-field coupling of electric or magnetic fields [6; 7; 8]. It is quite popular for short-distance applications such as charging consumer electronics, electric vehicles, and intra-vehicles. However, after a certain charging distance, its power transfer efficiency (PTE) decreases, and magnetic field leakage occurs. As shown in Figure 1, a stand-alone transmitting (Tx) coil can simultaneously generate a uniform magnetic field at its front and back. For charging applications, the receiving (Rx) coil is placed at the target area, and the magnetic field in the non-target area is called the magnetic field leakage. The magnetic field leakage can be harmful to people in the vicinity and cause electromagnetic interference to nearby equipment. According to the guidelines of the International Commission on Non-Ionizing Radiation Protection (ICNIRP), the magnetic field leakage should be minimized to a safe level of 270 mG for humans [9]. Several studies are underway to minimize magnetic field leakage and improve PTE [10; 11; 12; 13; 14; 15; 16; 17; 18; 19]. For example, the PTE can be improved using coated wires such as litz and magneto-plated wires [10], by adding relay coils [11], or by using metamaterials [17; 18; 19]. For magnetic shielding, placement of ferromagnetic materials or ferrites behind the Tx and Rx coils are widely used in very low frequency (VLF) to low frequency (LF) applications [12; 13]. In previous studies [14; 15; 16], magnetic shielding has been implemented using additional active or passive cancelation coils placed behind the Tx coils, which can generate the magnetic field in the opposite direction to the backside of the Tx coil. Even though this work can greatly mitigate magnetic field leakage, the complexity of the system increases, and it is not quite useful enough to improve the PTE performance of WPTSs. Another approach for achieving complete magnetic shielding while improving the PTE is to use a perfect magnetic conductor (PMC) as a back plate, which can be realized by designing artificial magnetic conductors (AMCs) [20]. Ideally, the AMC can provide a \(\pm 180^{\circ}\) reflection phase owing to its high surface impedance and parallel image current, and eliminate backward radiation while enhancing the radiation toward the front when it is placed behind the antenna [21; 22; 23; 24]. As it acts as a reflector, greatly enhancing unidirectional radiation with increased efficiency, the AMC design is widely used in the microwave frequency of the low-profile, relatively high-gain antenna design. However, its use at a relatively low frequency is limited [24] because the size of the AMC depends on its wavelength, making it large at low-frequency applications. Only a few studies have focused on using AMCs for WPTS applications. [PERSON] et al. [25] performed a simulation using the ideal PMC condition and verified that it improved the PTE performance compared with using an ideal PEC behind the Tx coil. [PERSON] et al. [26] designed an AMC for an operating frequency of 23 MHz. Meanwhile, [PERSON] et al. [27] designed an AMC using a ferrite substrate where the metallic frequency selective surface (FSS) pattern is placed directly on the ferrite to generate a frequency of 6.78 MHz, although the performance was verified only by simulations. The merit of these AMCs is in their magnetic shielding performances.