A Hybrid Numerical-Analytical Approach for Scalable Metasurface Design in Focused Long-Range Wireless Power Delivery

This paper presents a low-frequency metasurface that generates a highly focused magnetic field when excited by an actively fed transmitting coil for long-range resonant inductive wireless power transfer. A theoretical framework based on magnetic dipole theory is derived to calculate the optimal currents required to shape the magnetic field into a confined hotspot at a target working distance. The optimization process maximizes the correlation between the desired field distribution and the combined contributions of the metasurface and transmitter. To verify the design methodology, practical considerations are deployed to effectively design the metasurface unit cell, an asymmetrically twisted double-layer spiral, able to maximize inductance while maintaining the ohmic losses low. Then, a 5×5 metasurface array, covering an overall area of 22 cm × 22 cm and operating at 4 MHz, undergoes validation through numerical simulations and experimental testing. Simulations revealed a 40 mm diameter hotspot (~λ/1800) at a distance of 10 cm from the transmitter, with experimental results from a PCB prototype confirming these findings and estimating a power transfer 18 dB higher in the focusing region with respect to no metasurface configuration. Besides, the system demonstrated robustness by maintaining focus despite variations in the metasurface-to-transmitter distance. This work provides a practical, scalable solution to address distance limitations in magnetic near field focusing, eliminating the need for guiding structures such as ferrites and simplifying design for WPT applications.