Design and Optimization of the Cross-Frequency Negative Permeability and Near-Zero Permeability Metasurface for WPT System

Metasurface provides a promising solution to address the efficiency-distance-safety challenges in magnetic coupling resonant wireless power transfer (MCR-WPT) systems through subwavelength electromagnetic field manipulation. Current research primarily focuses on single-frequency operation or mostly MHz-band applications. It lacks theoretical and simulated studies of kHz band, let alone the cross-frequency band (both kHz and MHz simultaneously). In this article, a cross-frequency metasurface in the MCR-WPT system has been proposed. First, an equivalent circuit model of a cross-frequency metasurface has been derived. Then, EMF analysis of WPT system based on the cross-frequency metasurface has been presented. Particularly, an improved dual-population cooperative evolutionary algorithm has been employed to optimize both cross-frequency mu-negative (CF-MNG) and cross-frequency mu-near-zero (CF-MNZ) metasurfaces. Finally, the cross-frequency metasurface exhibits excellent performance on efficiency improvement and EMF leakage reduction in MCR-WPT system. The system with CF-MNG loading achieved nearly double the transfer efficiency at both 350 kHz and 6.78 MHz frequencies. Additionally, the decline of leakage electromagnetic field (EMF) with CF-MNZ metasurface can reach up to 2.42 and 6.51 dB at two frequencies, respectively. Therefore, this article not only provides significant guidance for low-frequency metasurface design but also offers potential for future applications in simultaneous power and information transfer systems.