Nonlinear Metamaterial Lenses for Inductive Power Transmission Systems Using Duffing-Resonator Based Unit Cells

Metamaterials (MTMs) based on a periodic array of resonant coils have been shown to behave as μ-negative (MNG), enabling the focusing of magnetic flux. The phenomenon has been deployed by designers to boost the efficiency of many inductively coupled systems, such as magnetic resonance imaging, underwater and underground communications, and charging base stations (CBS) for consumer electronics and implanted devices. However, due to their dependency on high-Q unit cells, linear MNG-like MTMs have limited bandwidth, restricting their use in many applications, notably in near-field simultaneous wireless information and power transmission (NF-SWIPT) systems. To improve the tight constraints of the amplitude-bandwidth trade-off of artificial magnetic lenses, this paper presents a theoretical analysis of nonlinear MTMs based on a lattice of Duffing resonators (DRs). Additionally, it introduces a criterium for the quantification and evaluation of the amplitude-bandwidth enhancement. The analytical results are based on a circuit model and further verified by numerical simulations using commercial software. The preliminary findings in this paper open up possibilities for nonlinear MTM lenses and can be applied to enhance the linear amplitude-bandwidth limit.