Abstract
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.
Highlights
Over the last 20 years or so, flat, compact, and light artificial lenses inspired by metamaterials (MTMs) have attracted a lot of attention due to their flexibility, controllability, low profile, and reduced cost
If the periodicity of such arrays and the dimensions of their cells are much smaller than their operating wavelength, they can be shown to behave as ideal left-handed materials with negative constitutive parameters, such as magnetic permeability μ, electric permittivity ε, and/or refraction index n, around its resonance frequency
This work theoretically investigates the potential use of nonlinear Duffing resonators (DRs) as the unit cells of MNG lenses with enhanced amplitude-bandwidth characteristics
Summary
Over the last 20 years or so, flat, compact, and light artificial lenses inspired by metamaterials (MTMs) have attracted a lot of attention due to their flexibility, controllability, low profile, and reduced cost. Lenses do not require a 3D nonuniform distribution of its constitutive parameters in order to focus the EM fields as the “positive” ones do This means that the concave or convex geometry of conventional lenses can be simplified to a flat structure, reducing the system’s profile and its manufacturing costs. This work theoretically investigates the potential use of nonlinear Duffing resonators (DRs) as the unit cells of MNG lenses with enhanced amplitude-bandwidth characteristics. Such a nonlinear resonance has been applied to radiofrequency (RF) energy harvesters and wireless power transmission using strongly coupled coils [14,15]. The presented analytical results are supported by numerical simulations using Keysight Pathwave ADS 2021
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