Analysis,Design,and Applications Of Low-Frequency Metamaterials

High-performance electromagnetic materials are the milestones in both enhancing the performances of existing electromagnetic devices and systems and developing novel ones.Consequently,the study of the high-performance electromagnetic material has been an eternal topic in electrical engineering,and has significant potential in both electromagnetism and engineering applications.Metamaterials(MTMs)are novel artificial materials,exhibiting exotic electromagnetic properties including negative permeability and/or permittivity on some frequencies.The theory and applications of MTMs in high-frequency electromagnetics and optics have been widely investigated.Recently,low-frequency MTMs in near field electromagnetic devices and systems,mainly covering wireless power transfer,magnetic resonance imaging,and magnetic shielding,have become an emerging research focus.Compared with that of high-frequency MTMs study,the state-of-art for low-frequency MTMs study is still in the concept proving,computer simulation,and experimental verification stage.Consequently,it is demanding for the systematic analysis theory and numerical computation methods.Moreover,the existing analysis methodologies for low-frequency MTMs are still basically inherited from those for high-frequency MTMs.For instance,the unit cell simulation,effective parameter extraction,and experimental methods of low-frequency MTMs are still based on electromagnetic wave theory.The time domain computation methods for MTM-included electromagnetic systems are also oriented for electromagnetic waves instead of low-frequency quasi-static fields.Nevertheless,because the spatial dimension of low-frequency near field systems are much smaller than the wavelength of the operation frequency,the electrical and magnetic fields are almost decoupled in such cases.As a result,the analysis and computation methods of low-frequency MTMs are inevitably not identical to those of high-frequency MTMs.In addition,the operating frequency of MTMs in existing low-frequency applications is usually in MHz frequency band.The low-frequency MTMs are still subject to great limitations including large spatial dimensions and monotonous application scenarios that preventing MTMs being applied in devices and systems operating at k Hz and even lower frequency bands.In this regard,based on a research project of national natural science foundation of China entitled “Analysis,theory,and design of low-frequency metamaterials and its applications”,this dissertation is dedicated to the analysis theory,the time domain numerical method,and the applications of low-frequency MTMs.The novelties are summarized as:1.The theory and design of miniaturized low-frequency magnetic MTMs based on the continuous media theory.Spirals on printed circuit board,connected with lumped capacitors,are used as the unit cells for the low-frequency MTMs,which reduces the resonance frequency to k Hz band while keeping the spatial dimension miniaturized.RLC circuit is used to characterize the response of the MTM unit cells,and the effective permeability of the MTM is deduced.The unit cell simulation method for low-frequency MTMs based on quality factor equivalency is proposed.The one-dimensional stacking MTMs are proposed and verified in experimental studies.The stored magnetic energy density in low-frequency MTMs is deduced based on electrodynamics,demonstrating the positive magnetic energy density in MTMs.2.The time domain finite element method for MTM-included low-frequency near field systems.The non-standard Lorentz model is used to characterize the magnetic response of lowfrequency MTMs.The governing equations are deduced using the convolution method and the auxiliary method,respectively.The accuracy of the proposed time domain methods is verified through a numerical case study.3.The Euler-Lagrange method for low-frequency MTMs.The MTMs are modeled as multidegree-of-freedom systems with damping.The Euler-Lagrange equation for low-frequency MTMs is derived.The system resonance is obtained from the characteristic equation.The proposed Euler-Lagrange method is verified by experimental studies on one-dimensional stacking MTMs and a two-dimensional MTM slab.The relation between the Euler-Lagrange method and the continuous media method,the physical mechanisms of low-frequency MTMs,and the rigorous and accurate modeling of two-dimensional MTMs(metasurface)are presented and discussed.4.Engineering applications of low-frequency MTMs.Based on the proposed one-dimensional stacking MTMs,the MTM-core eddy current nondestructive testing probe and the MTM-core concentric transformer are proposed,fabricated,and verified by both numerical and experimental studies.The MTM-core eddy current testing probe exhibits enhanced sensitivity near the electrical resonance frequency.The MTM-core transformer achieves extra-high voltage ratio and significant voltage phase shift on some frequencies,and exhibits band-stop characteristics in the active power transmission.