The Euler–Lagrange method is proposed for the rigorous modeling of low-frequency metamaterial (MTM) slabs in near field systems. The mechanisms of the extraordinary performance-enhancing capabilities of MTM slabs in near field systems are analyzed in numerical studies. The proposed method is verified by experimental studies of a prototype MTM-coil system. This work focuses on low-frequency MTM slabs and enables rigorous, flexible, and feasible analysis of MTM-based near field systems in electrical engineering.
HollowayC.L., A discussion on the interpretation and characterization of metafilms/metasurfaces: The two-dimensional equivalent of metamaterials, Metamaterials3 (2009), 100–112.
2.
GuanH.LiuL.YangS. and ChenX., Efficiency enhancement of wireless power transfer system by using resonant coil and negative permeability metamaterial, Int. J. Appl. Elctrom.59 (2019), 647–655.
3.
LuC., Investigation of negative and near-zero permeability metamaterials for increased efficiency and reduced electromagnetic field leakage in a wireless power transfer system, IEEE Trans. Electromag. Compat.61 (2019), 1438–1446.
4.
NumanA.B. and SharawiM.S., Extraction of material parameters for metamaterials using a full-wave simulator, IEEE Antenn. Propag. M.55 (2013), 202–211.
5.
ChoY., Thin hybrid metamaterial slab with negative and zero permeability for high efficiency and low electromagnetic field in wireless power transfer systems, IEEE Trans. Electromag. Compat.60 (2018), 1001–1009.
6.
AlmoneefT.S. and RamahiO.M., A 3-dimensional stacked metamaterial arrays for electromagnetic energy harvesting, Prog. Electromagn. Res.146 (2014), 109–115.
7.
GiessenH. and LiuN., Coupling effects in optical metamaterials, Angew. Chem. Int. Ed.49 (2010), 9838–9852.
8.
SersicI., Electrical and magnetic dipole coupling in near-infrared split-ring metamaterial arrays, Phys. Rev. Lett.103 (2009), 213902.
9.
GoldsteinH.PooleC. and SafkoJ., Variational principles and Lagrange’s equations, in: Classical Mechanics, Addison Wesley, 2000, pp. 34–64.
