Euler-Lagrange method for low-frequency metamaterials

Purpose The purpose of this paper is to develop a modeling method for the analysis of low-frequency metamaterials (MTMs) and their near-field applications. Design/methodology/approach The Euler-Lagrange method is introduced. An MTM is modeled as a multi-degree-of-freedom system without homogenization. The properties and the responses of the MTM in a near-field device are readily and rigorously studied through the motion equation derived from the Lagrange equations. The resonance frequencies and the corresponding resonance modes are solved from the characteristic equation. Findings The numerical results of the proposed method show good agreement with the experimental ones. A measurement of MTM-core coil resistance and inductance shows high accuracy of the proposed method. Originality/value The proposed Euler-Lagrange method provides a new study perspective and enables more flexible, rigorous and straightforward analysis of low-frequency MTMs in near-field applications. Consequently, the presented work greatly facilitates further explorations and studies on various novel MTM-based low-frequency near-field devices and systems.