Large surface LC-resonant metamaterials: from circuit model to modal theory and efficient numerical methods

We study the harmonic magnetodynamic behavior (without wave propagation) of a resonant surface metamaterial, made up of many identical and regularly arranged LC cells. The circuit model gives the exact solution, but is not numerically efficient for the simulation of very large structures (e.g. 1000x1000 cells). For the first time, we highlight the modal character of the solutions, which makes it possible to explain their frequency and spatial related properties. From these results, we show under what assumptions it is possible to homogenize the metamaterial, which opens the way for using this approach together with efficient numerical methods.