Large Surface LC-resonant Metamaterials: from Circuit Model to Modal Theory and Efficient Numerical Methods

Laurent Krähenbühl (1, 2) , Riccardo Scorretti (3, 2) , Arnaud Bréard (1, 2) , Christian Vollaire (1, 2) , Jean Michel Guichon (4, 2) , Olivier Chadebec (4, 2) , Gérard Meunier (4, 2) , A Urdaneta-Calzadilla (4) , Viviane Cristine Silva (5, 2) , Carlos Antonio França Sartori (5, 2)

1 MIS - Ampère, Département Méthodes pour l'Ingénierie des Systèmes
2 LIA817 - LIA franco brésilien James Clerk Maxwell (CNRS-CNPq)
3 BioIng - Ampère, Département Bioingénierie
4 G2ELab - Laboratoire de Génie Electrique de Grenoble
5 Escola Politecnica da Universidade de Sao Paulo [Sao Paulo]

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 giving 10^6 unknowns with full 10^6x10^6 matrix). For the first time, we highlight the modal character of the spatial 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 dramatically lighten the system of equations, which opens the way to develop more efficient numerical methods.

Mots clés: LC metamaterials; integral equations; matrix reduction; resonance; circuit analysis; modal analysis; homogenization

Domaines: Energie électrique; Electromagnétisme; Sciences de l'ingénieur [physics]

Laurent Krähenbühl, Riccardo Scorretti, Arnaud Bréard, Christian Vollaire, Jean Michel Guichon, et al.. Large Surface LC-resonant Metamaterials: from Circuit Model to Modal Theory and Efficient Numerical Methods. IEEE Transactions on Magnetics, 2020, 56 (2), pp.6701504. ⟨10.1109/TMAG.2019.2952541⟩. ⟨hal-02194948⟩