Effective medium theory of a concentric metamaterial bifunctional cloak

Abstract This study investigates a bifunctional cloak composed of concentric metamaterials arranged in 4N thin layers, where N denotes the number of periodic layer pairs within the structure. The structure includes an inner circular domain, an outer domain, and alternating sequences of 2N layers between them. We explore two models: one using isotropic materials and another one using anisotropic materials. The anisotropic model demonstrates superior cloaking performance for both electrical and thermal fields. Analytical solutions based on the Effective Medium Theory and boundary-value problems reveal the structure’s response under quasi-static conditions. Numerical simulations using COMSOL validate these findings, highlighting the cloak’s and concentration’s ability to manipulate external thermal and electric fields efficiently.