A Retrieval Method of Effective Electromagnetic Parameters for Inhomogeneous Metamaterials

In this paper, we develop a method to extract effective electromagnetic parameters of inhomogeneous metamaterials. Starting with a two-layer inhomogeneous structure, the relationship between S-parameters and effective electromagnetic parameters of each layer, including wave impedance and refractive index, is derived. A recursion procedure in terms of S-parameters is developed to deal with an m-layer inhomogeneous structure. To ensure consistency and correctness of the retrieved electromagnetic parameters, an iterative solution procedure is proposed. An iterative error analysis is given to show that with the increase of iterative steps, the resulting error is accumulated. Therefore, a direct solution approach based on nonlinear equation systems is developed. Several inhomogeneous examples, including material and metamaterial structures, are given to demonstrate validity, feasibility, and noise insensitivity of the proposed method.