An electromagnetic parameters extraction method for metamaterials based on phase unwrapping technique

Abstract

A new method of extracting effective permittivity and permeability of metamaterials has been developed in this paper. Scattering parameters are used to represent effective wave impedance and refractive index of the metamaterials. Considering analytical continuation of effective refractive index of the metamaterials in the upper half of a complex angular frequency plane, a phase unwrapping technique has been implemented to solve branch ambiguity of the refractive index caused by complex inverse cosine function. An empirical formula to estimate the starting frequency in the phase unwrapping technique has been developed to improve the efficiency of the parameter retrieval procedure. Numerical results including five slabs of rods and split-ring resonators (SRRs) and a structure composed of two SRRs and four capacitively loaded strips are given to demonstrate good accuracy, high efficiency, and noise insensitivity of the proposed retrieval method.