Retrieval of the effective quadratic and cubic susceptibilities in metamaterials

Abstract

The nonlinear metamaterial is considered as a cut-wire embedded in a nonlinear dielectric and its effective linear and nonlinear properties are simulated using a finite element-based software. First, the linear properties of the considered structure, the effective electric permittivity, and magnetic permeability, are determined using the standard retrieval method. Next, second- and third-order electric field localization factors are obtained, which are direct measures of the degree of inhomogeneity of the fields in the metamaterial structures. Then, considering second- and third-order nonlinearity for the embedding dielectric, complex amplitude of the fundamental and the generated nonlinear fields are obtained from transmitted and reflected signals. The effective susceptibility for each nonlinear process is retrieved using the relations obtained from the transfer matrix method. We find that the retrieved effective susceptibilities are larger compared to that of the dielectric material used in the metamaterial structure.