A retrieval method for nonlinear metamaterials

Metamaterials are engineered periodic structures for which it is possible to assign effective homogenized constitutive properties. In recent years, metamaterials in which the constituent elements are integrated with inherently nonlinear materials or electronic components have been considered for their potential impact on nonlinear wave propagation. As is the case with their linear counterparts, nonlinear metamaterials can also be assigned homogenized effective properties. The effective constitutive parameters of a metamaterial can be determined by a retrieval method applied to full-wave numerical simulations of a single layer of the structure. In this work, we present a transfer matrix approach that extends the retrieval of metamaterial properties to include the effective nonlinear susceptibilities. Comparisons with time-domain finite element simulations of continuous nonlinear slabs confirm the validity of this approach. The proposed approach is also applied to determine the nonlinear susceptibility of a simple nonlinear metamaterial.