title: Nonlinear parameter retrieval from three- and four-wave mixing in metamaterials.
abstract: We present a generalized nonlinear susceptibility retrieval method for metamaterials based on transfer matrices and valid in the nondepleted pump approximation. We construct a general formalism to describe the transfer matrix method for nonlinear media and apply it to the processes of three- and four-wave mixing. The accuracy of this approach is verified via finite element simulations. The method is then reversed to give a set of equations for retrieving the nonlinear susceptibility. Finally, we apply the proposed retrieval operation to a three-wave mixing transmission experiment performed on a varactor loaded split ring resonator metamaterial sample and find quantitative agreement with an analytical effective medium theory model.
authors.affiliation: Department of Electrical and Computer Engineering, Center for Metamaterials and Integrated Plasmonics, Pratt School of Engineering, Duke University, P.O. Box 90291, Durham, North Carolina 27708, USA.
authors.forename: Alec
authors.initials: A
authors.lastname: Rose
authors.forename: Stéphane
authors.initials: S
authors.lastname: Larouche
authors.forename: Da
authors.initials: D
authors.lastname: Huang
authors.forename: Ekaterina
authors.initials: E
authors.lastname: Poutrina
authors.forename: David R
authors.initials: DR
authors.lastname: Smith