Theoretical Study On Nonlinear Characteristics Of Metamaterials

Metamaterials are kinds of advanced artificial materils proposed in recent years, whose unit cells'dementions are far less than the wavelength of the incident electromagnetic waves interacting with them. Nonlinear metamaterials are important parts of metamaterials. In order to control the properties of the metamaterials, the nonlinear characteristics of metamaterials must be systematically investigated. This paper studies the nonlinear characteristics of a metamaterial created by arrays of wires and split-ring resonators embedded into a nonlinear dielectric. The main points are as follows:The epsilon's nonlinearity of a two-dimensional metamaterial is analyzed. The general mathematical expression of the effective permeability for three-dimensional metamaterial with the consideration of the effects of mutual interactions among the split-ring resonators is derived; and then the dependences of the effective permeability on the varying external magnetic field with and without the mutual interaction effects are addressed, which show some significant differences of the nonlinear magnetic response between the two cases. The switching behavior of the metamaterials among right-handed materials, epsilon-negative materials, and mu-negative materials is also discussed considering the epsilon's nonlinearity and the ways for controlling the attributive characters of the metamaterial is then suggested.Based on nonlinear electromagnetic theory, the general coupled-mode equations and the Manley-Rowe relations for Stimulated Raman Scattering and Two-Photon Absorption in lossless nonlinear metamaterials are deduced respectively. The conditions for occurring Two-Photon Absorption and Stimulated Raman Scattering in nonlinear metamaterials are also discussed.TE-polarized surface waves located at the interface between an anisotropic linear material and the isotropic composite with wires and plit-ring resonators are analyzed. The dependence of the dispersion of the nonlinear propagation constant and the energy flux density on the intensity and frequency of the incident wave are theoretically derived. The existing conditons for backward waves and forward waves are also obtained. According to the changing characteristics of the energy flux density, some potential applications of this interface are proposed.