Theoretical studies on the epsilon’s nonlinearity of a left-handed material

In order to realize the tunable transmission properties of left-handed materials (LHMs), based on the nonlinear optics theory, we study the epsilonpsilas nonlinearity of a two-dimensional composite created by arrays of wires and split-ring resonators embedded into a nonlinear dielectric. We calculate the dependences of the real part and imaginary part of the effective permittivity of the structure on the varying external magnetic field strength. The results show that the real part of the effective permittivity has hysteresis structures, and the switching of the material among different kinds (RHM, LHM, ENG, MNG) under some conditions can be controlled by a proper choice of the strength of the external magnetic field (intensity of incident electromagnetic waves) at a certain frequency. This phenomenon may be used to realize the switching between left-handed materials and right-handed materials.