Optical solitons in negative-index meta-materials

The nonlinear propagation of gigahertz electromagnetic wave propagation in the resonant region of a negative index meta-material is investigated. It is found that the negative refractive index is maintained within a narrow band of frequency which is more narrowed down with the intensity of the radiation. In the high frequency response, the nonlinear field dependent dispersion relation is obtained, and the corresponding group velocity is determined. In the low frequency response, coupled nonlinear Schrödinger equations are obtained which show the creation of bright and dark optical solitons. The bright soliton is a fast mode and it is modulationally unstable. The dark soliton is a slow mode and it is modulationally stable. Applications of these results to terahertz spectrums and in the photonic crystals are mentioned.