On Terahertz laser pulse propagation in negative index metamaterials

The nonlinear propagation of a terahertz laser pulse propagation in the resonant region of a negative index meta-material is investigated. The resonant frequency of a split ring resonator (SRR), comprosing the negative index metamaterial, is calculated to be in the order of terahertz. The analysis shows that the negative refractive index in SRR is maintained within a narrow band of the frequency, which is more narrowed down with the intensity of the laser radiation. From Maxwell’s system of equations, a system of coupled equations descring the nonlinear propagation of laser pulse in negative index metamaterials is obtained. The system of the coupled equations are solved analytically in the high frequency and in the low frequency responses. In the high frequency response, a nonlinear field dependent dispersion relation is obtained, and the corresponding group velocity is determined. In the low frequency response, introducing the Lorentz invariant stretched coordinates, a system of coupled nonlinear Schrödinger equations (NLSE) are obtained. Considering the equal intensities of electric and magnetic fields of the laser pulse, the coupled NLSE equations are solved , which shows that the laser radiation creates bright and dark optical solitons, respectively, before and after a critical frequency, within the narrow band, determined by the intensity of the laser radiation. The instability of the bright soliton is investigated while the dark soliton is modulationally stable.