Stability criterion for Gaussian pulse propagation through negative index materials

Abstract

We analyze the dynamics of propagation of a Gaussian light pulse through a medium having a negative index of refraction employing the recently reported projection operator technique. The governing modified nonlinear Schr\"odinger equation, obtained by taking into account the Drude dispersive model, is expressed in terms of the parameters of Gaussian pulse, called collective variables, such as width, amplitude, chirp, and phase. This approach yields a system of ordinary differential equations for the evolution of all the pulse parameters. We demonstrate the dependence of stability of the fixed-point solutions of these ordinary differential equations on the linear and nonlinear dispersion parameters. In addition, we validate the analytical approach numerically utilizing the method of split-step Fourier transform.