DARK SOLITON SOLUTIONS TO THE NONLINEAR SCHRODINGER EQUATION FOR ULTRASHORT PULSE PROPAGATION IN METAMATERIALS

The nonlinear Schrodinger equation for ultrashort pulse propagation in metamaterials with a nonlinear polarization is solved by an extended tanh function expansion method, and the dark solitary wave solutions for various conditions are obtained. The role of the dispersive magnetic permeability, which manifests itself as self-steepening and higher order nonlinear dispersion terms in the nonlinear Schrodinger equation in dark solitary wave propagation, is identified. It is found that the negative self-steepening effect in metamaterials makes the solitary wave move to the leading side, opposite to that in ordinary materials, in which the self-steepening effect is always positive. Most importantly, due to the role of the second order nonlinear dispersion, dark solitons can be formed in the absence of linear dispersion, or even in the case of anomalous linear group velocity dispersion, different from the conditions for dark soliton formation in ordinary materials.