Nonlinear wave propagation in negative index metamaterials

Wave propagation in nonlinear negative index metamaterials is investigated by directly implementing the reductive perturbation method to Faraday's and Ampére's laws. In this way, we derive a second-order and a third-order nonlinear Schrödinger equation, describing solitons of moderate and ultra-short pulse widths, respectively. We find necessary conditions and derive exact bright and dark soliton solutions of these equations for the electric and magnetic field envelopes. Directions of future work towards the modelling of wave propagation in more complicated types of nonlinear negative index metamaterials (e.g., chiral metamaterials) are pointed out.