Modeling of ultrashort pulse propagation in lossy nonlinear metamaterials

Wave propagation in lossy nonlinear metamaterials is analytically investigated by means of perturbation methods. In the left‐handed band of the nonlinear metamaterial, a higher‐order nonlinear Schrödinger equation is obtained, while in the frequency band gap, a dissipative short‐pulse equation is derived. In both cases, dissipation is described by linear terms, which lead to an exponential decay of the solutions. The decay rates, that is, the inverses of the linear loss coefficients in these two models, are found in terms of the dielectric and magnetic properties of the metamaterial. Copyright © 2016 John Wiley & Sons, Ltd.