The role of dispersive magnetic permeability in ultrashort electromagnetic pulse propagation in nonlinear metamaterials

Compared to the non-magnetic ordinary dielectrics, the negative-index metamaterials have not only a dispersive electric permittivity but also a dispersive magnetic permeability. The purpose of this paper is to identify the role of dispersive magnetic permeability in nonlinear propagation of ultrashort electromagnetic pulses in metamaterials. Firstly, we derived a generalized system of coupled three-dimensional nonlinear Schrodinger equations suitable for few-cycle pulse propagation in the metamaterial with both nonlinear electric polarization and nonlinear magnetization, which clearly demonstrates the role of dispersive permeability in nonlinear pulse propagation: In the linear propagation aspect, its contribution is buried in the ordinary dispersive terms; while in the nonlinear propagation aspect, the dispersive permeability manifests itself as a nonlinear polarization dispersion, although it is a linear parameter. Secondly, by exemplificatively using the coupled nonlinear Schrodinger equations in the Drude dispersive model, we quantitatively discussed the influence of dispersive permeability on pulse propagation in metamaterials.