Anomalous self-steepening, temporal pulse splitting and ring formation in a left-handed metamaterial with cubic nonlinearity

In this paper, starting with the Maxwell equations and the corresponding nonlinear wave equation, we derive a pulse evolution equation for a metamaterial with cubic (Kerr) nonlinearity. The given model equation goes beyond the commonly employed slowly evolving wave approximation (SEWA). The dispersive properties of the dielectric susceptibility and magnetic permeability are accounted for in accordance with the Drude model. Using this model equation, propagation properties of a single-cycle pulse and a 4-cycle pulse are studied numerically in a left-handed metamaterial (LHMM) with third-order nonlinearity.