Goos-Hänchen shift and time delay in dispersive nonlinear media

We present an analysis of the influence of the Goos-Hänchen effect on tunneling times, group delay and dwell time, of electromagnetic waves propagating through an obstacle made of left-handed metamaterial embedded in a dielectric which exhibits saturable type of nonlinearity. The derived equations show that only the group delay, is affected by the Goos-Hänchen shift without any impact on the dwell time. Besides the reduction of the group delay, the most remarkable result is the possibility for total reduction of the Goos-Hänchen shift for finite incident angles. These phenomena are observable in the frequency region for which metamaterial exhibits negative index of refraction.