Tunneling times in metamaterials with saturable nonlinearity

Tunneling times of electromagnetic planar wave propagating through a barrier made of split-ring resonators and long metallic wires embedded into a dielectric with saturable nonlinearity are analyzed. For such structure, analytical expressions for the tunneling times and relation between the group delay and the dwell time are obtained. The electric-field distribution inside the barrier is numerically evaluated and a detailed study of the influence of nonlinearity on the spectral structures of the tunneling times is performed. It is demonstrated that intensity variation in the incident field may change the wave propagation direction, the sign of the barrier's refractive index, and group delay.