Tunneling times in dispersive and third-order nonlinear optical metamaterials

Abstract

Investigating the propagation of electromagnetic radiation in linear and nonlinear materials (with third-order nonlinearity), we derived a general expression for the dwell time valid for all linear media, as well as its relation with the group delay. The obtained results indicate that, for a nonmagnetic lossless material, the group delay reduces to the sum of the dwell time and the self-interference time. Calculations confirmed the occurrence of the Hartman effect in negative-refractive-index metamaterials (the dwell time saturates with increasing obstacle length), as well as the negative group delay in a certain spectral regime. Analysis of the Goos-Hänchen shift, in case of an obstacle made of negative-refractive-index metamaterial embedded in a dielectric with saturable nonlinearity, showed that there is no impact on the dwell time, while various effects on the group delay may be achieved, including its reduction or even preservation for nonzero incident angles.