Influence of the Goos-Hanchen Shift on Tunneling Times in Dispersive Nonlinear Media

The Goos-Minchen effect is an optical phenomenon defined as a displacement of the reflected beam of linearly polarized light after the total internal reflection, which occurs perpendicularly to the direction of propagation. Due to this effect, when an optical wave propagates through a barrier, tunneling times may change accordingly. In this paper, we consider the impact of the Goos-Hanchen effect on group delay and dwell time for electromagnetic wave propagating through a nonlinear dispersive slab placed inside linear dispersive surroundings. Numerical calculations are performed for the special case, namely a double negative index metamaterial embedded into a material with a saturable nonlinearity, when a background medium is vacuum. The numerical results for tunneling times are calculated when the Goos-Hanchen effect is observed. It is shown that this approach gives more accurate expressions for tunneling times when the angle of incidence has a non-zero value.