Properties of group delay for photon tunneling through dispersive metamaterial barriers

We make a detailed investigation on properties of the group delay for photon tunneling through dispersive metamaterial barriers by employing stationary phase method. Due to the anomalous dispersion of the different barriers, it is found that the group delay is positive for double negative metamaterial (DNM) barrier, while for single negative metamaterial (SNM) and negative-zero-positive index metamaterial (NZPIM) barriers, they can change from negative to positive with variations of both frequency and incident angle. The lateral shift for the photon tunneling has also been studied, whose sign is found not to dominate the sign of the group delay. It is further confirmed that the group delay tends to a saturation value with increasing barrier length because of Hartman effect. These results may provide some ideas for further study on the photon tunneling, suggest the analogous phenomena of valence electron in graphene, and produce some potential application in integrated optics and optical devices.