Coherent Control of the Hartman Effect through a Photonic Crystal with Four-Level Defect Layer**Supported in part by the National Natural Science Foundation of China under Grant Nos. 11274132 and 11750110411

Abstract

In this paper, we examine the transmission of a probe field through a one dimensional photonic crystal (1DPC) when the sixth layer of the crystal is doped with four level atoms. We analyze effects of the external driving field on the passage of weak probe field across the photonic crystal. It is found that for the phase time delay of the probe photons, intensity of the driving field switches the Hartman effect from sub to superluminal character. It is interesting to note that in our model, the superluminal transmission of the probe pulse is accompanied by a negligibly small absorption of the incident beam. It ensures that the probe field does not attenuate while passing through the photonic crystal. A similar switching of the Hartman effect may be obtained by adjusting detuning of the probe field related to the excited states of the four-level doping atoms.