Controllable Hartman effect by vortex beam in a one dimensional photonic crystal doped by graphene quantum dots

The Hartman effect is studied in a one dimensional photonic crystal doped with graphene quantum dots. It is shown that the Hartman effect can be switched from negative to positive by increasing the Rabi-frequency of the controlling field and also by manipulating the relative phase of the applied fields. The effect of the vortex beam on the Hartman effect is also presented. We show that the orbital angular momentum (OAM) and the azimuthal phase of the vortex beam do not affect the probe filed transmission while they change the Hartman effect from positive to negative.