Hartman effect in one-dimensional photonic crystals with a three-level atomic defect layer

The Hartman effect in one-dimensional photonic crystals contained a defect layer doped with two-level, and three-level atoms is discussed. It is shown that the transmitted phase time in one-dimensional photonic crystals contained a defect layer reaches to a positive constant as the periodic number N increases. However, for a defect layer doped by two-level atoms, the transmitted phase time reaches to negative constant by increasing periodic number N. In addition, for defect layer doped by three-level atoms, the transmitted phase time can be controlled from positive to negative just by the Rabi-frequency of coupling field.