Continuum and undefine hole burning regions via pulse propagation in a four-level Doppler broadened atomic system

In this paper, we have theoretically examined and modified the spectral hole burning (SHB) in a tripod-type four-level Doppler broadened atomic medium. We have investigated a narrow spectral hole (Lamb dip) in the absorption spectrum, and subluminal/superluminal light propagation in the dispersion spectrum through Doppler broadened atomic medium as well. Furthermore, a theoretical demonstration is presented for the group index, advance/delay time and group velocity. Moreover, we investigate that the detuning of the control fields considerably shift the SHB at either side of the resonance line. For the first time, we have investigated the undefined hole burning regions by showing that the group index, advance/delay time, and group velocity are undefined in these regions. The results may have important applications in the developing technology of quantum optics and will open up new ways to investigate different phenomena inside the hole burning regions.