Control over spectral hole burning via spontaneously generated coherence and Kerr non-linearity

We study the control over spectral hole burning in four-level N-type system via spontaneously generated coherence (SGC) and Kerr nonlinearity in an inhomogeneous Doppler broadening medium. We consider a co-propagating probe laser beam and a counter-propagating control laser beam at the same time. Multiple spectral holes are created with the spontaneously generated coherence in the medium. The depth of the spectral holes gets deeper with increasing of the Kerr field. We study the group index and the transmission of probe laser pulse in SHB regions that lead us to achieve maximum transmission and much steeper group index in the system with increasing the strength of the Kerr field.