Some phenomena in susceptibility of atomic medium via the phases and direction of the Gaussian near-field

We display the phenomena of dark state, vanishing absorption and dispersion as well as the up-conversion and large refractive index with low absorption in a Doppler broadened four-level N-type atomic system which interacts with three fields. We take three cases for the field which representing by the spontaneously generated coherence and Gaussian near-field. The effect of the relative phase of the fields and the Gaussian field parameter on the spectrum of the probe field in the three cases of the field are discussed. The direction and magnitude of the pump field have an important role when we discuss these phenomena. The chance of obtaining the large refractive index with low absorption is achieved at specific conditions. Then the interesting results can be observed on the spectrum of the probe field depending on kind of the field.