Influence of relative phase on propagation effect in open V-type three-level system

In this paper we study the influence of the relative phase between the probe and driving fields on propagation effect in an open Doppler broadening V-type three-level atomic system with spontaneously generated coherence (SGC) by using the calculation result of the density matrix motion equations and the propagation equations of the driving and probe fields. It is shown that the relative phase (Φ) has remarkable periodical influence on the propagation effect, and the period is 2π. By selecting appropriate value of Φ, we can get larger lasing without inversion (LWI) gain and longer propagation distance in which gain exists, and hence obtain higher probe field (i.e. LWI) intensity. When Φ=π/2, the largest LWI gain and probe field intensity can be got. In addition, the atomic exit rate (γ ₀) and ratio (S) of the atomic injection rates also have a considerable modulation role on the phase-dependent propagation effect. In certain value range of γ ₀ (S), LWI gain and probe field intensity increase with γ ₀ (S) increasing. In the open system, LWI gain and probe field intensity much larger than those in the corresponding closed system can be obtained.