Abstract: With numerical solution of density matrix motion equations of an open V-type three-level atomic system with spontaneously generated coherence,we analyze transient evolution of gain of lasing without inversion(LWI).It is shown that relative phase(Ф) between probe and driving fields has a significant effect on transient evolution of gain regardless of incoherent pump;Greater transient and steady gains can be obtained by selecting φ;As incoherent pump is absent,longer time is needed to get the greatest transient gain and steady gain.Oscillation amplitude in the evolution process is greater,and gain is also greater;Changing atomic exit rate r₀(ratio of atomic injection rates S) leads to detail of gain transient evolution.In certain range of r₀(S),transient and steady gains increase with S(r₀).

Key words: open system, transient evolution, relative phase, lasing without inversion, gain