Influence of relative phase between probe and driving fields(Φ) Oil propagation effect of a Doppler broadened quasi-Λ type four-level atomic system with spontaneously generated coherence(SGC) is numerically studied.It is shown that by choosingΦ, we can obtain greater GWI and longer propagation distance where GWI exists and hence obtain higher LWI intensity.Doppler broadening width and propagation directions of probe and driving fields have considerable effect on phase·dependent spatial evolutions of GWI and LWI intensity.

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).

Effects of pulse width on ultrahort laser pulse and spectrum and their carrier-envelope phase(CEP)dependence in a dense V-type three-level atomic medium are investigated with numerical solutions of a full Maxwell-Bloch equation without slowly varying envelope and rotating wave approximations.It is shown that:As pulse width is small,pulse splitting number is less,spectrum is wide,high-frequency part of the spectrum is significant,CEP has great effect on pulse and spectrum,particularly effect on time interval between sub-pulses and strength of high-frequency part is more obvious;As pulse width increasing,pulse splitting number increases,width of spectrum narrows and high-frequency part of the spectrum decreases gradually,effect of CEP on pulse and spectrum weakens gradually.

In one-photon resonance and detuning cases,effect of relative carrier-envelope phase(RCEP) on evolution of two-color sech-type femtosecond pulses and spectrum in a dense V-type three-level atomic medium is investigated with full Maxwell-Bloch equations.Modulation of RCEP on pulse shape and spectral property of two-color pulses in detuning case is more evident than that in single-photon resonance case.And in detuning case we get spectrum broadening much greater than that in resonance case.Supercontinuum with the highest frequency of 18 times of incident frequency appears.

With numerical solution of full Maxwell-Bloch equations obtained by finite-difference time-domain method and iterative predictor-corrector method,spatial distributions of pulse and populations of few-cycle laser pulse propagates in a ladder-type three-level atomic medium are investigated.It shows that,spatial distributions changes evidently with pulse area.As the pulse area is smallr,the pulse shape is irregular and oscillation time increases.As the pulse area is large,the pulse shape becomes relatively regular and oscillation times decreases evidently.With increasing of pulse area,amplitude and group velocity of pulse increase progressively,oscillation times of populations increase gradually and variation of spatial distributions of the pulse and populations at different moments decreases considerably.Moreover,spatial distribution of populations correlates closely to spatial distribution of the pulse.

Full Maxwell-Bloch equations are solved with PC-FDTD method to investigate population evolution of dense V-type three-level medium in few-cycle laser pulses.It is shown that the ratio of transition dipole moments(γ) has strong influence on appearing time and oscillation frequency of population inversion.As γ=1 population inversion with LFC appears later than that without LFC and near dipole-dipole(NDD) interaction delays population inversion.As γ>1,appearing with LFC is earlier than that without LFC and NDD interaction accelerates the population inversion.The number of population inversion with unequal transition dipole moments is more than that with equal transition dipole moments.Moreover,evolution of populations in a dense medium is quite different from that in a dilute medium.At input surface,in a dilute medium,population inversion appears with time evolution.With increasing of medium density,populations show quasi-periodicity oscillation and oscillation frequencies of populations with LFC are less than that without LFC.