It is shown that in an open A-type system with spontaneously generated coherence, the transient evolution rule of the gain of lasing without inversion （LWI） is very sensitive to variation of the relative phase φbetween the probe and driving fields; the variety of the atomic exit rate γo and the ratio C of the atomic injection rates also have a considerable effect on the phase-dependent transient evolution rule of LWI gain. We find that when φ =0, the transient and stationary LWI gain increases with C increasing but decreases with γ0 increasing; when φ≠0, the effect of C and γ0 on LWI gain is just opposite to that when φb=0 ; in order to get the largest transient and stationary LWI gain, we need selecting suitable values of φ, γ0andC.
QIAO Hong-xia BU Fan-ge TAN Xia TONG Dian-min FAN Xi-jun
Propagation of a few-cycle laser pulses in a dense V-type three-level atomic medium is investigated based on full-wave Maxwell-Bloch equations by taking the near dipole-dipole （NDD） interaction into account. We find that the ratio, γ of the transition dipole moments has strong influence on the time evolution and split of the pulse： when γ≤ 1, the NDD interaction delays propagation and split of the pulse, and this phenomenon is more obvious when the value of γ is smaller; when γ =√2, the NDD interaction accelerates propagation and split of the pulse.
In an open ladder-type resonant atomic system, variation in relative phase between probe and driving fields does not affect the transient evolution of populations, but it has remarkable effects on gain and dispersion of the probe field. No matter whether an incoherent pump is present or absent, transient and stationary gains without inversion （GWI） always can be obtained by choosing an appropriate value of the relative phase. When the incoherent pump is absent, the values of transient and stationary GWIs are much larger and the time interval required to reach the stationary value is longer than those when the incoherent pump is present. Varying the exit rate and the ratio between injection rates can obviously change the phase-dependent GWI. In addition, in the transient evolution process, the phenomenon of high dispersion （refractive index） without absorption occurs at some values of relative phase. In the corresponding closed system, the stationary GWI can be obtained by choosing an appropriate value of relative phase only when incoherent pump exists, moreover the gain is smaller than that in the open system.
A study is made of the effects of Doppler broadening on pure gain without inversion, which means that neither one-photon nor two-photon inversions are allowed, and non-pure gain without inversion, which means that one-photon inversion does not occur but two-photon inversion is present, in a closed A-type three-level system with incoherent pumping. It is shown that when the driving field is resonant but the probe field is not, in a certain range of Doppler width, for the case of the lower degree of frequency up-conversion, generally, pure gain without inversion increases monotonically and non-pure gain without inversion does not monotonically increase or decrease with increasing Doppler width; for the case of the higher degree of frequency up-conversion, pure gain without inversion decreases monotonically but non-pure gain without inversion cannot be produced. In the case of two-photon resonance, in some range of Doppler width, pure gain without inversion does not monotonically increase or decrease while non-pure gain without inversion decreases monotonically with Doppler width increasing. Finally, an experimental scheme for examining our theoretical result is given.
The population transfer in a ladder-type atomic system driven by linearly polarized sech-shape femtosecond laser pulses is investigated by numerically solving Schr6dinger equation without including the rotating wave approximation （RWA）. It is shown that population transfer is mainly determined by the Rabi frequency （strength） of the driving laser field and the chirp rate, and that the ratio of the dipole moments and the pulse width also have a prominent effect on the population transfer. By choosing appropriate values of the above parameters, complete population transfer can be realized.
We have studied the effect of the spontaneously generated coherence （SGC） on gain of lasing without inversion （LWI） in a closed three-level A-type atomic system with Doppler broadening. It is shown that, regardless of the driving and probe fields being co- or counter-propagating, at a suitable value of the Doppler width, we can obtain a much larger LWI gain with SGC than that without SGC; and the region of the LWI gain spectrum with SGC is obviously larger than that without SGC. When the Doppler width takes a constant value, the gain does not monotonically decrease or increase with increasing strength of SGC, the largest LWI gain can be obtained by adjusting strength of SGC. Generally speaking, the co-propagating probe and driving fields is favourable to obtain a larger LWI gain.
