Effect of spontaneously generated coherence on inversionless lasing gain in an atomic system with Doppler broadening

We have studied the effect of the spontaneously generated coherence(SGC) on gain of lasing without inversion (LWI) in a closedthree-level $Lambda $-type atomic system with Doppler broadening. Itis shown that, regardless of the driving and probe fields being co-or counter-propagating, at a suitable value of the Doppler width, wecan obtain a much larger LWI gain with SGC than that without SGC; andthe region of the LWI gain spectrum with SGC is obviously larger thanthat without SGC. When the Doppler width takes a constant value, thegain does not monotonically decrease or increase with increasingstrength of SGC, the largest LWI gain can be obtained by adjustingstrength of SGC. Generally speaking, the co-propagating probe anddriving fields is favourable to obtain a larger LWI gain.