We report the effect of a coherent drive on transient lasing in three-level
Λ and Ξ configurations (c↔a↔b). We
show that the presence of a resonant coherent drive on the a↔c
optical transition can yield an order of magnitude enhancement of the output
laser energy on a a→b XUV or X-ray transition than with no
coherent drive. We demonstrate the crucial role of coherence ϱac for
the laser power enhancement. Contrary to the forward direction (with respect to
the pump), where forward gain can be enhanced for some choice of the drive Rabi
frequency Ωc, coherent drive on the ac transition always suppresses
the backward gain.Comment: 8 pages, 11 figure