Coherence Enhanced Transient Lasing

We study the effect of a coherent drive on transient lasing with inversion in three-level $\Lambda $ and $\Xi$ configurations ($c\leftrightarrow a\leftrightarrow b$). We show that the presence of a resonant coherent drive on the $a\leftrightarrow c$ optical transition can yield substantial enhancement of the output laser energy on a $a\rightarrow b$ XUV or X-ray transition. We demonstrate the crucial role of coherence $\varrho _{ac}$ for this laser power enhancement. Contrary to the forward direction, where forward gain can be enhanced for some choice of $\Omega_{c}$, coherent drive on the $ac$ transition always suppresses the backward gain. Thus, the use of a coherent drive at optical frequency could be a useful tool for increasing power of lasers in XUV and X-ray regions.