Injection time effects on LWI with microwave driven non-degenerate ground states

We present an analytical calculation to determine the atomic injection time effects on lasing without inversion (LWI) in a three level lambda system with its ground state driven by an arbitrarily strong classical microwave field. We systematically take into account subtle effects associated with the injection times. We derive an expression for the optical coherences and show that one gets amplification of the field without population inversion which is governed by a temporal phase, in addition to the initial (random) phases of the ground state coherence.