Lasing without inversion III: microwave coupling induced atomic coherence

We consider the nondegenerateA quantum beat laser, and investigate the possibility of lasing without population inversion when coherence is established, between the lower levels, by applying a strong microwave field. For a specific example we calculate how much coherence may be established between the lower levels using microwave coupling. Analytical calculations are presented for both the open and closed three level atomic systems, using perturbation theory up to third order in the optical fields. Taking the linear equations, we show numerically how gain may be achieved.