We have described here the physical basis for lasing without population inversion (LWOPI). This type of amplification is obtained basically by two mechanisms: (i) one is based on atomic interference and (ii) the other is based on Fano-type interference. We have shown here, in H₂ molecules, amplification without population inversion is feasible by considering both the mechanisms.

We have solved the time dependent Schrödinger equation by using the Chebyshev polynomial scheme and Fourier grid Hamiltonian method to calculate the dissociation cross section of NaH molecule by 1-photon absorption from the X¹Σ⁺ state to the B¹Π state. We have found that the results differ significantly from an earlier calculation [1] although we have used the same set of potential energy curves [2].

Dependence of amplification without inversion (AWI) on the relative strength of probe and coherent field Rabi frequencies has been studied in H₂ and LiH molecules for three-level Λ configuration. We have derived exact analytical expressions for coherences and populations keeping all the orders of probe field Rabi frequency (G) and coherent field Rabi frequency. (Θ) in the steady state limit. Previously, first-order approximation (i.e. keeping only the first-order term in G) was used and hence AWI was studied for the condition Θ>>G. Here, by using the exact analytical expressions of coherences and populations, we have shown that AWI is maximum when Θ is within the same order of probe field Rabi frequency G irrespective of the choice of different ro-vibrational transitions in both the molecules. However, the shape of the gain profile and the maximum value of gain on the probe field and the absorption on coherent field depend on the choice of different ro-vibrational levels as the upper lasing levels. Effect of bidirectional pumping, homogeneous and inhomogeneous broadening on AWI process has been studied. By solving the density matrix equations numerically it has been shown that both the transient and the steady state AWI can be obtained and the numerical values of coherences and populations at large time are in very good agreement with exact analytical values in the steady state limit. It has been shown that in molecules AWI can be obtained on probe field of smaller wavelength than that of the coherent field which has not been observed in atoms so far.