Theory of a three-level gas laser amplifier

A laser amplifier to be treated in this work consists of an ensemble of atoms three energy levels of which form two coupled transitions of arbitrary frequencies. Two classical monochromatic travelling light waves are to be close to resonance with the transitions. The gain profile (or spontaneous emission) on the transition corresponding to the weak “probe” wave, modified by the perturbing field on the other transition, is calculated via a susceptibility. Within this framework, the atoms are described by an ensemble-averaged density matrix with full account of level degeneracies, light polarizations, and inelastic and dephasing collisions; an extension to elastic collisions and disorientation is straightforward. An integration over the thermal velocity distribution gives results applicable to gas discharges: directionally anisotropic narrow structures superimposed on the Doppler-broadened probe-gain profile due to non-linear interference effects in addition to saturation. At alower probe frequency, a peculiar non-Lorentzian signal appears even with transparency on the perturbing transition. At low intensities a distinction is reasonable of frequency correlations due to generalized two-quantum processes, and of a dynamic Stark splitting. These effects permit an information on the linewidth of the third forbidden transition. The connection with numerous related approaches is pointed out.