Exact Solutions in the Semi-Classical Theory of a Gas Laser for Two Special Cases

Abstract

An exact expression of the gain constant of two-level molecules (or atoms) in a standing-wave optical field is obtained for a special case where the optical frequency is in exact resonance with the molecular transition and the longitudinal and transverse relaxations have equal decay constants. Secondly, an exact form of gain constant as a function of frequency detuning which decribes the shape of Lamb dip or saturated absorption is shown for another case where the transverse relaxation is much faster than the longitudinal relaxation. A flat velocity distribution of molecules at Doppler limit is assumed in either case.