Hermann Haken, R. der Agobian, M. Pauthier
Two- and three-step laser cascades have been recently detected experimentally in He-Ne mixtures and in pure neon. In the present paper a two-step cascade is treated in detail theoretically, starting with the density-matrix formulation. The corresponding equations can be simplified to rate equations under an assumption about the relative size of certain phase-memory times, which seems well justified in the present case. Because there are usually only minor differences in the results between a gaseous laser and a solid-state laser with an inhomogeneously broadened line, and because the mathematical treatment of the gas laser is more involved, the solid-state case will be treated here. The laser condition for both the lower and upper transitions is derived for the most general case, i.e., that all three levels are pumped. Finally, a special two-step cascade is treated in detail. The results are in qualitative agreement with the experimental findings, although a quantitative comparison is still impeded by the lack of an exact knowledge of some of the parameters, especially the radiative linewidth.
Physical Review•Oct 18, 1965•10 citations