The laser, Raman, and hyper-Raman processes are studied in a three-wave four-level system by means of a numerical analysis of the steady-state density matrix equations. Gain spectra curves are presented for IR-IR and IR-MW pumped systems and for two four-level systems in NH
3that yield 12.159 and 12.114 μm wavelength radiation. Using the gain spectra data, threshold pump intensities, output intensities, ac Stark shifts,

splittings, optimum NH
3pressures, and saturation are studied. The theoretical data agrees with the experimental data well within a factor of two. It is shown that the hyper-Raman process can lead to higher power, frequency stable, optically pumped lasers.