Nonlinear Effects in the Resonant Absorption of Several Oscillating Fields by a Gas

The lowest order nonlinear effects due to saturation in the simultaneous resonant absorption of several oscillating fields by a low-pressure gas are considered. The analysis is based on a perturbation solution of the Boltzmann equation for the density matrix of the gas in a quantum statistical description. Within certain ranges of the parameters involved, it is shown that: (1) When the gas is irradiated by two oscillating linearly polarized fields of different frequencies well within the Doppler-broadened width of the same absorption line, maximum absorption of both fields occurs when the two linear polarizations are perpendicular to each other. (2) When the gas is in a static magnetic field and irradiated by two right-circularly polarized fields at ${\omega }_0$ and ${\omega }_0+\Delta \omega$, and two left-circularly polarized fields at ${\omega }_0$ and ${\omega }_0-\Delta \omega$, all well within the Doppler width of the respective Zeeman components ($\Delta m=+1\mathrm{} \mathrm{and} -1\mathrm{}$) of the same absorption line, there exists a definite phase relationship among the fields whereby absorption of all four fields is simultaneously at a maximum. Although these effects are quite small in normal spectroscopic work, manifestation of both effects is readily observable in gaseous He-Ne optical masers.