Double-Resonance Phenomena in the Gaseous Laser

The theory of double-resonance phenomena, or the simultaneous action of optical transitions and rf perturbations between the Zeeman sublevels of an atom, is extended to the induced emission and absorption processes effected by the monochromatic radiation and the discrete resonances involved in the gas laser. Expressions for the probability amplitudes of the Zeeman sublevels under such conditions are derived from time-dependent perturbation theory, the lifetimes of the states being introduced in a phenomenological way. Zeeman splittings of both upper and lower states involved in the laser transition are considered, and an effective term diagram used to discuss the results. Small signal approximations are applied to consider some specific cases, which show that the light beats seen in spontaneous emission when the rf frequency ${\omega }_0$ equals the Larmor frequency, and in other instances, do not occur in induced emission unless such frequencies coincide with axial resonances of the laser cavity. Variations in the intensity and resonance effects are indicated at Zeeman splittings corresponding to ${\omega }_0$, with similar variations in the amplitude of any beat frequencies due to multiple axial resonances. Additional coherence effects occur where levels cross, which will give rise to changes in the intensity and polarization of the induced emission at the corresponding frequency.