Double resonance in gaseous lasers

The simultaneous action of a RF perturbation between the Zeeman sublevels of an atomic transition, which is also sustaining laser oscillations, is given further consideration. General equations are derived that describe the phenomena in a rotating effective magnetic field basis. These are valid for any level of the RF perturbation, being then solved by iteration to third order in the laser electric field and integrated exactly over the atomic velocity distribution. Results are given for single-π-mode laser operation on a
J = 1 \rightarrow 0
transition and for single-mode operation on each of the well-resolved σ components of the Zeeman splitting. The extension to more complex transitions, such as a
J = 1 \rightarrow 2
, is then given. A dominant resonance peak in the laser intensity occurs when the RF equals the Zeeman splitting of either the upper or lower states of the transition. Population differences amongst the upper sublevels are more effective than those between the lower sublevels and give the smallest resonance widths. For operation on the σ modes, the main effect is a reduction in the saturation coefficient β, together with smaller changes in the coupling coefficients θ between the oscillations. Such changes will affect the general behavior near the singular points of the nonlinear equations, and will change the shape of the curves of mode intensities as functions of cavity detuning and magnetic field.