Effects of Transverse and Axial Magnetic Fields on Gaseous Lasers

The effects of transverse magnetic fields on a $J=1\mathrm{}\to 0$ laser transition are considered, and expressions for the macroscopic-atomic-polarization terms are derived. The contributions from the $\sigma$ modes are combined, and equations for the intensities and frequencies of the $\pi$ and $\sigma$ oscillations are deduced. Various coupling terms occur because of the common lower level of the transition, and a quenching of the initial $\pi$-mode oscillation with a change to the $\sigma$ mode is indicated as the magnetic field increases from zero. With increased field, both modes oscillate simultaneously, and a beat occurs whose frequency depends on the operating conditions, and which may become zero again at higher magnetic fields. At line center the beat frequency should remain zero with increasing magnetic field, representing a method of laser tuning. Similar equations for the circularly polarized $\sigma$ oscillations in axial magnetic fields are deduced. Here the conditions for stable two-frequency operation are more readily satisfied, and no such quenching is indicated. Again there are zero-beat-frequency regions of magnetic field in which a mutual synchronization of the oscillations should occur. Some experimental results with transverse magnetic fields on the 1.153-μ He-Ne laser are given. These display the general features indicated by the theory. Thus a quenching of the initial $\pi$-mode oscillation occurs, with more or less abrupt changes to the $\sigma$ mode, depending on conditions. Similar single-beat-frequency variations with magnetic field occur, together with a region near the line center where the beat frequency, although finite, remains constant with increasing magnetic field.