Collision-Induced Anisotropic Relaxation in a Gas Laser

Abstract

A theory of a single-mode gas laser in a magnetic field has been derived, including the effects of collision-induced anisotropic relaxation. The theory is similar to that obtained by D'yakonov and Perel', but is more general in that it includes anisotropic relaxation, and does not use the Doppler limit to evaluate the third-order integrals. From this theory we have obtained an expression for the critical axial magnetic field strength, and shown that for $j=1\mathrm{}\leftrightarrow j=0\mathrm{}$ transitions this expression is particularly simple. Experimental values for the various collision cross sections were obtained by fitting the theoretical expression to the results of a series of measurements of the critical field strength for a He-Ne laser oscillating on the 1.52-μm ($2s_2\to 2p_1, j=1\mathrm{}\to j=0\mathrm{}$) transition. The cross sections for the relaxation of the electric quadrupole moment of the ${\mathrm{Ne}}^{20}$ $2s_2$ state as a result of collisions with ground-state ${\mathrm{Ne}}^{20}$, ${\mathrm{He}}^3$, and ${\mathrm{He}}^4$ atoms are 5±3, 2.99±0.32 and 2.78±0.37, respectively, in units of ${10}^{-15\mathrm{}}$ ${\mathrm{cm}}^2$. The corresponding cross sections for the relaxation of the magnetic dipole moment are a factor of $\frac{5}{3}$ larger. The total radiative lifetime of the Ne $2s_2$ state was found to be 10 nsec, in agreement with other experiments. The experimental cross sections are shown to be in satisfactory agreement with those calculated from the van der Waals collision model.