Influence of the hyperfine structure on the frequency reproducibility of an He–Ne laser with a methane absorption cell

An investigation is made of the influence of the hyperfine structure of the methane absorption line on the frequency reproducibility of an He-Ne/CH₄ laser. A calculation is made of the shift of a nonlinear resonance maximum of the methane absorption line as a function of the intensity of the saturating field for a wide range of values of the homogeneous line width γ allowing for the degeneracy of the components of the hyperfine structure along the projection of the magnetic moment M. The final results are presented in the form of simple analytic formulas applicable not only to the P(7) line of methane but also to any other line with a high value of j, having a hyperfine structure. The limits of the optical frequency standard reproducibility arising from the error in the determination of the saturation parameter are discussed. It is shown that by making an appropriate choice of stimulated emission conditions, a frequency reproducibility of 10^-13 can be achieved by an He-Ne/CH₄ laser.