Three-level approximation in calculating the parameters of optically detected magnetic resonance under conditions of strong laser pumping

An algorithm is proposed for the approximate solution of a purely nonlinear problem of the parameters of optically detected magnetic resonance in the ground state of alkali atoms in an optically dense medium under conditions of intense narrow-band optical pumping, which causes, first, bleaching of the atomic medium, and, second, partial suppression of spin-exchange broadening. The direct solution of the Liouville equation under these conditions is complicated by the fact that the relaxation time of each of the levels of the hyperfine and Zeeman structure of the ground state is determined by the populations of the remaining levels, which leads to the necessity of solving a self-consistent problem in a multilevel system, and, as a rule, requires the use of supercomputers. In this paper, approximations are proposed that make it possible to significantly simplify and speed up the calculation by orders of magnitude, and the results are compared with experimental data using the example of a two-beam M$_{X}$ scheme of a magnetometric sensor