Dmitrii Kouznetsov

“ The McCumber relation [1] [2] expresses the emission cross-seccion in terms of the absorption cross-section :
where is temperature, is Boltzmann constant and is zero-line frequency, at which the emission and absorption cross-sections are equal. The relation (mc) is validated for various media [1] [2] [3] [4] [5] .
The original deduction of the McCumber relation [1] , as well as the adaptation in the textbook [2] assume, that all active centers are equal. It cannot be applied as is to the broadband laser materials with different sites of the active centers. ”

“ In any of these cases, the medium cannot be characterized with the single-valued emission cross-section function ; the effective cross-sections should be defined for each site, and the kinetic of the transfer of the excitations should be considered.
The effective emission cross-section and the McCumber relation have the same range of validity. The deviation from a constant of the right-hand side of the estimate (check) for the steady-state ratio of populations characterizes the error of measurement of the effective cross-sections. ”

“ In the following, the consideration of relations between Einstein coefficients [12] [13] [14] [15] is rewritten, taking into account sublevels (Fig.1) .
Detailed balance Functions , and of frequency are related, as the Einstein coefficients are. These relations can be found from the principle of detailed balance.
Although the expression (g) is good for a non-equilibrium medium, it is valid also at the thermal equilibrium, when the spectral rate of emission (both spontaneous and stimulates) of photons at any frequency is equal to that of absorption. ”