Comparative analysis of the adequacy of different models for description of the spectroscopic properties of laser materials doped with trivalent erbium and thulium ions

The purpose of this work is to determine the most adequate model for describing the experimental values of the intensities of the absorption bands of laser materials activated by trivalent erbium and thulium ions. Such materials are used as active media for lasers generating radiation in the infrared range of 1.5-2.8 μm. Calculation formulas are given for the oscillator strengths of absorption transitions in the Judd - Ofelt (J-O) model, the modified Judd - Ofelt (mJ-O) model, and in the approximation of an intermediate configurational interaction (ICI). To compare the adequacy of different models, the results of describing the experimental oscillator strengths of absorption transitions in six crystals activated by erbium ions and five crystals activated by thulium ions are considered. The most accurate description of ten of the eleven samples under consideration was obtained in the ICI model. In the calculations, we used the procedure for minimizing the error functional composed of the sum of the squared deviations of the calculated oscillator strengths from the corresponding experimental values. The criterion for choosing the best parameterization scheme is the minimum value of the root mean square deviations. A particularly noticeable improvement in the description is observed when using the ICI model for crystals activated by thulium ions. This is explained by the fact that multiplets with the same value of the total moment J combine into groups under the action of strong spin - orbit interaction. The action of excited configurations on any one multiplet is transmitted to all multiplets of the group. Thulium has a number of multiplets and consequently groups is much less than that of erbium. Therefore, the effect of excited configurations on thulium multiplets is more differentiated and easier to detect in the description.