T. H. Keil
R. S. Quimby
The power of the McCumber theory [D. E. McCumber, Phys. Rev. 136, A954-957 (1964)] consists in its ability to accurately predict emission cross section spectra from measured absorption, and vice versa, including both absolute values and spectral shapes. While several other theories only allow the determination of integrated cross sections, the McCumber theory is unique in generating the spectral shape of a cross section without any direct measurements regarding that cross section. The present work is a detailed study of the range of validity of the McCumber theory, focussing particularly on those aspects that most critically affect its applicability to transitions of rare earth ions in glasses. To analyze the effect of the spectral broadening on the accuracy of the technique, experiments were performed at room and low temperature. The theory was tested by comparing the cross sections calculated using the McCumber relation with those obtained from measurements. At room temperature, a number of ground state transitions of three different rare earth ions (Nd, Er and Tm) in oxide and fluoride glass hosts have been studied. Special attention was paid to the consistency of the measurements, using the same experimental setup, same settings and same detection system for both absorption and fluorescence measurements. Other aspects of the experimental procedure that could generate systematic errors, like fluorescence reabsorption and baseline subtraction uncertainties in the absorption measurements, were carefully investigated. When all these aspects are properly accounted for, we find in all cases an excellent agreement between the calculated and the measured cross section spectra. This suggests that the McCumber theory is not limited to crystalinne hosts, but describes quite well the reciprocity between emission and absorption for the broader transitions of rare earths in glassy hosts. This good agreement does not hold, however, for the low temperature results. The distortion observed in this case follows the theoretically predicted behavior, and corresponds to the amplification of the gaussian wings that describes the inhomogeneous type of broadening. Our results suggest that the McCumber theory must be used with caution for temperatures below 200 K.
Worcester Polytechnic Institute
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Martin, R. M. (2006). Reciprocity between Emission and Absorption for Rare Earth Ions in Glass. Retrieved from https://digitalcommons.wpi.edu/etd-dissertations/201
homogeneous broadening, McCumber theory, emission and absorption cross sections, rare earth ions, inhomogeneous broadening, Rare earth ions, Spectra