General procedure for the analysis of Er^3+ cross sections

We have applied the theory of McCumber to the (4)4I(13/2) ? (4)I(15/2) transition of Er(3+) -doped glasses and confirmed its ability to provide both spectra and accurate values of cross sections. For an Al/P-silica fiber, the exact McCumber treatment is within 3% of the measured emission cross section, whereas an Einstein analysis is off by >50%. An approximate treatment that eliminates the McCumber theory's requirement of detailed electronic structure has been developed and found to usually provide more accurate values than an Einstein analysis.