Abstract

Despite the high level of activity in the area of Er-doped fiber lasers and amplifiers, questions still remain regarding the values of the absorption and stimulated-emission cross sections. The disagreement between experimental and calculated values arises from a breakdown in the conventional Einstein A and B coefficient analysis when the necessary assumptions of uniform Stark-level occupations or equal transition strengths are not satisfied. By means of experimentally measured absorption and emission cross sections, we verified that the more general theory of McCumber¹ successfully relates cross sections for the ⁴I_13/2 ↔ ⁴I_15/2 transitions. In McCumber's analysis, the emission and absorption cross sections at a given wavelength are connected by a known wavelength-dependent factor and an unknown wavelength-independent factor. Close agreement was found between the shapes of the experimental emission cross-section spectra and those calculated from the absorption cross section. To generate absolute cross sections, we developed an empirical procedure using measured linewidths to calculate the wavelength-independent factor. This technique is accurate to 15% for most glasses and, with few exceptions, is significantly better than an Einstein A/B analysis. In this way one may determine either the absorption or emission cross section if only the other is known.

© 1990 Optical Society of America