Determination of stimulated emission cross sections for Er-doped glass

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 4I13/2 ↔ 4I15/2 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.