MODELING THE GAIN DEGRADATION OF HIGH-CONCENTRATION ERBIUM-DOPED FIBER AMPLIFIERS BY INTRODUCING INHOMOGENEOUS COOPERATIVE UP-CONVERSION

The gain degradation of erbium-doped fiber amplifiers (EDFA's) with high erbium ion (Er3+) concentration at 1.48- and 0.98-mum pump wavelengths is modeled by introducing inhomogeneous cooperative up-conversion (IhCU). General formulas describing the gain degradation as a function of IhCU rate are obtained by solving rate equations for population probabilities in the relevant Er3+ energy levels. To allow numerical calculations, the distribution of IhCU rate are approximated in two steps. Gain of EDFA's with Er3+ concentrations of 470 and 140 ppm are measured. The experimental results, such as low gain for high Er3+ concentration, and higher saturated gain with counter-propagation than with copropagation pumping, which have not yet explained theoretically, are qualitatively explained by this model. Good agreement between the measured and calculated gain is obtained. The gain degradation characteristics at 1.48- and 0.98-mum pump wavelengths are analyzed with this model. The advantage of counter-propagation pumping is determined qualitatively. The noise figure degradation is also evaluated.