Nonlinear upconversion-rate in Er-doped fibers

Energy transfer between excited rare-earth ions has been widely used for re alizing upconversion lasers and also recognized as a gain limiting factor i n high-concentration Er-doped amplifiers. The energy transfer leads to upco nversion of the excitation which for randomly distributed (not clustered) i ons is called homogeneous upconversion. It was commonly assumed that the ra te of homogeneous upconversion is a linear function of the population inver sion N-2. However, recently published Monte Carlo simulations predict that the homogeneous upconversion rate is a nonlinear function of N-2 and that i t, moreover, depends on the pump and signals rates. In this paper we review some of our experimental results confirming those predictions. We also pro pose a statistical, analytical model describing the observed homogeneous up conversion behavior in Er-doped fibers.