Abstract
Measurements of time evolution of amplified spontaneous emission for square-wave modulated pump were made on a highly erbium-doped silica photonic crystal fiber and fitted to theoretical results calculated using different formalisms to describe the ${\rm Er}^{3+}$ -ion migration-assisted co-operative upconversion mechanism in the population densities rate equations. The determined characterization parameters are the constant homogeneous upconversion coefficient, 3.0 $\times 10^{-24}~{\rm m}^{3}/{\rm s}$ , the critical radii for upconversion and migration, 10.5 and 14A, respectively, and the rate of clustered ions, 14%. These parameters are analysed and compared to those obtained with continuous-wave pump characterization techniques. Although similar values are obtainable for many parameters using steady-state and dynamic characterization techniques, if a careful enough modelling is carried out, dynamic techniques are preferable to assess the presence of pair-induced quenching.
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