Dynamic Characterization of Upconversion in Highly Er-Doped Silica Photonic Crystal Fibers

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 14Å, 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.