“…Our analysis is based on a general PDFFA model [3], which assumes a steadystate ampli® cation regime. The rate equations include the following transitions: pump ground-state absorption (GSA) 3 H4± 1 G4, signal transition used for ampli-® cation 1 G4± 3 H5, pump ESA 1 G4± 3 P0, signal GSA 3 H4± 3 F4, signal ESA 1 G4± 1 D2, and the corresponding non-radiative multiphonon decay processes (see the sim-pli® ed energy level diagram for Pr 3+ in [3]).…”