We present an extension to our earlier proposed statistical model [Phys. Rev. B 62, 15628 (2002)] for studying migration-assisted homogeneous upconversion in erbium-doped fibers. The extension takes into account minimum proximity distance between erbium ions randomly distributed in the host material and the nonuniformity of the excitation distribution among them. We derive a transcendental equation for the population inversion and find the dependence of the upconversion rate on the population inversion and the pump power for the entire range of feasible Er concentrations. We verify the validity and accuracy of the model by means of time-resolved Monte Carlo simulations.
© 2005 Optical Society of America
(060.2410) Fiber optics and optical communications : Fibers, erbium
(130.3130) Integrated optics : Integrated optics materials
(140.4480) Lasers and laser optics : Optical amplifiers
(160.5690) Materials : Rare-earth-doped materials
(250.4480) Optoelectronics : Optical amplifiers
Dmitry Khoptyar, Sergey Sergeyev, and Bozena Jaskorzynska, "Homogeneous upconversion in Er-doped fibers under steady state excitation: analytical model and its Monte Carlo verification," J. Opt. Soc. Am. B 22, 582-590 (2005)