Strength numerical calculation of the upconversion luminescence in Er3 +-doped pentaphosphate crystals

Using the rate equations describing the dynamic processes of the system, how the strength of the upconversion luminescence change with the Er 3+ ion concentration and the pump power was analyzed. The spontaneous radiative processes, multiphonon nonradiative processes, absorption of the pump photons and the possible energy transfer processes between all states of Er 3+ ions were included in the rate equations, and the pump power was supposed to be unchanged with time. It came to the result that when x change from 0.1% to 100% in Er x La 1-x P 5 O 14 crystal, lager x benefit the population of all states higher than 4 F 9/2 in the whole range of pump power we considered, except for a small range of pump power in which smaller concentration result in larger ion number of some high lying states. It can be interpreted as that the increasing of the concentration of Er 3+ ions increases both energy transfer processes which populate the upper states of the upconversion luminescence and the cross relaxation processes which depopulate these states. Since the strength of upconversion luminescence is in proportion to the ion numbers of the upper states of the luminescence, the total result is that the upconversion luminescence from 4 S 3/2 would increase with the concentration of Er 3+ ions, and the strength of this upconversion luminescence were most strong in ErP 5 O 14 crystal; for a small range of pump power, the strength of upconversion luminescence from level ( 2 G 4 F 2 H) 9/2 and 4 G 11/12 of Er ions in Er 0.8La(subscript 0.2 P 5 O 14 crystal was most strong, for all the other range of pump power, this luminescence was also strongest in ErP 5 O 14 crystal.