Power dependence of upconversion luminescence in lanthanide and transition-metal-ion systems

We show theoretically with the simplest possible model that the intensity o f an upconversion luminescence that is excited by the sequential absorption of n photons has a dependence on absorbed pump power P, which may range fr om the limit of P-n down to the limit of P-1 for the upper state and less t han P-1 for the intermediate states. The two limits are identified as the c ases of infinitely small and infinitely large upconversion rates, respectiv ely. In the latter case, the dependence of luminescence intensities from in termediate excited states on pump power changes with the underlying upconve rsion and decay mechanisms. In certain situations, energy-transfer upconver sion and excited-state absorption can be distinguished by the measured slop es. The competition between linear decay and upconversion in the individual excitation steps of sequential upconversion can be analyzed. The influence of nonuniform distributions of absorbed pump power or of a subset of ions participating in energy-transfer upconversion is investigated. These result s are of importance for the interpretation of excitation mechanisms of lumi nescent and laser materials. We verify our theoretical results by experimen tal examples of multiphoton-excited luminescence in Cs3Lu2Cl9:Er3+, Ba2YCl7 :Er3+, LiYF4:Nd3+, and Cs2ZrCl6:Re4+.