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

Abstract

We show theoretically with the simplest possible model that the intensity of an upconversion luminescence that is excited by the sequential absorption of n photons has a dependence on absorbed pump power P, which may range from the limit of P n down to the limit of P 1 for the upper state and less than P 1 for the intermediate states. The two limits are identified as the cases of infinitely small and infinitely large upconversion rates, respectively. In the latter case, the dependence of luminescence intensities from intermediate excited states on pump power changes with the underlying upconversion and decay mechanisms. In certain situations, energytransfer upconversion and excited-state absorption can be distinguished by the measured slopes. 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 results are of importance for the interpretation of excitation mechanisms of luminescent and laser materials. We verify our theoretical results by experimental examples of multiphoton-excited luminescence in Cs 3 Lu 2 Cl 9 :Er 3ϩ , Ba 2 YCl 7 :Er 3ϩ , LiYF 4 :Nd 3ϩ , and Cs 2 ZrCl 6 :Re 4ϩ .

Preparation and characterization of stable aqueous suspensions of up-converting Er3+/Yb3+-doped LiNbO3 nanocrystals

“…10. As it can be observed, they follow the expected quadratic power dependence, associated to the above described two-photon excitation mechanism [28].…”

Excitation energy migration dynamics in upconversion nanomaterials

“…The details of this model have already been intensively discussed. 2,16 However, it is worth noting that in this model, the difference caused by the spatial distribution of the donor and accepter might be overlooked since the energy transfer coefficients (W 0 and W 1 ) take the statistically average values. Here the ETU process can be simplified to an energy transfer process View Article Online between two neighboring donor-acceptor ions, which we named as the ''short-range energy transfer model'' in this text.…”

“…In the year 2000, Pollnau et al modeled the relationship of excitation density P with upconversion emission intensity I, and found that I p P n under low excitation power density. 16 The value of n indicates the number of NIR excitation photons required to generate one upconversion photon. This popular and distinct description is based on a simplified upconversion picture and a low density excitation assumption.…”

Investigation of the Up-conversion Properties of Er-Yb-doped Calcium Tantalates with Various Ca/Ta Ratios

“…5. For the unsaturated UC process, the number of photons which are required to populate the upper emitting level can be obtained by relationship (1) [21]:…”