A "characteristic" saturation phenomenon of upconversion fluorescence resulted from energy diffusion

This paper reports an interesting "characteristic" saturation phenomenon of upconversion luminescence of TmYb codoped ZBLAN glass when excited by 966nm-diode laser. That is the log-log plot of upconversion fluorescence intensity upon laser power is a straight line basically, however the slope of the log-log curve of two-photon and three-photon upconversion fluorescence intensity upon laser power is smaller than 2 and 3 very evidently respectively in laser focus point. It is very interesting that the slope would be enlarge clearly if the facula of pumping laser was increased. It could be believed that this phenomenon is not a simple "typical" saturation phenomenon that is caused by population exhausting in ground state, which F-P log-log curve is gradually bending. The only reason is just the energy diffusion. That is said, because of the resonant energy transfer among Yb3+ ions, Yb3+ ions which are within the laser facula and absorbs photon energy of pumping laser would diffuse energy to those Yb3+ ions which are out the laser facula. This process would cause energy density waste. And the slope would reduce also. Especially the proportion of wasting energy density is independent to pumping laser power, so the slope would be a straight line basically However if laser facula was bigger than energy diffusion length, the energy density waste caused by energy diffusion would have be zero basically. Under this case, the slopes of log-log variation F-P curve are quite near the normal multi--photon relation. The similar mechanism has not been reported internationally up to now.