Ensities from Er3 4 G11/211/2,HH9/2,four F5/2, 4F7/2, , S3/2, 4F9/2,9/2 , and levels a Figure Measured emission intensities from Er3 4G , 2 29/2 , 4F5/2 4 F7/2 four 4 S3/2 , four F and 4I9/2 4I 382, levels 452, 490, 541, 654, 541, 654, and 807 nm, respectively, within the 10Er sample versusthe pumpin 9/2 408, at 382, 408, 452, 490, and 807 nm, respectively, inside the 10Er sample versus the pumping powers980(a) 980(b) 1530 nmnm excitation. The numbersdenote the slopes on the power powers of (a) of and and (b) 1530 excitation. The numbers denote the slopes with the energy de dependencies. pendencies.3.three. Modeling the Fluo-4 AM Data Sheet Upconversion Luminescence ProcessesWe further setup simplified price equations to calculate the theoretical slopes of your energy We further setup making use of a five- (Figure 6a) and calculate the theoretical slopes dependences of Er3 UCL,simplified rate equations to eight-energy-level (Figure 6b,c) of th power dependences of Er3 UCL, working with a five-The facts of andestablishment from the (Figur model for 980 and 1530 nm excitation, respectively. (Figure 6a) the eight-energy-level 6b,c) model for nicely as the extraction with the slopes, refer for the reports elsewhere establishmen price equations, as 980 and 1530 nm excitation, respectively. The information with the [49].3.three. Modeling the Upconversion Luminescence Processesof the price equations, as well because the extraction on the slopes, refer for the reports else exactly where [49].Figure six. Simplified power levels of Er3 with the dominant upconversion pathways upon (a) 980 nm excitation, (b) weak 1530 nm excitation, and (c) robust 1530 nm excitation.Figure 6. Simplified energy levels of Er3 together with the dominant upconversion pathways upon (a) 98 nm excitation, (b) weak 1530 nm excitation, and (c) robust 1530 nm excitation.Nanomaterials 2021, 11,eight of3.three.1. Excitation at 980 nm As pointed out above, we assume the ESA and ETU processes dominate Er3 green and red UCL mechanisms upon 980 nm excitation, respectively (Figure 6a). The corresponding price equations can be provided as follows: 1 : 0 N0 – 1 N1 – W N1 N3 – A1 N1 two A2 N2 = 0 two : 2W N1 N3 three A3 N3 – A2 N2 = 0 3 : 1 N1 – 3 N3 – W N1 N3 4 A4 N4 – A3 N3 = 0 four : 3 N3 – A4 N4 =(1)exactly where Ni , i , , W, Ai , and i stands for the population density of level i (i = 0, 1, 2, three, and four); absorption cross Licoflavone B Autophagy section for level i; pumping price (proportional to incident laser energy); ET price involving power levels 1 and 3; transition rate of level i, including the radiative transition towards the ground state and also the multiphonon-assisted decay to its reduce level; and fraction with the multiphonon-assisted decay price, respectively. For the 980 nm weak pumping scenario, the downward decay Ai Ni dominates the depopulation of each state, then we acquire: 1: two: three: 4: 0 N0 – A1 N1 = 0 3 A3 N3 – A2 N2 = 0 1 N1 – A3 N3 = 0 3 N3 – A4 N4 = 0 N1 N2 N3 N4 P1 P2 P2 P(2)For 980 nm robust pumping, because the ESA and ET processes boost more evidently with the incident laser power than the multiphonon-assisted decay course of action, we assume that the upward ESA (1 N1) dominates the depopulation of energy level 1, along with the ET approach dominates the depopulation of power level 3 (WN1 N3 three A3 N3). Moreover, the fraction four is set to become 1, due to the closely distributed states of Er3 inside the greater power area. We consequently obtain: 1 : 0 N0 – 1 N1 = 0 two : 2W N1 N3 – A2 N2 = 0 3 : 1 N1 – W N1 N3 – A3 N3 = 0 4 : three N3 – A4 N4 = 0 N1 N2 N3 N4 P0 P1 P1 P(3)From above, it could be concluded that the slope values n stand for the photon.