# Spectral Separation of Up-Conversion Luminescence Processes
## 4 Results
Vertical lines marked by the numbers 1, 2, and 3 show positions of the pump power values \(\rm I_{1}=980\) mW, \(\rm I_{2}=1435\) mW, and \(\rm I_{3}=1825\) mW used for spectrum separation in Figure 4.  
One can see in Figure 4 that the results of the spectral component separation obtained for different pump powers are in good agreement with each other, despite the noise present in the data. The influence of noise is more pronounced for lower levels of the UCL signal at the line edges. Nevertheless, the component spectral shapes inferred for different pump powers are quite close even, at the edges. To add, the \(n(\lambda,I_{1})\) evaluated for \(I_{1}\) pump power (large dots in Figure 4) is much noisier and different in values than sets of \(n(\lambda,I_{2,3})\) for two other pump power values \(I_{2,3}\). In spite of that, the spectral separation results remain similar. So, it is possible to conclude that, for the considered UCL processes, our inference procedure (7) is quite robust. It should also be pointed out that such self-testing robustness can also show the region of pump powers when the cross-relaxation influence is significant and leads to factorization breaking in the vicinity of the chosen pump power [15; 16]. Notice also that self-testing might uncover more subtle effects of additional nonlinear effects starting to play for some value of pump power, or such experimental imperfection as spectral drift of the pumping laser when increasing power of the output [52]. To give more examples of how our spectral separation works, we performed it for three spectral intervals: 440-500 nm (Figure 5), 620-680 nm (Figure 6), and 720-840 nm (Figure 7). For all of the figures (Figures 5-7), the solid line corresponds to the measured compound up-conversion signal J normalized to its maximal value \(J_{max}\); stars and circles correspond to the inferred components spectral profiles; and dots show \(n(\lambda,I_{1})\) of the compound process estimated at the corresponding wavelength. For Figure 5, the spectral separation was performed for the pump power \(I_{4}=783\) mW with the averaging region for finding log-log derivative from 390 mW, to 783 mW  
instance, in the absorption spectra [55; 56].This consideration is corroborated by the results of [23; 24; 55; 56; 57]. There, it is shown that both UCL processes \({}^{1}\)D\({}_{2}\rightarrow\)\({}^{3}\)\(H_{6}\) and \({}^{1}\)G\({}_{4}\rightarrow\)\({}^{3}\)\(H_{6}\) are characterized by a doublet line structure. So, the changes in EN near 470 nm might be indeed connected with additional processes associated with transitions from the upper levels of the \({}^{3}\)G\({}_{4}\) band, or perhaps to a transition from \({}^{1}\)\(D_{2}\) band to the upper and lower levels of the \({}^{3}\)\(H_{6}\) band. Figure 6: The spectral separation in the interval 620–680 nm. The solid line corresponds to the measured total normalized up-conversion signal \(\mathrm{J}/\mathrm{J}_{\mathrm{max}}\). The circles show the spectrum corresponding to the process \({}^{1}\)D\({}_{2}\rightarrow\)\({}^{3}\)\(H_{4}\). Stars show the spectrum corresponding to the process \({}^{3}\)G\({}_{4}\rightarrow\)\({}^{3}\)\(H_{6}\). The EN \(n(\lambda,\mathrm{I}_{2})\) of the total UC signal. The spectra separation is for the pump power \(\mathrm{I}_{2}=1435\) mW. Figure 7: The spectral separation in the interval 720–860 nm. The solid line corresponds to the measured total normalized up-conversion signal \(\mathrm{J}/\mathrm{J}_{\mathrm{max}}\). The circles show the spectrum corresponding to the process \({}^{1}\)G\({}_{4}\rightarrow\)\({}^{3}\)\(H_{5}\). Stars show the spectrum corresponding to the process \({}^{3}\)\(H_{4}\rightarrow\)\({}^{3}\)\(H_{6}\). Dots show the EN \(n(\lambda,\mathrm{I}_{2})\) of the total UC signal. The spectra separation is for the pump power \(\mathrm{I}_{2}=1435\) mW. Another interesting and insightful feature can be noticed in Figure 6, and especially in Figure 7, where the component spectra are strongly overlapping.