## 5 Discussion of the Results
### Influence of the Optical Transport Parameters of the Examined Systems  
A sufficiently larger rate of \(M_{3}\) increase with an increasing wavelength for the titania-based system can be interpreted in terms of high efficiency of fluorescence excitation in a relatively thin subsurface layer of the system compared to the silica-based system. This is consistent with a significantly larger integrated fluorescence yield \(Q\) and fluorescence spectrum expansion in the long-wavelength region (Figure 6, curve 3) which resulted from a significantly smaller value of the transport mean free path in the ensemble of densely packed titania particles. These features can be considered using the following qualitative phenomenological model. Under the used fluorescence excitation conditions (in particular, a sliding fall of the laser beam onto the sample surface), the penetrating pumping light propagates in a thin subsurface layer of the sample undergoing gradual absorption and simultaneous transformation to a diffuse component. The characteristic scale of the light propagation in the random media is related to the extinction length \(l_{ext}\), which is inverse of the extinction coefficient \(\mu_{ext}\):  
\[l_{ext}^{-1}=\mu_{ext}=\mu_{a}+\mu_{s}=l_{a}^{-1}+l_{s}^{-1}, \tag{13}\]  
where \(\mu_{a},\mu_{s}\) are absorption and scattering coefficients of the medium, and \(l_{s}\) is the scattering mean free path. A near-isotropic scattering occurs in the examined systems and, therefore, we can set \(l_{s}\approx l^{*}\). Consequently, the extinction length is approximately equal to \(l_{ext}\approx l_{a}l^{*}/(l_{a}+l^{*})\). Based on the characterization results for the examined systems we can see that, in the case of titania-based system at 532 nm, the absorption length is significantly larger than \(l_{TiO_{2}}^{*}\). Correspondingly, \(l_{ext,TiO_{2}}\approx l_{TiO_{2}}^{*}\). The SiO\({}_{2}\) -based system is characterized by a sufficiently larger value of the extinction length \(l_{ext,SiO_{2}}>>l_{ext,TiO_{2}}\). Therefore, we can conclude that transformation of the pumping light to the fluorescence radiation occurs in a sufficiently thinner subsurface layer in the TiO\({}_{2}\)-based system compared to the SiO\({}_{2}\)-based system. In the spectral region of interest, from 600 nm to 700 nm, the absorbance of the system is governed only by self-absorption of fluorescence radiation and the absorption length is expected to be larger than in the case of 532 nm. As a result of sample characterization (Section 3.2), we can assume that the fluorescence radiation field is mainly localized in the subsurface layer of the TiO\({}_{2}\)-based sample with the thickness of the order of few micrometers. In this case, the average path-length difference \(\langle\Delta s\rangle\), which determines \(M_{3}\) for the non-polarized light under the given value of \(l_{c}\), is proportional to \(l_{TiO_{2}}^{*}\). In contrast, the zone of fluorescence radiation localization is distributed over the entire thickness of the SiO\({}_{2}\)-based sample. For such radiation conditions, the average path-length difference becomes dependent not only on the transport mean free path \(l^{*}_{TiO_{2}}\), but also on the sample thickness. In any case, \(\langle\Delta s\rangle_{SiO_{2}}>\langle\Delta s\rangle_{TiO_{2}}\), and this is manifested in the larger values of \(M_{3}\) for the TiO\({}_{2}\)-based samples. In addition, it is necessary to note that the average volume density of fluorescence radiation energy is substantially higher in titania-based systems due to a smaller localization zone compared with the silica-based system. This is the reason for the abovementioned features of the fluorescence spectrum of the TiO\({}_{2}\)-based system.