*5.2. Considerations Regarding Nonlinear Refraction*

It should be mentioned that both model approaches allowed for estimating the nonlinear refractive index as well, and such like calculations could be compared to the reported experimental data collected in Table 2. This is shown in Figure 10 (excluding the extraordinarily large value from Reference [24]). The predictions of the Sheik–Bahae model (assuming the input data from Table 1) almost coincided with the chosen ordinate scaling and were in reasonable agreement with the experimental data from References [20–23,26]. The ß\_do model delivered results in the infrared that practically coincided with the Sheik–Bahae model predictions up to the TPA threshold. At higher wavenumbers, both approaches delivered divergent results. Note that none of the models was able to reproduce the strongly negative *n*<sup>2</sup> value from Reference [19], but the Sheik–Bahae model came at least close to this value. This is not astonishing, because in the ß\_do approach (Equations (3) and (4)), only the TPA resonant contribution to *n*<sup>2</sup> is taken into account, while nonresonant contributions are not considered at all.

**Figure 10.** Measured nonlinear refractive indices from different TiO2 modifications compared to simulations in terms of the Sheik–Bahae approach as well as Equations (3) and (4).

The relative stability of the Sheik–Bahae approach with respect to correlated changes in the optical gap and the refractive index makes it difficult to understand density-related differences in the nonlinear response of different TiO2 modifications. Nevertheless, a density dependence of *n*<sup>2</sup> and β is physically reasonable and expected. It seems to be an advantage of the ß\_do model that differences in the density are explicitly taken into account in terms of the model parameter *J*; consequently, the modeled *n*<sup>2</sup> data for the IBS film is larger than those of the PIAD film. This way, the ß\_do model might provide access to explaining the significant scatter in measured nonlinear constants, as has been reported in the different studies cited. For future practical modeling, it might therefore be useful to merge both models in a suitable way.
