*5.1. Film Absorption*

Linear absorption in TiO2 films at 800 nm has been shown to be as low as a few ppm, but varies over two orders of magnitude. No correlation was found between linear and nonlinear absorption properties. The observed TPA coefficients were less than one order of magnitude higher than previously published TPA coefficients in the range of 0.9–1.5 <sup>×</sup> 10−<sup>11</sup> cm/W (measured at 800 nm in bulk rutile (TiO2)) [25]. However, this finding is in agreement with earlier experimental results for fluoride thin films at 193 nm [34]. Here, it was demonstrated that the TPA coefficients of thin films were significantly larger than those obtained for the corresponding bulk materials.

On the other hand, the TPA coefficients observed in this study were about three orders of magnitude smaller than the values published in Reference [19] (compare Table 2), which was obviously a result of the different wavenumbers. Indeed, the photon energy in our study was still slightly below the value of *Eg*/2 (which we will further call the TPA threshold energy), while in Reference [19], the photon energy was well above that value. In order to visualize that, Figure 9 presents the measured TPA coefficients together with those calculated according to both the Sheik–Bahae (Equation (1), solid lines) and ß\_do (dashed lines) models. Note that both models predicted an increase in β by almost three orders of magnitude when the wavenumber was changed from 12,500 to 18,800 cm<sup>−</sup>1. This way, both models reproduced the dynamic range observed in the measured values. What is particularly remarkable is the good mutual agreement between both model approaches in the mentioned spectral region: The models delivered remarkably different results only when the photon energy came close to the single photon absorption edge at wavenumbers around 26,500 cm−1. For reference purposes, we parametrized the dielectric function of the IBS sample specified in References [17,18] in terms of the ß\_do model and included corresponding estimations of the TPA coefficient with Figure 9: Similarly to what is shown in Figure 1, the Sheik–Bahae model predicted a wavenumber shift of the spectral features without significant changes in the maximum absorption. On the contrary, note that in the ß\_do model, the larger density of the IBS layer resulted in an increase in β, so that the calculated TPA coefficient came closer to the rutile value from Reference [19]. Again, for reference purposes, we included the rutile TPA simulation in terms of Equation (1) with Figure 9.

Note that the wavenumbers around 12,500 cm−<sup>1</sup> fell close to the TPA threshold wavenumbers in TiO2. In the case of the rutile data from Reference [25], the Sheik–Bahae model (dark cyan line) provided a good theoretical reproduction of the TPA coefficients, because the excitation wavenumbers (Table 2) were still higher than the corresponding TPA threshold wavenumber (12,177 cm<sup>−</sup>1, compare Table 1), which was required for calculation in terms of Equation (1). However, the measured PIAD data could not be reproduced in terms of the Sheik–Bahae model (solid black line) with the parameters given in Table 1. The reason is that in Equation (1), the excitation wavenumber should exceed the TPA threshold, which corresponds to 13,345–13,490 cm−<sup>1</sup> for the PIAD samples (Tables 1 and 4). This was not achieved in our measurements. Clearly, the PIAD films were essentially amorphous, such that the optical gap (and correspondingly the TPA thresholds) did not represent "hard" threshold energies. Instead, band tailing allowed for absorption even when the photon energy was smaller than the corresponding "threshold". Note that in this connection, the ß\_do model predicted a certain TPA even below the thresholds, which turned out to be less than one order of magnitude smaller than the measured absorption. Clearly, films produced by evaporation are usually highly defective and maybe

somewhat contaminated, and it is therefore not so surprising that the measured absorption values somewhat exceeded the modeled ones.

**Figure 9.** Measured TPA coefficients from rutile and PIAD TiO2 compared to simulations in terms of Equations (1), (3), and (4).
