*3.4. Direct Absorption Measurements*

Light absorption measurements in TiO2 films were measured directly using a laser-induced deflection (LID) technique [30,31]. This technique belongs to an ensemble of photothermal techniques with a pump–probe configuration. When the pump laser hits the sample under investigation, the absorbed pump laser power forms a temperature profile (Figure 3, left). The latter is turned into a refractive index profile (=the thermal lens) by both the thermal expansion and the

temperature-dependent refractive index. The refractive index gradient accounts for a deflection of the probe beams (from the same laser source) that is proportional to the absorbed pump laser power.

**Figure 3.** General scheme for the laser-induced deflection (LID) photothermal technique (**left**) and the measurement concept for rectangular substrate geometries (**right**).

Figure 3 (right) shows the applied measurement concept for the investigated rectangular substrate geometry (20 <sup>×</sup> <sup>20</sup> <sup>×</sup> 6 mm3) with one coated surface. Two-probe beams above/beneath the irradiated spot utilize the probe beam deflection perpendicular to the pump beam direction. To measure coatings, the probe beams pass the sample close to the coated surface. In the case of transparent coatings, the probe beam deflection always comprises both the coating and substrate absorption. In order to distinguish both absorption contributions, an uncoated reference substrate of the same geometry/material is measured additionally, and the difference in the deflection signals is assigned to the coating absorption.

Calibration of the measurement setup is required to obtain absolute absorptance data from the deflection signals. For the LID technique, electrical calibration is applied, i.e., the thermal lens is generated by particular electric heaters. In the case of coating/surface absorption, small surface-mounted device (SMD) elements—fixed onto a very thin copper plate (thickness ~200 μm)—are placed centrally onto the surface of a reference substrate (of the same geometry and material) [32]. The copper plate allows for the required high thermal conduction to the sample. The validity of this calibration approach has been verified through separate measurements of reflectance, transmittance, absorptance, and scattering for different materials and coatings. The results of these energy balance measurements confirmed that in terms of measurement accuracy, a value of 1 was obtained in each of the investigations [33]. The calibration procedure itself is composed of measuring the probe beam deflection as a function of the electric power. Plotting the deflection signals versus electrical power (Figure 4) gives a linear function that spans several orders of magnitude for electric power, and the calibration coefficient *FCAL* is defined by the slope of the linear function (including the zero-point, i.e., no electrical power means no probe beam deflection) [31]. From the LID deflection signal *ILID* (for the sample under investigation), the corresponding mean pump laser power *PL*, and the calibration coefficient *FCAL*, the coating absorptance (defined as the ratio of the absorbed and incident light intensity) is calculated by

$$\text{Absorption} = \frac{I\_{LID}}{F\_{CAL}P\_L}.\tag{5}$$

Laser irradiation at around 800 nm was realized by two different laser sources. For low-intensity measurements, an 808-nm continuous-wave semiconductor laser (HangZhou Naku Technology Co., Ltd.) with a maximum output power of 10 W was applied. The laser beam was shaped to a spatial profile of about 2 <sup>×</sup> 2 mm<sup>2</sup> on the sample. For elevated laser intensities in the GW/cm<sup>2</sup> range, an 800-nm Femtosecond laser (Astrella-V-F-1k, Coherent Inc.) with a pulse duration of 82 fs, a repetition rate of 1 kHz, and an average power of up to 2.1 W was used. In order to vary the laser intensity and maintain the laser pulse duration, a combination of a thin-film polarizer and a polarizing beam splitter was

placed into the beam path. A telescope was used to shape the Gaussian laser output beam to a 1/e2 Diameter of 5.4 mm on the sample under investigation.

**Figure 4.** Measured deflection signal as a function of the electrical power (dots) and the linear fit without offset (red line) used for a determination of the calibration coefficient.

For a wavelength of 800 nm, the optical thickness of a 200-nm-thick TiO2 film is not equal to λ/4 or multiples of λ/4. Therefore, laser beam reflection at the interface of the air/TiO2 film was not negligible. The calculated reflectance amounts (up to about 15%) were taken into account for the determination of the average laser power *PL* inside the TiO2 film.
