## 2 Materials and Methods  
Figure 1 shows the optical part of the TPCI scheme, which we modified in comparison with its first version [17] to study the effect of ambient air absorption on measurements [22]. The essence of the modification was to employ a system of lenses L\({}_{1}\), L\({}_{2}\), and L\({}_{3}\) and lenses L\({}_{4}\) and L\({}_{5}\) to eliminate technically caused radiation distortions in the waist area of the heating and probe laser beams, respectively (these distortions appeared when the radiation was focused into the center of the sample with a single lens). This was modified to better match the measurement conditions and theoretical approximations and improve the accuracy of the calculation of absorption values. Due to these lens systems, a Gaussian-like laser radiation profile with the required transverse size of the beam waist was formed along the entire length of the sample. The waist radius at the 1/e level was \(a_{\text{h}}=47\) um and \(a_{\text{probe}}=100\) um for the heating and probe beams, respectively. The waist length of the heating beam in the sample, equal to \(4\text{m}a_{\text{h}}^{2}/\lambda_{\text{h}}\) (n is the refractive index of the sample and \(\lambda_{\text{h}}=1070\) nm), was 2.9 cm, and the length of the sample we used was \(\approx\)8 cm. Thus, the radius of the Gaussian-shaped heating beam varied from 47 um in the waist to 110 um at the sample boundaries. The waist length of the probe beam in the sample was 29 cm. To measure the radii of the beams, a digital video camera with a pixel size of 4 um was employed. The radius values were calculated by processing a digital signal, averaged over 100 realizations. The accuracy of calculating the characteristic time of heat diffusion is estimated at \(\pm\)3%. As before [17, 20, 21, 22], a single-mode fiber ytterbium laser (\(\lambda\) = 1071 nm, M\({}^{2}\) = 1.08) operating in a pulse-periodic regime was used as a heating laser, and a continuous-wave single-mode He-Ne laser (\(\lambda\) = 633 nm) with an output power of 2 mW was employed as a probe laser. Figure 2 shows a block diagram of the electronic part of the setup. The driving pulse generator set the repetition rate as well as the duration of the heating laser pulse, which varied from 100 us to 100 us in the experiment. The pulse repetition rate ranged from 10 Hz to 30 Hz. The output energy of the heating laser radiation pulse varied from 1 to 40 mJ due to the laser control unit. The radiation pulse had a quasi-rectangular temporal shape, the structure of the leading edge of which, with a duration of about 7 us, was determined by the process of the build-up of the stationary generation of a fiber laser. The duration of the trailing edge, measured using a fast diode and a broadband oscilloscope, was \(\approx\)10\({}^{-8}\) s.  
The beams of heating and probe radiation were coaxial. The probe beam waist was located near the heating beam waist in the center of the sample. Pulsed heating radiation created a time-varying, spatially inhomogeneous distribution of temperature deformations in the sample, and the diffraction of the probe beam by them led to the appearance of a time-varying component of the probe radiation power. This component was recorded using a system consisting of a photodiode with 70% quantum efficiency at the probe radiation wavelength, a diaphragm, a matte plate (to smooth out the effect of the inhomogeneity of the photodiode cathode and speckle structure on measurements [23]), lens L\({}_{6}\) (see the description of Figure 1), and an amplifier (a gain of 40 dB in the frequency band from 16 Hz to 50 kHz), in which its time-varying component of power was singled out. A 100-fold  
Figure 1: The optical part of the TPCI scheme.