## 2 Materials and Methods

Table 1: The values of physical parameters included in the formula for the characteristic heat diffusion time \(\tau_{\rm diff}\) for the tested samples. The values of heat capacity, density, and heat conductivity are given with three significant figures after the point, i.e., the accuracy is \(\approx\)\(\pm\)1%. The measurement accuracy of \(\tau_{\rm diff}\) is estimated at \(\pm\)3%. Figure 2: Electronic part of the TPCI scheme. In the experiments described below, the heating pulse duration was chosen to be 1 ms, which increased the sensitivity of measurements by almost 10 times compared to the case where the pulse duration was 100 \(\upmu\)s [17]. This enabled one to perform measurements on crystalline quartz samples with an absorption coefficient of \(\alpha\) \(\sim\)10\({}^{-7}\) cm\({}^{-1}\). As can be seen in Table 1, \(\tau_{\rm diff}\) was \(\approx\)1/2 of the heating pulse duration. Figure 3 shows typical oscillograms of the time-varying component averaged over \(\leq\)10\({}^{4}\) events and obtained under conditions where the duration of the heating pulse was 1 ms, the pulse power was 33 W, and the pulse repetition rate was 30 Hz. The red curve was obtained with a crystalline quartz sample having an absorption coefficient of \(\alpha\) = 8 \(\times\) 10\({}^{-6}\) cm\({}^{-1}\); the black curve, with a Suprasil 311 sample having an absorption coefficient of \(\alpha\) = 2.6 \(\times\) 10\({}^{-6}\) cm\({}^{-1}\); and the blue curve, in the ambient air with an absorption coefficient of \(\alpha\) \(\sim\)10\({}^{-9}\) cm\({}^{-1}\)[17]. The figure shows that the heat diffusion effect leads to a drastic change in the oscillograms of the time-varying component. Thus, for air, for which \(\tau_{\rm diff}\approx\) 100 \(\upmu\)s, which is a factor of 10 less than the heating pulse duration \(\tau_{\rm pulse}=\) 1000 \(\upmu\)s, this distortion leads to a weak dependence of the pulse amplitude of the time-varying component on pulse duration. While in the case of quartz glass, for which \(\tau_{\rm diff}\) is about 2.5 times greater than \(\tau_{\rm pulse}\), the growth of this amplitude over time shows only a slight deviation from linearity. For crystalline quartz, the degree of distortion of the oscillogram shape is intermediate between the two values considered. In this example, the Suprasil 311 quartz glass sample was used as a calibration sample for absorption measurements in crystalline quartz. All physical constants necessary for calculating thermo-optical parameters are known for these samples. The absorption coefficient of glass \(\alpha\) = 2.6 \(\times\) 10\({}^{-6}\) cm\({}^{-1}\) was measured by us earlier [17] for the heating pulse duration 100 \(\upmu\)s, i.e., under the condition \(\tau_{\rm pulse}\ll\tau_{\rm diff}\), where the heat diffusion effect could be neglected with a sufficient degree of accuracy. In the presented experiment, the task was to calculate the absorption coefficient of crystalline quartz using the observed oscillograms for quartz glass and crystalline quartz. The fact that the observed distortions of the temporal shape were due to the effect of heat diffusion is confirmed by Figure 4, which shows the oscillograms of Figure 3 processed as follows. The oscillograms were plotted as functions of the times normalized to the corresponding heat diffusion time \(\tau_{\rm diff}\), and the heights of the oscillograms were normalized to the products of the corresponding absorption coefficients and thermo-optical parameters. Figure 4 clearly shows that, with the accuracy of the presented measurements,  
Figure 3: Oscillograms U(t) of the time-varying component of the probe radiation power, which were obtained for SCQ (red) and Suprasil 311 quartz glass (black), as well as in the absence of samples, i.e., when the entire propagation path of the heating and probe beams passed through the ambient air (blue). The red and blue oscillograms were corrected with allowance for the ambient air effect [22].