## 4 Discussion and Comparison with Experiments
### LFC of Tempered Glass  
In the experiment [5; 6], a smooth laser cutting of chemically-tempered Corning \({}^{\text{\textregistered}}\) Gorilla \({}^{\text{\textregistered}}\) Glass 5 with a thickness of 550 \(\upmu\)m has been observed at speeds up to 4 m/s. The depth of the hardened layer (DOL, depth of layer) on the front and back of the plate was 20 \(\upmu\)m. According to the reports of these authors, the laser source (Spirit\({}^{\text{\textregistered}}\) HE laser, from Spectra Physics, Rankweil, Austria) had pulse energies of \(>\)120 \(\upmu\)J and average output powers of \(>\) 16 W. The laser offers also process flexibility at the wavelengths of 520 and 1040 nm with programmable pulse energy, repetition rate, and pulse width between 340 fs and 10 ps. The femtosecond pulses can be also supplied in a burst train with a controlled number of pulses up to 20 and with the time spacing between the pulses in the burst around 13 ns. Besides chipping free edges, the quality of a laser cut (defined by the average roughness of the cross-section) of \(<\) 0.1 \(\upmu\)m has been achieved using the developed at Spectra-Physics process ClearShapeTM. This process is not disclosed in the papers [5; 6], but authors report that at a wavelength of 1040 nm it allows glass cutting by using relatively low average power of \(<\) 4 W.  
We will try now to explain these experimental parameters of radiation, which actually provide for this material a smooth separation, based on the proposed model. Note that according to the model, chemically tempered glass is preferred for obtaining smooth separation by its properties, since, as the criteria (86) and (88) necessary for obtaining a separation with better smoothness for amorphous material are met (see Table 2). It means that the predominant mechanism of the impact zone formation around the filament for this material is the thermal, rather than the shock-wave one. When calculating the irradiation parameters \(E_{1}\), \(\tau\), \(s_{1}\), \(f\), \(P\) and \(u\) necessary for smooth separation, we follow below the algorithm scheme shown in Figure 7.  
The radius of the filament in this experiment is not reported. However, as in the case of sapphire in Section 4.1, it can be estimated theoretically: for \(M^{2}=\)1.25, \(\lambda=\) 1.04 \(\upmu\)m and the numerical focusing aperture NA = 0.6 according to (19), with \(q\approx\) 1, as discussed, we obtain \(\tau_{f}\approx\) 0.49 \(\upmu\)m. In the absence of data on the length of the filament in the experiment under consideration, we take \(H=\) 45 \(\upmu\)m, as for the LFC of sapphire in Section 4.1 above. For the tempered glass, we take \(w_{dis}=\) 64 kJ/cm\({}^{3}\)[52], \(P_{c}\) (\(\lambda\)=1040 nm) = 5 MW [19] and \(\Gamma=\) 1-2. We also put \(A_{L,P}=\) 0.8 and \(A_{P,H}=\) 0.9, as discussed earlier. For the thermal mechanism in this case, \(\gamma_{tw}=\) 1/e = 0.37. It is also assumed for estimates, as above for sapphire, that \(K_{tw}\approx K_{sw}\), and hence, taking into account the relation (14), \(K_{tw}\approx\) 0.5. Reference data from Table 2 are used in the model: \(\rho=\) 2.43 g/cm\({}^{3}\), \(T_{strain}=\) 571 \({}^{\circ}\)C [55], T\({}_{i}=\) 20 \({}^{\circ}\)C and \(C_{2}=\) 0.94-1.0 J/(g\(\times\)K). According to Figure 7, all these data are used as input parameters. Next, in stage 1, we select VED bounds as \(w_{1}=\) 336 kJ/cm\({}^{3}\) and \(w_{2}=\) 396-480 kJ/cm\({}^{3}\) according to calculations given in Table 1 for this material and for a very close value of \(\tau_{f}=\) 0.5 \(\upmu\)m. For the thermal modification mechanism, which is the dominant one, in this case, we choose for a certainty the high-frequency range of pulse repetition frequencies, i.e., \(f\geq\)\(f_{1}\). The exact value of the limiting frequency \(f_{1}\) will be found below.