## 1 Introduction
In fact, the laser microstructuring of glasses makes it possible to form micron-sized domains that are close to spherical or ring-shaped, with a modified glass structure at the periphery of the domains [19; 33; 35; 39; 45; 48; 49; 50; 51; 52]. For example, the local modification of silver-doped phosphate glasses with laser pulse energies \(E_{p}\) in the range of 10-100 nJ led to the formation of micron-sized ring-shaped domains due to the aggregation of silver nanoclusters at the periphery of the domains [48]. Laser pulse energy \(E_{p}\) and pulse repetition rate play an important role in the microstructuring of glass-forming materials. In fact, laser pulses with a sufficient repetition rate can provide cumulative heating near the focus of the laser beam. In this article, we will focus on the effect of single laser pulses (the effect of repetition rate will be discussed in a separate article). The temperature change associated with the heating pulse is on the order of \(\Delta T=E_{p}/C_{loc}\), where \(C_{loc}=\rho c_{p}V_{0}\) and \(V_{0}\) are the heat capacity and volume of the heating zone, and \(\rho\) and \(c_{p}\) are the density and specific heat capacity, respectively, of the material. The thermal effect caused by elastic deformations is negligible compared to \(\Delta T\), at least at a moderate \(E_{p}\), in the range of, say, 10-100 nJ for a focal region with a radius of about 1 \(\mu\)m. Indeed, the thermoelastic pressure in the hot zone is less than the maximum pressure response \(p_{max}=K_{B}\alpha_{V}\Delta T\) to the temperature change \(\Delta T\) at constant volume, where \(K_{B}\) and \(\alpha_{V}\) are the bulk modulus and the volumetric thermal expansion coefficient. However, the volume of the hot zone is not  
Figure 1: Schematic diagram of the specific volume \(V\) as a function of temperature \(T\) for glass-forming materials at different cooling rates of \(-\mathcal{R}_{1}\) and \(-\mathcal{R}_{2}\). Liquid structures freeze to a glassy state with \(V_{2}(\mathcal{R}_{2})>V_{1}(\mathcal{R}_{1})\) at \(|\mathcal{R}_{2}|>|\mathcal{R}_{1}|\). rigidly fixed by the material surrounding this zone. In fact, a pressure wave is created around the hot zone [53; 54]. In this case, the thermoelastic pressure is even less than \(p_{max}\). Thus, the elastic energy associated with the thermoelastic pressure in the hot zone of volume \(V_{0}\) is less than \(E_{TE}=\frac{1}{2}K_{B}(\alpha_{V}\Delta T)^{2}V_{0}\). Therefore, the relative effect associated with thermoelastic deformations does not exceed \(E_{TE}/E_{p}=\frac{1}{2}K_{B}(\alpha_{V})^{2}\Delta T/\rho c_{p}\). For example, for sodium-limine-silicate glasses with the composition Na\({}_{2}\)O-2 CaO\(\cdot\)3 SiO\({}_{2}\), \(E_{TE}/E_{p}\) is about 1% at \(\Delta T=2000\) K, \(K_{B}=55\) GPa, \(\rho=2.8\) g/cm\({}^{3}\), \(c_{p}=1.14\) J/gK, \(\alpha_{V}=3\alpha\), and linear thermal expansion \(\alpha=7.7\cdot 10^{-6}\) 1/K [55; 56; 57; 58; 59]. This ratio is even lower for borosilicate glasses with a low coefficient of thermal expansion [60]. For example, for borosilicate glasses such as Pyrex, the \(E_{TE}/E_{p}\) ratio is about 0.1% at \(\Delta T=2000\) K, \(K_{B}=33\) Gpa, \(\rho=2.23\) g/cm\({}^{3}\), \(c_{p}=1.1\) J/gK, and \(\alpha=3.3\cdot 10^{-6}\) 1/K [61; 62; 63]. However, \(E_{TE}\) becomes comparable with \(E_{p}\) at laser pulse energies approximately two orders of magnitude higher than those considered in this work. We are interested in local temperature changes in a micron-sized hot zone at \(t>\tau_{p}\), when the pressure waves created around the hot zone are already at a distance of more than 1-2 \(\upmu\)m from the hot zone. However, at the same time, the front of the temperature change extends only about ten nanometers from the periphery of the hot zone. Thus, we consider the change in local temperature after the local pressure in the hot zone has almost stabilized.