## 1 Introduction  
Optical glasses are the main materials for manufacturing linear optical elements (waveguides, splitters). However, recently, primarily in view of the advance of fiber optics, optical glasses have also been used as nonlinear elements in various optical devices, modulators, optical switches, and frequency converters. Compared to the crystals typically utilized in nonlinear optics, glasses are more cost-effective and involve easy-to-use engineering materials, which is especially important in passive or active fiber networks. The third-order nonlinear coefficient of glasses, for example, the Kerr coefficient \(n_{2}\), lies in a wide range of values [1,2]: from \(\sim\)10\({}^{-16}\) cm\({}^{2}\)/W for silicate and fluoride glasses to 10\({}^{-14}\) cm\({}^{2}\)/W for tellurite and \(\sim\)10\({}^{-13}\) cm\({}^{2}\)/W for chalcogenide glasses. The glasses of the latter two families, by virtue of such a large nonlinearity and a broad transmission window, are particularly promising materials in near- and mid-IR nonlinear photonics, including supercontinuum [3,4] and frequency comb [5] generation, the development of fiber optical parametric oscillators [6], and others. Actually, due to macroscopic centrosymmetry, second-order nonlinear phenomena are prohibited in the bulk of the glasses, which limits their nonlinear applications compared to crystals. To overcome this limitation and break the centrosymmetry, different poling techniques have been successfully used [2], including thermal [7, 8, 9, 10] and optical [11, 12, 13] poling, which have become proven and efficient approaches to induce second-order optical properties in glasses. In both techniques, the most likely mechanism for the occurrence of quadratic nonlinearity is associated with the formation of a built-in (\"frozen\") static electric field \(E_{froz}\) due to the separation and subsequent freezing of charges on the application of a strong external DC field [14; 15; 16]. In the case of thermal poling, such charge separation occurs due to the displacement of cations (for example, the alkali ions Na\({}^{+}\) or Li\({}^{+}\) typically present in silica glass as impurities [10]) from an anode at a high temperature; in the case of optical poling, due to the displacement of photocarriers excited by short-wavelength optical radiation (UV, blue or green light). As a result, an effective second-order nonlinear susceptibility \(\chi^{(2)}_{eff}=3\chi^{(3)}E_{froz}\) arises through the electro-optical effect from the third-order nonlinear susceptibility \(\chi^{(3)}\)[17]. In a particular (most applicable) case in which poled glasses are used for second-harmonic generation (SHG), two optical frequencies experience nonlinear mixing with the zero frequency of the DC field corresponding to \(\chi^{(3)}=\chi^{(3)}(-2\omega;\omega,\omega,0)\). However, in most studies of glass poling, \(\chi^{(3)}\) is usually taken from (or assumed to be close to) the all-optical third-order nonlinear susceptibility related to the optical Kerr effect (OKE) (\(\chi^{(3)}=\chi^{(3)}(-\omega;\omega,-\omega,\omega)\)) or third-harmonic generation (THG) (\(\chi^{(3)}=\chi^{(3)}(-3\omega;\omega,\omega,\omega)\)). In other words, the weak dispersion of \(\chi^{(3)}\) is generally implied [9; 18; 19]. For silicate glasses, this assumption seems to be reasonable in view of the experimentally demonstrated small contribution of nuclear nonlinearity compared to that of electronic nonlinearity [20; 21]. Additionally, the direct experimental measurement of the third-order nonlinear susceptibility for some silicate glasses by electric-field-induced SHG (EFISHG) [22; 23] in comparison with DC or the optical Kerr effect [24] (including z-scan measurements [25]) and THG [26] showed that the corresponding \(\chi^{(3)}\) coefficients are, indeed, rather close to each other.