# Theoretical Modelling of Ion Exchange Processes in Glass: Advances and Challenges
## 4 Future Challenges
### Glass Poling  
Glass poling is the distribution of the electric charges of the glass. This may result in a permanent electric field inside the glass, which can give rise to relevant non-linear effects on light propagation. Applications of glass poling include grating fabrication [83], second-harmonic generation [84] or the fabrication of optical waveguides with profiled electrodes [85]. Glass poling was initially applied to silica glass [86], which contains  
Figure 3: Simulation similar to that in Figure 2, but for a field-assisted IE with \(J_{0}/C_{0}=80\,\mathrm{nm/s}\). residual amounts of cations (\(C_{0}\sim 10^{23}\) m\({}^{-3}\)). It is realized by subjecting the sample to a strong potential difference \(U\) (typically, a few kV) at a temperature of about 250-300 \({}^{\circ}\)C and, usually, not allowing charged species to enter the glass (\"blocking anode\") [87]. Therefore, the field rearranges the cations until a new equilibrium is achieved when the original field inside the glass is cancelled by charges located near the glass surface. That is, the applied field creates a layer, under the anode, a few micrometers thick and depleted of cations. Obviously, charge neutrality is not fulfilled here. Instead, the one-dimensional form of Equations (3) and (10) of the basic model shows that the layer thickness \(d\), in equilibrium, is given by:  
\[d=\sqrt{\frac{2 eU}{eC_{0}}}\,. \tag{37}\]  
This layer is charged and has a high electrical resistivity since its anions are fixed to the glass network. Furthermore, because the field is cancelled in the glass bulk, the applied voltage drops across the depleted layer. Therefore, a very strong field arises, which is independent of the thickness of the substrate. Besides, potentials above \(\sim\)1 kV generate structural changes in the layer [88]. Then, if the sample is sharply cooled to room temperature, the distribution of charges becomes frozen. Electric fields inside the silica glass can reach \(\sim\)10\({}^{7}\) V/m, which induces a non-linear coefficient \(\chi(2)\sim 1\) pm/V [89]. However, this process is idealized. In practice, other cations are often involved due to the high applied voltages. One of the possible cations is hydronium (H\({}_{3}\)O\({}^{+}\)) from air water vapour that forms a naturally hydrated layer in the glass. In this situation, called poling with a non-blocking anode, Equation (37) is no longer valid. Instead, a stable profile, such as described in Section 2.4, is formed because hydronium moves slower than sodium. In this case, a partially depleted region is still formed before the electric field increases enough to move the hydronium cations significantly [90]. The charge and the electric field are expected to be at their greatest values when the hydronium layer begins to form. Subsequently, a part of the applied voltage \(U\) drops across the hydronium layer [91]. In glasses with high alkali content, the situation is somewhat different, since air cannot provide hydronium at a sufficient rate. Moreover, as \(C_{0}\) is large, \(d\) is small (see Equation (37)), and the electric field can become high enough to move other cations such as Ca\({}^{+2}\) or Mg\({}^{+2}\)[31; 92]. Another situation of interest occurs when a BK7 glass, which contains sodium and potassium, is poled. Initially, only sodium cations are removed from the glass surface, as they move faster. Then, the field increases in the charged layer until potassium cations start to move and accumulates behind the sodium ones, filling the empty sites that the latter have just left. Simultaneously, a fully depleted surface layer is formed [92]. Poling of double-alkali glasses, with a non-blocking anode, was also simulated with similar conclusions [93]. One interesting result, which is obtained in high-alkali glasses, is the formation of a waveguide next to the depleted layer, this having non-linear properties. In all the previously cited works about the simulation of glass poling, the authors assumed diffusion coefficients constant, which is only an approximation.