# DC Voltage Induces Quadratic Optical Nonlinearity in Ion-Exchanged Glasses at Room Temperature
## 3 Results and Discussion
### The Dynamics of the Phenomenon  
Using transparent ITO electrodes, we measured the dynamics of the SON formation/degradation in the IE glass after switching the DC voltage on/off. The angle of incidence of the fundamental beam on the specimen surface was set corresponding to the maximum SH signal evaluated from the MF (see Figure 1a). Also, for these measurements, we prepared specimens with a different kind of invasive ion (Ag\({}^{+}\)). In the experiments, we used the K\({}^{+}\) specimen exchanged for 2 h and the Ag\({}^{+}\) specimen exchanged for 20 min. As is known [27; 28; 29; 30], Ag\({}^{+}\) ions are noticeably faster than K\({}^{+}\) ions, but still slower than Na\({}^{+}\) ions, and the choice of the durations of the IE process provides comparable penetration depths. Thus, because of the different ionic mobilities and, correspondingly, the conductivities of the IE regions, there should be a difference in the dynamics of the Maxwell-Wagner charge formation and in the EFISH in the Ag\({}^{+}\)- and K\({}^{+}\)-enriched glass slides.  
In Figure 4a, we present the temporal dependences of the current flowing through the specimens while they are exposed to 1300 V DC. The dependences represent a typical charging process, like an RC circuit under DC voltage: the current decays as the charge accumulates in the specimen. The presented current decay behavior, which is of the essence, is well reproduced in our experiments, while the values of the currents fall in the range from several nA to hundreds of pA within a single temporal measurement. The current actually decays to a non-zero constant value, which corresponds to a simple Ohmic current through a specimen. Note that we normalized the dependences to fit in the [0;1] range for the sake of visual clarity. This way, we clearly see that the Ag\({}^{+}\) specimen charges much faster than the K\({}^{+}\) specimen: the corresponding exponential decay times are \(\sim\)25 s vs. \(\sim\)220 s. There are known ratios according to which the mobility of K\({}^{+}\) ions in glass is about 80 times less than that of Na\({}^{+}\) ions, while the mobility of Ag\({}^{+}\) ions is about 10 times less compared to the mobility of Na\({}^{+}\)[27; 28; 29; 30]. Thus, the Ag\({}^{+}\) ions should be about 8-10 times faster than the K\({}^{+}\) ions. Note that the estimations above are valid for elevated temperatures, while the mobility values at room temperature are uncertain. Nonetheless, these estimations correlate with the difference in the characteristic times of the Maxwell-Wagner charge accumulation in the specimens.  
The dynamics of the process is also evident from the SHG measurements. In Figure 4b, we present temporal dependences of the SH signal from these specimens after a 1300 V DC voltage was applied and after the DC voltage was turned off. There, we similarly observe a much faster development of the optical nonlinearity and, consequently, much faster decay of the nonlinearity in the Ag\({}^{+}\) specimen. Also, the magnitude of the SH signal in the Ag\({}^{+}\) specimen is about 2.5 times lower than in the K\({}^{+}\) specimen (for the sake of visual comfort in Figure 4b, the dependence for the Ag\({}^{+}\) specimen is 2.5 times enhanced). This also follows from the electric-field-driven nature of the nonlinearity: because Ag\({}^{+}\) ions move faster  
Figure 3: Maximal SH signal as a function of the square of the voltage applied to the sodium-for-potassium IE specimen (\(t_{IE}\) = 2 h). Each measurement was taken after the specimen was kept under the corresponding voltage for 20 min. The blue boxes are the experimental data, and the red dashed line is a guide for eyes demonstrating the linearity of this dependence.  
than K\({}^{+}\) ions, there is a smaller conductivity gradient in the Ag\({}^{+}\) specimen, resulting in the accumulation of less Maxwell-Wagner charge and a weaker electric field.