## 5 Conclusions  
It was found that the Pockels effect of interfacial water on an electrode can be observed using a single electrode without the need for a separate counter electrode. The magnitude and polarity of the Pockels signal change following the distribution of the electric field perpendicular to the electrode surface, which is generated depending on the potential distribution in the electrode plane. Although the interfacial Pockels effect of water is largest on the surface of transparent conductive  
Figure 6: (**a**) Geometrical configuration assumed for the calculation of the electric–field distribution. (**b**,**c**) Calculated results of the electric-field (**b**) \(\left(E_{x},E_{y}\right)\) and (**c**) \(E_{y}\) distribution on the horizontal (\(xy\)) plane at \(z=25\) perpendicular to the electrode surface. The contour plot of the electric field \(E_{y}\) is also shown in (**c**). oxide electrodes to date, it has been found to occur not only with the combination of transparent oxide electrodes and water but also with a variety of electrodes and polar organic solvents, although the magnitude of the signal varies depending on the combination [22; 23; 24; 26]. Recently, there have been reports of light modulators using the interfacial Pockels effect [28; 29], so the single-electrode Pockels effect will enable light modulators using a variety of materials in an even simpler arrangement. The fact that the signal depends on the surface potential distribution generated may be useful for sensor applications in solution, such as measuring electric field distribution. In addition, since the generation of a Pockels signal indicates the occurrence of a potential difference on the interface, it may be applied to the non-contact search and screening of thermoelectric materials [32; 33; 34] without the need for wiring. This can be achieved by creating a temperature gradient upon pump light irradiation and detecting the generation of the potential difference from probe light reflection change on the material surface immersed in water or alcohol solution [26]. However, since quantitative evaluation of thermoelectric constants such as Seebeck coefficient is difficult with this method as long as the interfacial Pockels coefficient of the sample is unknown, a theory that can predict the Pockels coefficient at the interface between arbitrary materials is demanded. Conceptualization, E.T., H.K. and K.M. ; methodology, E.T. and H.K. ; software, K.M. ; formal analysis, K.M. ; investigation, K.M., T.I. and A.O. ; writing--original draft preparation, K.M. and E.T. ; writing--review and editing, E.T. and T.K. ; visualization, E.T. ; project administration, E.T. ; funding acquisition, E.T. All authors have read and agreed to the published version of the manuscript. This research was funded by Grant in Aid for Scientific Research(B) (grant Number JP20 H02659) and the Japan Society for the Promotion of Science (JSPS). Not applicable. The data that support the findings of this study are available from the corresponding author upon reasonable request. The authors declare no conflicts of interest. Appendix A Position Dependence on a Single Copper Electrode of the Pockels Signal Induced by Current Parallel to the Electrode Surface  
To demonstrate the universality of the single-electrode Pockels effect, we report experimental results confirming that the same phenomenon occurs at copper electrodes. For the measurement, the copper tape sample shown in the upper left of Figure 11 was attached to a glass slide with adhesive (Cemedine). The backside was used as the light-illuminated side because of the PET insulating treatment on the surface. Other types of copper tape and copper plate samples were also measured, with the result that the signal qualitatively had the same characteristics. Reflectance spectra in air were measured with a spectrophotometer (SolidSpec-3700 DUV, Shimadzu, Kyoto, Japan).