## 1 Introduction  
The electric double layer (EDL) at the electrode-solution interface plays an important role as a stage for electrochemical reactions [1, 2, 3, 4]. In addition, it finds a large variety of applications such as EDL capacitors [5], EDL transistors [6, 7, 8], light-emitting and power-generating devices [9, 10], electric field-induced ferromagnetism [11, 12], and electric field-induced superconductivity [13, 14]. Furthermore, the electrode interface is an interesting research target from the viewpoint of nonlinear optics [15, 16, 17] because of its broken spatial inversion symmetry. In other words, second-order nonlinear optical effects such as sum frequency generation [18, 19] and Pockels effect appear.  
The interfacial Pockels effect was first observed at the interface of a transparent oxide electrode and an aqueous electrolyte solution [20, 21], and has since been observed not only on various electrodes [22, 23, 24, 25] and with polar solvents [26] but also at solid-solidinterfaces [27]. Recently, it has been successfully demonstrated that the Pockels effect of interfacial water can be applied as an electro-optic modulator (=EDL light modulator) [28; 29]. Although the response speed is currently limited, deep optical modulation is realized at an extremely low cost and with a simple configuration, and there is potential for applications such as optical sensors in liquids. In previous reports on the interfacial Pockels effect, two electrodes have always been used, one for observing the Pockels effect of water at the interface and the other for its counter electrode. In this paper, in contrast, we report the observation of the Pockels signal by applying a potential difference to both ends of a single electrode. The signal's magnitude and sign change depending on the location of the electrode, and this behavior is found to be correlated with the electric field distribution perpendicular to the electrode interface, generated by the potential distribution due to the in-plane parallel current.  
The results of this paper may stimulate fundamental research on the properties of the electric double layer in orientations parallel to the electrode surface, which have not been dealt with extensively, and may lead to useful general-purpose techniques for non-contact observation of current and voltage distributions on electrode surfaces, as described below. In anticipation of the arrival of the Internet of Things (IoT) society [30], there is a growing interest in harvesting and reusing energy that was discarded at present. In particular, attention is being paid to thermoelectric power generation [31], which can supply power to devices such as low-power sensors by using waste heat that is ubiquitous around us. For this purpose, the search for novel materials with highly efficient thermoelectric conversion functions is being conducted worldwide [32; 33; 34]. This exploratory research is experimentally conducted through contact measurements involving wiring, where a spatial temperature difference is applied to the sample, and the potential difference generated in the section is measured. This requires a process associated with wiring, making exhaustive experiments difficult. In contrast, if the presence of a potential difference could be detected only through non-contact optical measurements without wiring, it would contribute to the screening of potential thermoelectric materials. We would also like to mention the potential applications of the results of this paper in this field.