## 1 Introduction  
When a voltage is applied between electrodes immersed in a solution, charged particles in the solution redistribute to cancel out the potential difference in the bulk solution, forming an electric double layer (EDL) with a concentrated electric field at the electrode-solution interface [1, 2]. The EDL at the electrode interface has traditionally been studied as a stage for electrochemical reactions, but in recent years it has been widely used for EDL capacitors [3], EDL transistors [4, 5], electric field-induced ferromagnetism [6], and electric field-induced superconductivity [7]. Ionic liquids have been attracting attention as a new material suitable for these applications. Therefore, researches to obtain a fundamental understanding of the properties of the EDL of ionic liquids has been actively conducted both experimentally and theoretically [8, 9, 10, 11]. The electrode interface is also an interesting object of study from the viewpoint of nonlinear optics because of its broken spatial inversion symmetry. In other words, second-order nonlinear optical effects, such as sum frequency generation and Pockels effect, appear. The Pockels effect at the solid-liquid interface was first observed in the EDL of water at the interface of transparent oxide electrodes [12], and was found to have a Pockels coefficient an order of magnitude larger [13] than that of the electro-optic crystal LiNbO\({}_{3}\)[14; 15], which has been put to practical use. In a series of subsequent studies, it was reported that the Pockels effect at the solid-liquid interface is relatively large even in hydrogen-bonding solvents, such as alcohols [16], that it is small in water at the interface of noble metal electrodes, such as platinum and silver [17; 18], and that an optical modulator with a practical level of signal magnitude is possible using the Pockels effect in water at the transparent electrode interface [19; 20]. In the observation of the Pockels effect, an electrolyte is dissolved in the solvent to make it conductive and form an EDL, and it is known that the effect does not depend on the type of electrolyte ion [12; 16]. Among the liquid-electrode combinations investigated so far [13; 16; 17; 18; 21], the Pockels coefficient of water at the transparent oxide electrode interface is reported to be the largest (\(\sim\)200 pm/V) to date. However, it is unclear why this combination exhibits this value, i.e., what are the physical factors that determine the magnitude and sign of the Pockels coefficient of the liquid at the electrode interface, and it is desirable to elucidate the physical mechanism that can predict the Pockels coefficient at any given interface. If this can be clarified, it will be possible to develop optical modulators and interfacial sensors using the interfacial Pockels effect that is ubiquitous at all interfaces. The factors suggested so far are that the hydrogen bonding network of the solvent and the interaction of the solvent molecules with the oxide or polar surface may be important, since the coefficient is relatively large for hydrogen bonding solvents and small for noble metal interfaces [16; 17; 18]. In this paper, we present an experimental study to measure the Pockels coefficient at the transparent electrode interface of formamides [22; 23] (formamide (FA), \(N\)-methylformamide (NMF), dimethylformamide (DMF), the first two of which are solvents with a larger static dielectric constant than water), and an ionic liquid (IL) ([BMIM][BF\({}_{4}\)]-1-butyl-3-methylimidazolium tetrafluoroborate) [24; 25], which is a unique liquid consisting only of electrolyte ions, was experimentally studied to determine the Pockels coefficient at the transparent electrode interface. One of the main features that distinguish water from other solvents is the strong hydrogen bonding and the large static dielectric constant [26; 27]. Since formamide and methylformamide have larger dielectric constants than water, if a large Pockels coefficient is obtained, it would indicate that dielectric constant is an important factor.