## 2 Materials and Methods  
In the experiment, we measured the change in the transmitted light intensity proportional to the electric field applied to the solution (\(\Delta T\)) and the magnitude of the electric field actually felt by the solution (\(E\)). Then, based on these data, we estimated the refractive index change of each layer by simulation using the transfer matrix method and determined the Pockels coefficient, following the procedure in Refs. [12; 13; 16]. For sample solutions, electrolytes were added to make a 0.1 M solution in 10 mL of each solvent. Deionized water was used as a 0.1 M NaCl aqueous solution and FA (98.5+%, Fujifilm Wako, Osaka, Japan), NMF (99.0+%, Fujifilm Wako, Osaka, Japan), and DMF (99.5+%, Fujifilm Wako, Osaka \(\lambda\)Japan) were used without further purification as 0.1 M LiCl solutions. [BMIM][BF\({}_{4}\)] (\(\geq\)98%, Merck, Darmstadt, Germany) was used as it was without any dissolved electrolyte because it is an electrolyte itself. [BMIM][BF\({}_{4}\)] was selected because it is a commonly used ionic liquid that is relatively inexpensive to obtain and its physical properties show typical values for ionic liquids. An open rectangular glass or quartz cell of a size appropriate for the following light transmission measurement was about 80% filled with each solution. The experimental setup for electro-modulation spectroscopy is shown in Figure 2. First, we measured the change in the transmission spectrum (\(\Delta T\)) due to the application of an external electric field. For this purpose, two 12 \(\times\) 50 mm ITO transparent electrodes (Geomatec, Yokohama, Japan) with a 300 \(\pm\) 20 nm thick indium tin oxide (ITO) film (carrier density \(1\times 10^{21}\) cm\({}^{-3}\) resistivity \(1.2\times 10^{-4}\)\(\Omega\)/cm) on a 1.1 mm thick glass substrate were prepared. The two electrode plates were immersed in each solution, facing each other with the conductive side facing inward. The electrode plates were immersed up to 25 mm in the lower half. Collimated white light from a laser-driven light source (LDLS Xe lamp, EQ-99X, Energetiq, Wilmington, MA, USA) was used as the probe light, and its beam diameter was narrowed down to about 8 mm with an iris to be transmitted only through one electrode. An alternating current (AC) voltage was applied to this electrode and the other electrode was grounded. In all experiments, the cells were set up in such a way that light was transmitted from the solution to the ITO thin film and then to the glass substrate in that order. The light transmitted through the electrode, and through the solution and glass cell, was spectrally dispersed into 128 wavelengths with a spectrometer and sent through a bundled fiber array to 128 avalanche photodiodes (APDs, S5343, Hamamatsu Photonics, Hamamatsu, Japan), respectively. The photocurrent detected with each APD was converted to a voltage by a transimpedance preamplifier and sent to a 128-channel lock-in amplifier (MLA, 7210, Signal Recovery, Edinburgh, UK). The transmitted intensity change spectrum (\(\Delta T\)) synchronized with the AC voltage of frequency \(f\) applied between the electrodes was detected simultaneously at 128 wavelengths. The spectrometer was used with a diffraction grating with 150 lines/mm and a blaze wavelength of 500 nm. In order to measure water and [BMIM][BF\({}_{4}\)] in the ultraviolet region (shorter than 350 nm), which is absorbed by glass, the glass cell and all the lenses were replaced with those made of quartz, and the grating was changed to that with 150 lines/mm and 300 nm blaze. An AC voltage of 210 Hz with 1 V amplitude was applied to all the solutions. All the experiments were performed at room-temperature (20 \({}^{\circ}\)C). Since \(\Delta T\) reflects the spectral intensity of the