## 2 Materials and Methods  
Figure 1 shows a block diagram of the experimental setup. We used a commercially available transparent conductive-oxide (TCO) electrode on glass substrates (Geomatec, Yokohama, Japan). The electrode consisted of a TCO substrate made of soda-like glass (1.1 mm)/ITO (300 nm)/SnO\({}_{2}\) (100 nm) with 5 \(\Omega\)/sq. ITO (Indium Tin Oxide) is an \(n\)-type semiconductor and is transparent in the visible spectrum. The thickness, resistivity, and carrier density of the ITO substrate were measured at 300 nm, 1.2 \(\times\) 10\({}^{-4}\)\(\Omega\)cm, and 1.0 \(\times\) 10\({}^{21}\) cm\({}^{-3}\), respectively. Compared with ITO, TCO is highly resistive to acid and can withstand a higher applied voltage in an electrolyte aqueous solution.  
Electric field modulation spectroscopy of water at the electrode interface was performed by applying an AC voltage between the terminals attached to both ends of a single TCO electrode immersed in aqueous electrolyte solution. The AC voltage of frequency \(f\) was generated by a Function Generator and amplified by a High Speed Power Amplifier (4020, NF Corporation, Yokohama, Japan) because of the large current flow in this arrangement. White collimated light (with a beam diameter of about 10 mm) was extracted from a Laser Driven Light Source (LDLS EQ-99 X, wavelength range of 170 to 2100 nm, Energeticq Technology, Wilmington, MA, USA), which is an Xe lamp source, and the light (\(T\)) transmitted through the TCO in the aqueous solution was incident through a fiber into the entrance slit of a monochromator (SpectraPro 300i, Acton Research Co., Acton, MA, USA). The white light was monochromatized with a grating of 150 gr/mm and 500 nm blaze, and then received through a bundle fiber array on the monochromator output focal plane by 128 avalanche photodiodes (S5343, Hamamatsu Photonics, Hamamatsu, Japan) for each wavelength. The components modulated at frequency \(f\) were dual-phase lock-in detected by a 128-channel lock-in amplifier (7210, Signal Recovery, Edinburgh, UK) as and \(\Delta T_{y}\). This yields the electric field modulated transmittance change spectrum (\(\Delta T_{x,y}/T\)) of the electrode, using the \(T\) spectrum measured beforehand by chopper modulation. All lenses were SQ lenses, and the experiments were performed at room temperature (293 K). The transmission spectrum of the TCO electrode in air was measured separately with a spectrophotometer (SolidSpec-3700 DUV, Shimadzu, Kyoto, Japan).  
In order to measure the electrode position dependence of the transmitted light, a TCO electrode, cut to a size of 60 mm (width) \(\times\) 40 mm (height), was used and immersed about 3/4 into a glass cell filled with a 0.1 M NaCl aqueous solution. The two corners of the electrode above the water surface were clamped with alligator clips, with an indium wire inserted to improve the contact, and an AC voltage was applied. The position of the transmitted light was set to No. 1-No. 5 at 1 cm intervals, as shown in Figure 1, with No. 3 being the center of the electrode, No. 1 being grounded, and No. 5 being supplied with the voltage. The transmission position was changed by moving the cell by 1 cm to the left and right, and the dependence of the \(f\) signal on the transmission position was measured.  
Figure 1: **Top**: Experimental setup for electro-modulation transmission spectroscopy of interfacial water on a mono-electrode and the labels of the probed positions on the electrode (lower left). **Bottom**: The photo of the TCO electrode immersed in a glass cell filled with 0.1 M NaCl aqueous solution. The electrode connection position is about 5 mm from the top of the TCO and 5 mm from the side, (x,z) = (5,35), (55,35). The water surface is about 30 mm from the bottom of the TCO, and the probed positions were taken 5 mm below the water surface at 10 mm intervals, (x,z) = (10,25), (20,25), (30,25), (40,25), (50,25) (See Figure 6a).