## 3 Results
### Analysis Methods  
3.1.1 Estimation of \(\Delta n\) from Electro-Modulation Spectra Simulated by Transfer Matrix Method  
To reproduce the experimental \(\Delta T/T\) spectra, the calculations were performed with a self-made Visual Basic program using the transfer matrix method [30], assuming a change in the refractive index of each solvent \(\Delta n\) on the electrode, to obtain the results shown by the blue lines in Figure 3. By application of the voltage, the EDL (EDL) is formed on the surface of the ITO electrode where the charge is accumulated, and the refractive index is considered to change in this layer compared to the bulk. At the same time as the EDL is formed, the refractive index change due to the shift in the effective band gap energy [31] caused by the band-population effect [32; 33] of the n-type degenerate semiconductor also occurs on the ITO surface induced by the strong electric field at the interface. This region is called the space charge layer (SCL) [12; 13; 16]. As shown in Figure 4, therefore, firstly we calculated the transmittance before a voltage is applied, \(T\), through a single layer structure with a bulk ITO film sandwiched between a semi-infinite solution and a semi-infinite glass. Secondly, we calculated the transmittance \(T^{\prime}\) when the voltage is applied, through a three-layer structure in which light is incident from the semi-infinite bulk solution, transmitted through the EDL of the solution, the SCL of ITO, and the bulk ITO film, and exits onto the semi-infinite glass substrate. As a result, the calculated \(\Delta T/T\) spectra were obtained with \(\Delta T=T^{\prime}-T\). In the actual experiment, the probe light entered the solution again after transmitted through the glass substrate, but this part can be ignored because we only consider the difference before and after the refractive index change. In reality, the refractive index change in the EDL and SCL is spatially distributed, but we assume that the layers have effective thickness with spatially uniform refractive index change as before [12; 13; 16]. Figure 3: Experimental \(\Delta T/T\) spectra of FA, NMF, DMF, water, and IL (black lines) and calculated \(\Delta T/T\) spectra of them assuming \(\Delta n\) within the EDL of the liquid. The sign of the refractive index change is defined as negative because the refractive index change at the electrode interface is negative when positive voltage is applied. In order to determine the \(\Delta n\) that occurs in the EDL, we have to exclude the refractive index change \(\Delta n_{\text{SCL}}\) that occurs in the SCL. This was handled as follows. The refractive index change of solution EDL has almost no wavelength dependence in the range of 300 to 650 nm, reflecting the transparency of the solution, while that of the SCL in ITO has a wavelength dependence because it is caused by the net absorption change at the band edge due to the blue/red shift in the effective band gap upon positive/negative voltage application (as proved by the transmittance increase around 310 nm in Figure 3) and, thus, the refractive index change has the wavelength dependence associated with the absorption change through the Kramers-Kronig (KK) relations. Therefore, we determined the complex refractive index \(\Delta n_{\text{SCL}}+i\Delta\kappa_{\text{SCL}}\) (\(\kappa_{\text{SCL}}\): extinction coefficient) calculated from the complex permittivity assuming a multi-oscillator Lorentz model, so that \(\Delta\kappa_{\text{SCL}}\) reproduces the spectrum of \(\Delta T/T\) around 310 nm (net absorption decrease, \(\Delta\kappa_{\text{SCL}}<0\)). In this way, we uniquely determined the \(\Delta n_{\text{SCL}}\) in the visible region that satisfies the KK relations with \(\Delta\kappa_{\text{SCL}}\). The \(\Delta T/T\) in the visible region cannot be reproduced by this \(\Delta n_{\text{SCL}}\) alone, but it can only be reproduced by adding \(\Delta n\) without wavelength dependence in the EDL. As a result, \(\Delta n\) was uniquely determined.