Pockels Effect at the Interface between Water and Ti Electrode

Featured Application: Electro-optic modulators or interfacial sensors involving water in the ultraviolet region


Introduction
Since the interface between different materials breaks the spatial inversion symmetry, the first-order electro-optic effect, the Pockels effect (refractive index change proportional to the applied electric field ∆n = n 1 F) [1] may take place [2,3].Among the interfacial Pockels effects, water at the interface between water and transparent oxide electrodes (water in the electric double layer) is found to have a Pockels coefficient of r 13 = 200 pm/V, one order of magnitude larger than that of the electro-optic crystal LiNbO 3 in practical use [4], and this effect is being studied for its application in the extraction of optical modulation signals of practical size [5,6].In particular, water is transparent, extending to 170 nm [7], which is promising for potential applications in UV-tolerant spatial light modulators for ultraviolet (UV) light [8], which are currently underdeveloped.If spatial light modulators (SLMs) can be used for beam shaping of 248 nm KrF and 193 nm ArF lasers [9], we may expect to see innovations in laser microfabrication and semiconductor photolithography.Water is almost the only material available for SLM in that wavelength range.
However, the physical mechanism that determines the value (magnitude and sign) of the Pockels coefficient [approximately equivalent to n 1 , strictly defined as r ij by the formula: ∆n i = n i − n = − 1 2 n 3 r ij F j with the refractive index n of the material] of water at the electrode interface is unknown.Previous studies [10,11] have shown that the Pockels coefficient of electrode interfacial water is orders of magnitude smaller at the interface of noble metals, such as Pt and Ag, where surface oxide films are not formed and might be comparable in magnitude at the base metal interface, where oxide films are formed, to at the transparent oxide electrode interface.It is also reported that Pockels coefficients of alcohols are comparable with and those of non-hydrogen-bonding solvents are much smaller than that of water at the transparent oxide electrode interface [12].Therefore, the oxide electrode and hydrogen bonding have attracted attention as factors that determine the magnitude of the interfacial water Pockels effect.In particular, it has been reported by S. Yukita that the bulk water Pockels signal-the origin of which has been concluded to be the Pockels effect of the electrode interfacial water-in the Ti-Ti electrode combination shows a magnitude comparable to that of the ITO-ITO (indium tin oxide) combination as shown in Appendix A [10,13,14].It is interesting to note that Ti is known to be a robust metal with high corrosion resistance due to the formation of a natural oxide film, TiO 2 , on its surface [15,16] and that TiO 2 is a typical photocatalyst [17].
Electroreflectance of TiO 2 (also an N-type semiconductor) by the electrolyte methods has been studied for a long time, and characteristic signals have been obtained near the band gap energy [18].There is also a report on electroreflectance focusing on the oxide film of Ti [19].However, at that time, before the discovery of the interfacial Pockels effect, the Pockels effect of water in the electrical double layer at the electrode interface was not known, and thus, the Pockels coefficient as a nonlinear optical effect has not quantitatively been estimated.Therefore, this paper aims to estimate the Pockels coefficient of water in contact with the oxide film of Ti electrodes.

Samples
Ti plates of pure titanium grade 2 (TP340) with purity >99.7%, 10 × 30 × 1 mm 3 , and mirror-polished on one side (Kobayashi Kengyo Co., Niigata, Japan) were used as electrodes.All the experiments were performed at room temperature, using the polished surface (the surface to which the light is irradiated).

Reflectance Measurement
The absolute reflectance of Ti electrodes was measured at an incident angle of 5 • with unpolarized light.A spectrophotometer (SolidSpec-3700 DUV, Shimadzu, Kyoto, Japan) was used for the measurements.

Reflectance Change (Electroreflectance) Measurement by Electromodulation Spectroscopy
Electroreflectance (electric-field modulated reflectance change) spectra of Ti electrodes were measured using the optical system shown in Figure 1 with a multi-lock-in amplifier.Ti electrodes were immersed in 0.1 M NaCl aqueous solution in a quartz cell, facing each other at opposite corners of the cell with 15 mm electrode spacing.The Ti electrodes were cleaned with alcohol immediately before the experiment, and the lead wires were  Ti electrodes were immersed in 0.1 M NaCl aqueous solution in a quartz cell, facing each other at opposite corners of the cell with 15 mm electrode spacing.The Ti electrodes were cleaned with alcohol immediately before the experiment, and the lead wires were connected to the electrodes with clips.An AC voltage with a frequency of f = 20 Hz and an amplitude of 2 V was applied between the electrodes using a function generator.
White probe light from an LDLS (Laser-Driven Light Source EQ-99 X, wavelength range of 170 to 2100 nm, Energetiq Technology, Wilmington, MA, USA) was collimated and focused on the sample (the surface of the voltage-applied electrode facing the ground electrode) with unpolarized light and 25 • angle of incidence.The optics were arranged so that the probe light intensity was as low as possible: The probe light was irradiated onto the electrode at a position out of focus, so that the diameter of the light spot size was about 8 mm, compared to the 10 mm width of the electrode.The white light intensity was approximately 5.6 mW/cm 2 .The reflected light was collimated and focused onto an optical fiber bundle and led to a spectrometer (Acton SpectraPro-300i, Acton Research Co, Acton, MA, USA) for spectral analysis.Light for each wavelength was sent through a bundled fiber array to the APD + preamplifier for conversion into an electrical signal, and the component whose intensity changed synchronized with f was detected with a multi(128)-channel lock-in amplifier (7210, Signal Recovery, Edinburgh, UK) [11,20].
To obtain high transmittance of the UV component of the probe light, synthetic quartz (90% transmittance up to 200 nm) is used for the lens.Although chromatic aberration causes differences in light collection efficiency at the fiber incidence plane, the optics were adjusted so that the blue-UV component of the detected white light spectrum is enriched in order to measure signals in the UV region with the best possible S/N ratio.Since the signal is normalized to (the reflected light intensity change ∆R)/(reflected light intensity R), the magnitude and shape of ∆R/R are not affected by chromatic aberration.The diffraction grating in the spectrometer was 150 lines/mm, and the blaze wavelength of 300 nm.The wavelength (photon energy) resolution was 3.2 nm (0.030 eV) at 365 nm (3.396 eV).
Here, the intensity measured by the multi-lock-in amplifier is the root mean square (RMS) value of the signal component.In order to obtain the Pockels coefficient accurately, a correction of 1/ √ 2 must be made to the obtained signal ∆R/R.All experimental results in this paper have been subjected to this correction.
Using the same optical setup, the effect of stationary UV light irradiation on the electroreflectance spectra was also investigated with a UV spotlight source (L8333-04, Hamamatsu Photonics, Hamamatsu, Japan).The UV-blue light from a mercury Xe lamp (ozoneless type L8251, Hamamatsu Photonics, Hamamatsu, Japan) in the source was irradiated on the Ti electrode using a light guide with bundled fibers to cover the white light probe light spot.The intensity was about 190 mW/cm 2 .

Impedance Measurement
To evaluate the Pockels coefficient of the interfacial layer involved, information on the electric field in the layer, as well as the refractive index change in the layer, is necessary.Therefore, the voltage distributed to each layer was evaluated by the AC impedance method.Measurements were made by the two-terminal method using an impedance/gain-phase analyzer (Model 1260, Solatron, Victorville, CA, USA) and a potentiostat/galvanostat (Model 1287, Solatron, Victorville, CA, USA).
The working and counter electrode terminals were connected to the galvanostat and Ti electrode, respectively, and the Ti electrode and quartz cell were the same as those used in the electroreflectance measurement, and the inside of the cell was filled with NaCl solution (0.1 M) in the same manner.The electrodes were placed at opposite corners of the cell, as in the electroreflectance measurement.The experimental apparatus was controlled using the ZPlot 3.5g software.The software allows the user to set the amplitude of the applied voltage, the range of the measurement frequency, and the incremental width.In this measurement, the amplitude was set to 10 mV AC, and the frequency range to 10 −1 ∼ 10 6 Hz.Even though it is preferable to apply the same voltage of 2.0 V as in the reflectance change experiment, impedance measurement at higher voltages may induce disturbances in the measurement.For this reason, calculations were made based on impedance data obtained under lower voltage conditions.

Reflection Spectra
Figure 2 shows absolute reflection spectra in air (unpolarized light, 5 • incidence) of three Ti electrodes: a new Ti electrode stored in air, a Ti electrode immersed in 0.1 M NaCl electrolyte solution for about 3 h in an electroreflectance experiment, and a Ti electrode that has been used in electroreflectance experiments for more than 10 times (more than 30 h in an electrolyte solution) over 1 year.There is a clear difference in the reflection spectra for each electrode, and this difference is attributed to the difference in the thickness of the surface oxide film: anodic oxidation occurs by the electromodulation experiment in an electrolyte solution, and the formation of the surface oxide film progresses.The longer the experiment time, the thicker the surface oxide film becomes, which changes the position of the dip in the reflection spectrum depending on the thickness of the oxide film.
in the electroreflectance measurement, and the inside of the cell was filled with NaCl solution (0.1 M) in the same manner.The electrodes were placed at opposite corners of the cell, as in the electroreflectance measurement.The experimental apparatus was controlled using the ZPlot 3.5g software.The software allows the user to set the amplitude of the applied voltage, the range of the measurement frequency, and the incremental width.In this measurement, the amplitude was set to 10 mV AC, and the frequency range to 10 −1 ~10 6 Hz.Even though it is preferable to apply the same voltage of 2.0 V as in the reflectance change experiment, impedance measurement at higher voltages may induce disturbances in the measurement.For this reason, calculations were made based on impedance data obtained under lower voltage conditions.

Reflection Spectra
Figure 2 shows absolute reflection spectra in air (unpolarized light, 5° incidence) of three Ti electrodes: a new Ti electrode stored in air, a Ti electrode immersed in 0.1 M NaCl electrolyte solution for about 3 h in an electroreflectance experiment, and a Ti electrode that has been used in electroreflectance experiments for more than 10 times (more than 30 h in an electrolyte solution) over 1 year.There is a clear difference in the reflection spectra for each electrode, and this difference is attributed to the difference in the thickness of the surface oxide film: anodic oxidation occurs by the electromodulation experiment in an electrolyte solution, and the formation of the surface oxide film progresses.The longer the experiment time, the thicker the surface oxide film becomes, which changes the position of the dip in the reflection spectrum depending on the thickness of the oxide film.

Electroreflectance Spectra 3.2.1. Electroreflectance Spectra by Only AC Electric-Field Modulation
The electroreflectance spectra of the Ti electrode, which has been used for more than 30 h, in 0.1 M NaCl solution are shown in Figure 3. Since the ∆R/R spectra showed excellent reproducibility, the thickness of the surface oxide film is considered stable.No degradation of the Ti electrode was observed even after repeated experiments.The obtained signal is due to the Pockels effect, because it was synchronized with f , and it increased almost in proportion to the applied AC voltage, as shown in Figure 4.As expected from the results of the Pockels effect in bulk water (Appendix A), a relatively large signal is obtained.The magnitude of the signal is comparable to that of ∆T/T observed at the water-ITO interface (comparison of maximum values).By contrast, the electroreflectance experiment with new Ti electrodes stored in air showed that ∆R/R was an order of magnitude smaller than the results in Figure 3, and showed poor reproducibility due to changes in the thickness of the oxide film during the experiment.
almost in proportion to the applied AC voltage, as shown in Figure 4.As expected from the results of the Pockels effect in bulk water (Appendix A), a relatively large signal is obtained.The magnitude of the signal is comparable to that of Δ/ observed at the water-ITO interface (comparison of maximum values).By contrast, the electroreflectance experiment with new Ti electrodes stored in air showed that Δ/ was an order of magnitude smaller than the results in Figure 3, and showed poor reproducibility due to changes in the thickness of the oxide film during the experiment.

Electroreflectance Spectra under DC Electric Field
Since the Pockels effect of interfacial water on the ITO electrode by electromodulation has been observed to depend on a DC bias voltage (unpublished), we studied whether there is a DC bias voltage dependence on the water-Ti electrode interface as well.See

Electroreflectance Spectra under DC Electric Field
Since the Pockels effect of interfacial water on the ITO electrode by electromodulation has been observed to depend on a DC bias voltage (unpublished), we studied whether there is a DC bias voltage dependence on the water-Ti electrode interface as well.See Figure 5 for comparison with the graph of Figure 3 without DC voltage: at DC +1.0 V, the magnitude of the signal increased about three times without change of the sign; at DC −1.0 V, the magnitude of the signal increased three times with the sign reversed.

Electroreflectance Spectra under Steady-State UV Irradiation
Titanium dioxide is known as a photocatalyst and exhibits strong oxidizing power when irradiated with UV light.The Honda-Fujishima effect [17] is one of the photocatalytic effects using titanium dioxide: UV light irradiation on a titanium dioxide electrode decreases the bias voltage required for the electrolysis of water.We measured the effect of UV light irradiation on the Pockels effect due to the change in optical constants at the electrode interface.Figure 6 shows the electroreflectance spectra upon UV light irradiation.The sign of the X signal is reversed by UV light irradiation, where there was a delay in response with irradiation (significant Y component), while there was little delay in response (little Y component) without UV light irradiation.The magnitude of the signal ( √ X 2 + Y 2 did not change substantially.Note that no bubbles due to the photocatalytic effect were visually observed during this experiment.

Electroreflectance Spectra under DC Electric Field
Since the Pockels effect of interfacial water on the ITO electrode by electromodulation has been observed to depend on a DC bias voltage (unpublished), we studied whether there is a DC bias voltage dependence on the water-Ti electrode interface as well.See

Electroreflectance Spectra under Steady-State UV Irradiation
Titanium dioxide is known as a photocatalyst and exhibits strong oxidizing power when irradiated with UV light.The Honda-Fujishima effect [17] is one of the photocatalytic effects using titanium dioxide: UV light irradiation on a titanium dioxide electrode decreases the bias voltage required for the electrolysis of water.We measured the effect of UV light irradiation on the Pockels effect due to the change in optical constants at the electrode interface.Figure 6 shows the electroreflectance spectra upon UV light irradiation.The sign of the  signal is reversed by UV light irradiation, where there was a delay in response with irradiation (significant  component), while there was little delay in response (little  component) without UV light irradiation.The magnitude of the signal (√ 2 +  2 did not change substantially.Note that no bubbles due to the photocatalytic effect were visually observed during this experiment.

Results of Impedance Measurement
The results of the impedance measurement are shown in Figure 7 as a Nyquist plot (complex plane) and a bode diagram (magnitude and phase as a function of frequency).They were analyzed using the ZView 3.5g software.
The equivalent circuit was estimated so that the fitting curves matched the Nyquist plot and the Bode diagram.The best fit was obtained using the equivalent circuit in Figure 8.In this case, the two electrodes are symmetrical because they are opposing Ti electrode plates with the same surface area.Therefore, the circuit should be valid for each electrode.Figure 7 shows the results of fitting with the equivalent circuit in Figure 8.The values of each circuit element obtained from the fitting are summarized in Table 1.
The Ti surface oxide film is known to be an N-type semiconductor TiO2 and many impedance measurements have been made on it [21][22][23][24]; the magnitudes of the resistance and capacitance components of the TiO2 space charge layer (SCL) in Table 1 are in good agreement in order of magnitude with those values reported previously.The magnitudes of the resistance and capacitance components of the EDL of water are also in order of

Results of Impedance Measurement
The results of the impedance measurement are shown in Figure 7 as a Nyquist plot (complex plane) and a bode diagram (magnitude and phase as a function of frequency).They were analyzed using the ZView 3.5g software.
The equivalent circuit was estimated so that the fitting curves matched the Nyquist plot and the Bode diagram.The best fit was obtained using the equivalent circuit in Figure 8.In this case, the two electrodes are symmetrical because they are opposing Ti electrode plates with the same surface area.Therefore, the circuit should be valid for each electrode.Figure 7 shows the results of fitting with the equivalent circuit in Figure 8.The values of each circuit element obtained from the fitting are summarized in Table 1.From the results in Table 1, the voltage distributed to each layer can be calculated.To find the Pockels coefficient in the EDL of water at the Ti electrode interface, the distributed voltage within the EDL is calculated.The impedances of the SCL and the EDL are   and   , respectively.From the results in Table 1, the voltage distributed to each layer can be calculated.To find the Pockels coefficient in the EDL of water at the Ti electrode interface, the distributed voltage within the EDL is calculated.The impedances of the SCL and the EDL are   and   , respectively.Table 1.The values of each element in the equivalent circuit in Figure 8 are determined by fitting in Figure 7.The meaning of each fitting parameter is described in Appendix B.

Resistance Constant Phase Element Warburg Impedance
Bulk 31.9 Space Charge Layer (SCL) The Ti surface oxide film is known to be an N-type semiconductor TiO 2 and many impedance measurements have been made on it [21][22][23][24]; the magnitudes of the resistance and capacitance components of the TiO 2 space charge layer (SCL) in Table 1 are in good agreement in order of magnitude with those values reported previously.The magnitudes of the resistance and capacitance components of the EDL of water are also in order of magnitude agreement with previously reported values [25].
From the results in Table 1, the voltage distributed to each layer can be calculated.To find the Pockels coefficient in the EDL of water at the Ti electrode interface, the distributed voltage within the EDL is calculated.The impedances of the SCL and the EDL are Z S and Z EDL , respectively.
The AC voltage applied is 2.0 V between the electrodes so that the voltage V at each electrode is 1.0 V.Note that V S and V EDL obtained in the above process are complex numbers, and the following distributed voltages are absolute values.The distributed voltage to the EDL at 20 Hz and 2.0 V was calculated from the values of each element obtained by impedance measurement to be |V EDL | = 0.145 V. On the other hand, the voltages distributed to the SCL and bulk water + bulk Ti are |V S |= 0.895 V and |V B | = 0.0567 V, respectively.

Estimation of Thickness of Surface Oxide Film on Ti Electrode and Interfacial Water Pockels Coefficient
In Appendix C, Fresnel's formula is derived for the reflectance of bilayer when light is incident at 0 • from a semi-infinite bulk medium (with a refractive index) into a semi-infinite bulk metal (with a complex refractive index) across layers of thicknesses d 1 and d 2 .Here, the refractive index of the layer of thickness d 1 is taken to be real (specifically, the EDL of water is assumed), and that of the layer of thickness d 2 is taken to be complex (specifically, the oxide film is assumed).The calculations were performed using Python 2.7.16 as follows.
(A) The reflection spectrum R of the Ti electrode in air was calculated assuming that the bulk medium is air with a refractive index of 1, d 1 = 0, and d 2 = 0. (B) The reflection spectrum R of the Ti electrode in water without the applied electric field was calculated assuming that the bulk medium is water with a refractive index of 1.33, d 1 = 0, and d 2 = 0. (C) The reflection spectrum R of the Ti electrode in water under the electric field was calculated assuming a water layer of thickness d 1 with a refractive index change and a TiO 2 layer of thickness d 2 with an energy shift in the complex refractive index, sandwiched between bulk water with a refractive index of 1.33 and bulk Ti, and ∆R = R − R was obtained.The energy dispersions of the complex refractive indices in Ti and TiO 2 are taken from the refractive index database [26-28].
However, the values of the complex refractive index have a variation depending on the literature and are not always accurate [29,30].Therefore, the complex refractive index of Ti was adjusted by using values in the literature, as depicted in Figure 9, to fit any sets of the reflection spectra of the Ti electrode samples with three different oxide thicknesses.For the complex refractive index of TiO 2 , the data were extrapolated smoothly, as shown in Figure 10, because the wavelength range was insufficient.

Calculation of Reflection Spectra in Air
The reflection spectra measured in air (dashed lines) of Ti electrodes used in an electromodulation experiment for more than 30 h, used for 3 h, and stored in air and not used (shown in Figure 2) were fitted by the spectra calculated (solid lines) by the method (A) with the thickness  2 of the surface oxide film TiO2 as a parameter.Figure 11 shows the results of the fitting.Here, as noted earlier, the complex refractive index of Ti is adjusted from the literature values.Since  2 = 6 nm for natural oxidation in air,  2 = 11 nm for 3 h of electromodulation experiments, and  2 = 14 nm for 30 h or more reproduce the experimental  spectra with an acceptable degree of agreement; the complex refractive index dispersion (Figures 9 and 10) for Ti and TiO2 used can be considered reasonable.The oxide film thickness increased by 5 nm for 3 h, whereas for 30 h or more, it increased by only 3 nm relative to the 3 h film, indicating that the increase in film thickness has been saturated.Combined with the good reproducibility of the experimental results, it can be concluded that 14 nm is a stable oxide film thickness that does not change under the current conditions of electromodulation.

Calculation of Reflection Spectra in Air
The reflection spectra measured in air (dashed lines) of Ti electrodes used in an electromodulation experiment for more than 30 h, used for 3 h, and stored in air and not used (shown in Figure 2) were fitted by the spectra calculated (solid lines) by the method (A) with the thickness  2 of the surface oxide film TiO2 as a parameter.Figure 11 shows the results of the fitting.Here, as noted earlier, the complex refractive index of Ti is adjusted from the literature values.Since  2 = 6 nm for natural oxidation in air,  2 = 11 nm for 3 h of electromodulation experiments, and  2 = 14 nm for 30 h or more reproduce the experimental  spectra with an acceptable degree of agreement; the complex refractive index dispersion (Figures 9 and 10) for Ti and TiO2 used can be considered reasonable.The oxide film thickness increased by 5 nm for 3 h, whereas for 30 h or more, it increased by only 3 nm relative to the 3 h film, indicating that the increase in film thickness has been saturated.Combined with the good reproducibility of the experimental results, it can be concluded that 14 nm is a stable oxide film thickness that does not change under the current conditions of electromodulation.Although the experiment was performed at the incident angle of 25 • , the spectra of the bilayer were calculated at 0 • incidence for simplicity (not too complicated that the analytical equation can be written down) since it is confirmed by calculation that the Ti reflection spectrum is almost the same at 0 • and 25 • incidence.

Calculation of Reflection Spectra in Air
The reflection spectra measured in air (dashed lines) of Ti electrodes used in an electromodulation experiment for more than 30 h, used for 3 h, and stored in air and not used (shown in Figure 2) were fitted by the spectra calculated (solid lines) by the method (A) with the thickness d 2 of the surface oxide film TiO 2 as a parameter.Figure 11 shows the results of the fitting.Here, as noted earlier, the complex refractive index of Ti is adjusted from the literature values.Since d 2 = 6 nm for natural oxidation in air, d 2 = 11 nm for 3 h of electromodulation experiments, and d 2 = 14 nm for 30 h or more reproduce the experimental R spectra with an acceptable degree of agreement; the complex refractive index dispersion (Figures 9 and 10) for Ti and TiO 2 used can be considered reasonable.The oxide film thickness increased by 5 nm for 3 h, whereas for 30 h or more, it increased by only 3 nm relative to the 3 h film, indicating that the increase in film thickness has been saturated.Combined with the good reproducibility of the experimental results, it can be concluded that 14 nm is a stable oxide film thickness that does not change under the current conditions of electromodulation.

Calculation of Electroreflectance Spectra in Aqueous Solution
Next, the oxide film thickness was fixed at  2 = 14 nm, and the Δ/ spectra were calculated using the method in (B,C), assuming that an EDL of water with a refractive index changed from bulk was generated between the oxide film and bulk water.As shown in Figure 12a, the experimental result was reproduced when it is assumed that with a positive voltage application of +2 V, an EDL of water (Δ ×  1 = 0.0255 nm) was generated, and the photon energy dependence of the complex refractive index in the TiO2 layer was red-shifted by 1.5 meV.The assumption of an energy shift in the complex refractive index of TiO2 (SCL in TiO2) in contact with the EDL of water follows the method used in the analysis of the Pockels effect of water at the ITO electrode interface, which assumed a shift in the ITO band edge due to the band population effect [4,12,20,31].On the other hand, assuming that only the refractive index change of the water EDL (Figure 12b) or only the red-shift of the complex refractive index of the TiO2 layer (Figure 12c) occurred, the Δ/ spectral features could not be reproduced even qualitatively.The complex refractive index change in the TiO2 film assumed in the calculations of Figure 12 is shown in Figure 13.

Calculation of Electroreflectance Spectra in Aqueous Solution
Next, the oxide film thickness was fixed at d 2 = 14 nm, and the ∆R/R spectra were calculated using the method in (B,C), assuming that an EDL of water with a refractive index changed from bulk was generated between the oxide film and bulk water.As shown in Figure 12a, the experimental result was reproduced when it is assumed that with a positive voltage application of +2 V, an EDL of water (∆n × d 1 = 0.0255 nm) was generated, and the photon energy dependence of the complex refractive index in the TiO 2 layer was red-shifted by 1.5 meV.The assumption of an energy shift in the complex refractive index of TiO 2 (SCL in TiO 2 ) in contact with the EDL of water follows the method used in the analysis of the Pockels effect of water at the ITO electrode interface, which assumed a shift in the ITO band edge due to the band population effect [4,12,20,31].On the other hand, assuming that only the refractive index change of the water EDL (Figure 12b) or only the red-shift of the complex refractive index of the TiO 2 layer (Figure 12c) occurred, the ∆R/R spectral features could not be reproduced even qualitatively.The complex refractive index change in the TiO 2 film assumed in the calculations of Figure 12 is shown in Figure 13.

Calculation of Electroreflectance Spectra in Aqueous Solution
Next, the oxide film thickness was fixed at  2 = 14 nm, and the Δ/ spectra were calculated using the method in (B,C), assuming that an EDL of water with a refractive index changed from bulk was generated between the oxide film and bulk water.As shown in Figure 12a, the experimental result was reproduced when it is assumed that with a positive voltage application of +2 V, an EDL of water (Δ ×  1 = 0.0255 nm) was generated, and the photon energy dependence of the complex refractive index in the TiO2 layer was red-shifted by 1.5 meV.The assumption of an energy shift in the complex refractive index of TiO2 (SCL in TiO2) in contact with the EDL of water follows the method used in the analysis of the Pockels effect of water at the ITO electrode interface, which assumed a shift in the ITO band edge due to the band population effect [4,12,20,31].On the other hand, assuming that only the refractive index change of the water EDL (Figure 12b) or only the red-shift of the complex refractive index of the TiO2 layer (Figure 12c) occurred, the Δ/ spectral features could not be reproduced even qualitatively.The complex refractive index change in the TiO2 film assumed in the calculations of Figure 12 is shown in Figure 13.

Estimation of Pockels Coefficients
The Pockels coefficient can be calculated from the following equation [4].

Estimation of Pockels Coefficients
The Pockels coefficient can be calculated from the following equation [4].
The distributed voltage  in the EDL was determined from the impedance measurements, and the refractive index change Δ in the EDL was estimated from the experimental fitting.This allowed us to evaluate the Pockels coefficient at the Ti electrode interfacial water without DC voltage as follows.As is clear from the derived equation, the assumed thickness of the EDL,  1 , cancels out in the numerator and denominator and does not affect the evaluation of the Pockels coefficient.Note that +1 V and −1 V DC voltage application increases the Pockels signal by a factor of about 3 and −3, respectively, so the Pockels coefficient may also increase by a factor of about 3 and −3.Strictly, however, the reliable estimation of the Pockels coefficients under DC bias needs the impedance measurement on the same conditions.
From |  | = 0.895 V in the SCL, the Pockels coefficient corresponding to the maximum refractive index change (0.00128) of TiO2 at photon energy 3.53 eV, as shown in Figure 13, is  13 = −2.3pm/V (SCL).
It should be noted that the magnitude of the Pockels coefficient of the Ti electrode interfacial water obtained is the maximum possible value due to the uncertainties in the distributed voltage to each of the layers involved, as shown below.The Pockels effect of water at the electrode interface refers to the Pockels effect of water in the EDL, which is currently understood to consist of three layers [32].The inner Helmholtz layer, where electrolyte ions are specifically adsorbed on the electrode surface; the outer Helmholtz layer, where hydrated ions are in the closest contact with the electrode; and the diffuse layer, where ion concentration follows a Boltzmann distribution due to equilibration by thermal diffusion of ions at the ambient temperature.The Helmholtz layer is also called the Stern layer or compact layer.At room temperature with 0.1 M electrolyte concentration, the thickness of the diffuse layer is calculated to be about 1 nm in equilibrium (under constant DC voltage application), while the Helmholtz layer is on the order of one water molecule layer (~0.3 nm).Although the equivalent circuit in Figure 8 perfectly fits the impedance measurement result in Figure 7, it only separates the bulk layer, the SCL of the oxide film, and the EDL of water (the amount of information in the impedance measurement data is too small to fit a more multi-layered equivalent circuit), and the Helmholtz layer is not separated, so the distributed voltage to it is undetermined.The maximum magnitude for The distributed voltage V in the EDL was determined from the impedance measurements, and the refractive index change ∆nd in the EDL was estimated from the experimental fitting.This allowed us to evaluate the Pockels coefficient at the Ti electrode interfacial water without DC voltage as follows.
As is clear from the derived equation, the assumed thickness of the EDL, d 1 , cancels out in the numerator and denominator and does not affect the evaluation of the Pockels coefficient.Note that +1 V and −1 V DC voltage application increases the Pockels signal by a factor of about 3 and −3, respectively, so the Pockels coefficient may also increase by a factor of about 3 and −3.Strictly, however, the reliable estimation of the Pockels coefficients under DC bias needs the impedance measurement on the same conditions.
From |V S | = 0.895 V in the SCL, the Pockels coefficient corresponding to the maximum refractive index change (0.00128) of TiO 2 at photon energy 3.53 eV, as shown in Figure 13, is r 13 = −2.3pm/V (SCL).
It should be noted that the magnitude of the Pockels coefficient of the Ti electrode interfacial water obtained is the maximum possible value due to the uncertainties in the distributed voltage to each of the layers involved, as shown below.The Pockels effect of water at the electrode interface refers to the Pockels effect of water in the EDL, which is currently understood to consist of three layers [32].The inner Helmholtz layer, where electrolyte ions are specifically adsorbed on the electrode surface; the outer Helmholtz layer, where hydrated ions are in the closest contact with the electrode; and the diffuse layer, where ion concentration follows a Boltzmann distribution due to equilibration by thermal diffusion of ions at the ambient temperature.The Helmholtz layer is also called the Stern layer or compact layer.At room temperature with 0.1 M electrolyte concentration, the thickness of the diffuse layer is calculated to be about 1 nm in equilibrium (under constant DC voltage application), while the Helmholtz layer is on the order of one water molecule layer (~0.3 nm).Although the equivalent circuit in Figure 8 perfectly fits the impedance measurement result in Figure 7, it only separates the bulk layer, the SCL of the oxide film, and the EDL of water (the amount of information in the impedance measurement data is too small to fit a more multi-layered equivalent circuit), and the Helmholtz layer is not separated, so the distributed voltage to it is undetermined.The maximum magnitude for |r 13 | is 150 pm/V if the voltage distributed to the Helmholtz layer is included in | V EDL |= 0.145 V.If it is included in |V S | = 0.895 V, |r 13 | will be smaller.To eliminate this uncertainty, impedance and electroreflectance measurements over a wider frequency range should be performed to increase the number of circuit elements in the equivalent circuit required for fitting, and the frequency dependence of the magnitude and shape of the ∆R/R spectrum and that of the voltage distributed to each layer should be carefully compared [4,12].

Discussion
As expected from the experimental results of the Pockels effect in bulk water, the magnitude of the Pockels coefficient of interfacial water on a Ti electrode was found to reach 150 pm/V at largest, comparable to that on an ITO electrode and orders of magnitude larger than those of the noble metal Pt and Ag electrode.
It should be noted that the sign of the Pockels coefficient is negative, opposite to that on the ITO.Although the sign was not determined for the Pockels coefficients of interfacial water on Pt and Ag, it was suggested that the sign could be negative for Pt and Ag [10,11].The present results for Ti indicate that the Pockels coefficient of the interfacial water may be negative not only for Ti but also for Pt and Ag (note the distinction between r 33 and r 13 for the case of Ag).
Furthermore, it is noteworthy that the magnitude of the Pockels signal is almost three times larger when a DC voltage of +1 V is applied, and that it is also nearly three times larger with the sign reversed when a DC voltage of −1 V is applied.Although the mechanism of this DC voltage dependence is not obvious, it can be interpreted qualitatively as the fact that the presence of an electrode interface breaks the spatial inversion symmetry of interfacial water compared to bulk water, and the application of DC voltage has the effect of further strengthening the inversion symmetry breaking.In fact, in the optical Kerr effect of bulk water with inversion symmetry, the Pockels effect can be manifested by the application of a DC electric field [33,34].
Therefore, let us estimate the expected DC electric field-induced Pockels coefficient from the well-known value of the nonlinear refractive index due to the optical Kerr effect in bulk water [35].Using the recently reported value n 2 = 1.9 × 10 −20 m 2 /W (wavelength of the measurement laser pulse: 815 nm, pulse width: 90 fs) [36], from n 2 I = n * 2 E 2 and I = 1 2 ε 0 E 2 c, we obtain n * 2 = 2.4 × 10 −23 m 2 /V 2 .Then, if the DC voltage 1 V all falls on the 1 nm thick EDL of water, E DC = 10 9 V/m, so the DC electric-field induced Pockels coefficient is n * 2 E DC = 2.4 × 10 −14 m/V = 2.4 × 10 −2 pm/V.This value is four orders of magnitude smaller than the present observation, indicating that the interfacial water Pockels effect has a different origin from that in the bulk water Kerr effect.However, it is known that the optical Kerr nonlinearity of liquids is dependent on the laser pulse width used in the measurement because of the inertial molecular motion of the composing relevant liquid [37].The above values measured with femtosecond pulses are due to the contribution of the purely electronic response only, while the use of ps or longer pulses will increase the effective n 2 due to the inclusion of the nuclear response.The Pockels coefficient of interfacial water measured with continuous white light should be compared with the effective n 2 measured with a long pulse; n 2eff = 14 × 10 −20 m 2 /W, which was measured with a pulse of 1064 nm peak wavelength and 16 ps duration [38].Even in this case, the DC field-induced Pockels coefficient is only increased by one order of magnitude, and is still three orders of magnitude smaller than the present observation.
An interesting result is that UV irradiation inverts the sign of the electroreflectance signal.This is considered to be related to the change in the optical constants due to the increase in carrier density in the oxide film upon UV light irradiation above the 3.2 eV band gap of TiO 2 , but further research is needed to elucidate the mechanism as well as the effect of DC bias voltage.

Conclusions and Prospects
The Pockels effect of interfacial water was investigated by electroreflectance of a Ti electrode with an oxide film TiO 2 on its surface in 0.1 M NaCl aqueous solution with an AC voltage of 2 V applied at a modulation frequency f = 20 Hz.The reflection spectrum R of the Ti electrode had a dip structure in the UV (3.5-4.5 eV) due to the interference of a thin oxide film.Analysis of the reflection spectra of the multilayer films showed that an oxide film of 6 nm was formed when stored in air, and up to 14 nm when immersed in an aqueous electrolyte solution and subjected to electromodulation experiments.The electroreflectance spectral signal was large ( ∆R/R ∼ 0.01) in the UV (3.5-4.5 eV) and showed a characteristic dispersive shape.The signal reproducibility was high, indicating that the Ti electrode with oxide coating is highly corrosion-resistant and robust.
As an interfacial effect between the water and TiO 2 layer under the application of an electric field, an EDL is generated on the water side and an SCL on the TiO 2 side.Assuming that the water in the EDL has a uniform refractive index change without wavelength dependence and that a complex refractive index change due to an energy shift at the band edge occurs in the SCL of TiO 2 as in ITO, we were able to fit the experimental results and determine the (complex) refractive index change within each layer.
The ∆R/R spectrum is well reproduced, assuming that (with a positive voltage applied) the complex refractive index of the 14 nm TiO 2 layer (SCL) is red-shifted (1.5 meV) and an EDL of thickness d with a refractive index change of ∆nd = 0.026 nm (∆n > 0) is formed between electrode and bulk water.The Pockels coefficient of water at the interface of the Ti electrode (with oxide film) was found to reach r 13 = −150 pm/V as the maximum value of magnitude, based on the distributed voltage to the EDL obtained from the fitted AC impedance measurements assuming an equivalent circuit.The reason the magnitude may be smaller than this value is that the voltage distributed to the compact layer has not been determined.
When a DC voltage was applied simultaneously with an AC voltage of frequency f for measuring the electromodulation spectrum, the signal was about three times larger at +1 V, and at −1 V the sign was reversed and the magnitude of the signal was about three times larger.The sign of ∆R/R was inverted when simultaneously (without DC voltage) irradiated with UV light containing wavelengths exceeding the band gap of TiO 2 of 3.2 eV.The fact that the sign of the Pockels coefficient is opposite to that of the ITO interfacial water and that the sign is easily reversed by DC electric field or UV light irradiation is an outstanding feature of the Ti electrode interfacial water.
No degradation of the Ti electrode was observed after repeated experiments.When experiments were conducted with new Ti electrodes stored in air, a change in the thickness of the surface oxide film was observed, but after experiments were performed over a certain period of time, the thickness of the oxide film stabilized and a highly reproducible Pockels signal was obtained.This is a clear advantage when compared to ITO, which shows severe degradation when high voltage is applied.
The mechanism of the threefold increase in the electroreflectance signal of a 2 V AC voltage application by the application of a ±1 V DC bias voltage is unknown, but the robustness of the Ti electrode with oxide film suggests that it may be possible to obtain even larger Pockels signals by further increasing the amplitude of the DC and AC voltages.The Pockels signal of the interfacial water at the Ti electrode, including the contribution of the Pockels effect of the surface oxide layer, is particularly large in the UV region (3.5-4.5 eV), and the robustness of the electrode has potential for application to optical modulators in the UV region.In this study, the Pockels coefficient of Ti electrode interfacial water with the oxide film of 14 nm was investigated, but it is not known whether this film thickness is optimal, and there is a possibility of further increasing the Pockels coefficients by optimizing the film thickness.

Figure 2 . 2 .
Figure 2. Reflection spectra measured in air (unpolarized light, 5° incidence) of three Ti electrodes: a new Ti electrode stored in air, a Ti electrode immersed in 0.1 M NaCl electrolyte solution for about Figure 2. Reflection spectra measured in air (unpolarized light, 5 • incidence) of three Ti electrodes: a new Ti electrode stored in air, a Ti electrode immersed in 0.1 M NaCl electrolyte solution for about 3 h in an electroreflectance experiment, and a Ti electrode that has been used in electroreflectance experiments for more than 30 h.

Figure 3 .
Figure 3. Electroreflectance spectra of the Ti electrode, which has been used for more than 30 h, in 0.1 M NaCl aqueous solution at 2 V and 20 Hz.  and  represent the cos and sin components of the lock-in signal.

Figure 3 .
Figure 3. Electroreflectance spectra of the Ti electrode, which has been used for more than 30 h, in 0.1 M NaCl aqueous solution at 2 V and 20 Hz.X and Y represent the cos and sin components of the lock-in signal.Appl.Sci.2023, 13, x FOR PEER REVIEW 6 of 18
Figure 5 for comparison with the graph of Figure 3 without DC voltage: at DC +1.0 V, the magnitude of the signal increased about three times without change of the sign; at DC −1.0 V, the magnitude of the signal increased three times with the sign reversed.
Figure 5 for comparison with the graph of Figure 3 without DC voltage: at DC +1.0 V, the magnitude of the signal increased about three times without change of the sign; at DC −1.0 V, the magnitude of the signal increased three times with the sign reversed.

Figure 5 .
Figure 5. DC voltage dependence of electroreflectance spectrum ( signal at 2 V AC and 20 Hz.As in Figure 4, the  signal was neglected because it is much smaller than the  signal).

Figure 5 .
Figure 5. DC voltage dependence of electroreflectance spectrum (X signal at 2 V AC and 20 Hz.As in Figure 4, the Y signal was neglected because it is much smaller than the X signal).

Figure 7 .
Figure 7. Results of the impedance measurement (dashed lines) and fitting curves (solid lines).

Figure 8 .
Figure 8.The equivalent circuit assumed for fitting in Figure 7. W represents the Warburg impedance.The impedance and other information indicated by each element are given in Appendix B.

Figure 7 .
Figure 7. Results of the impedance measurement (dashed lines) and fitting curves (solid lines).

18 Figure 7 .
Figure 7. Results of the impedance measurement (dashed lines) and fitting curves (solid lines).

Figure 8 .
Figure 8.The equivalent circuit assumed for fitting in Figure 7. W represents the Warburg impedance.The impedance and other information indicated by each element are given in Appendix B.

Figure 8 .
Figure 8.The equivalent circuit assumed for fitting in Figure 7. W represents the Warburg impedance.The impedance and other information indicated by each element are given in Appendix B.

Figure 9 .
Figure 9. Complex refractive index  +  of Ti (left: refractive index, right: extinction coefficient).The blue dashed line is the value from the literature[27], and the red is the value adjusted to reproduce the experimental results.

Figure 10 .
Figure 10.Complex refractive index  +  of TiO2 film assumed in the calculation.Orange: the literature data [28] Blue: Extrapolated from the literature data.

Figure 9 .
Figure 9. Complex refractive index n + iκ of Ti (left: refractive index, right: extinction coefficient).The blue dashed line is the value from the literature[27], and the red is the value adjusted to reproduce the experimental results.

18 Figure 9 .
Figure 9. Complex refractive index  +  of Ti (left: refractive index, right: extinction coefficient).The blue dashed line is the value from the literature[27], and the red is the value adjusted to reproduce the experimental results.

Figure 10 .
Figure 10.Complex refractive index  +  of TiO2 film assumed in the calculation.Orange: the literature data [28] Blue: Extrapolated from the literature data.

Figure 10 .
Figure 10.Complex refractive index n + iκ of TiO 2 film assumed in the calculation.Orange: the literature data [28] Blue: Extrapolated from the literature data.

Figure 11 .
Figure 11.Measured reflection spectra (dashed lines) in Figure 2 at an angle of incidence of 5 degrees in the air of Ti electrodes used in electromodulation experiments for more than 30 h (14 nm), for 3 h (11 nm), and not used (6 nm) and calculated spectra (solid lines) assuming a TiO2 surface oxide film with the respective thickness.

Figure 12 .
Figure 12.Experimental (dashed line) and calculated (solid line) electroreflectance spectra.(a) Assuming refractive index change in the EDL of water (Δ > 0) and complex refractive index change in the TiO2 film (red-shift by 1.5 meV).(b) Assuming only the refractive index change (Δ > 0) in the EDL of water.(c) Assuming only complex refractive index change (red-shift by 1.5 meV) in TiO2 film.

Figure 11 .
Figure 11.Measured reflection spectra (dashed lines) in Figure 2 at an angle of incidence of 5 degrees in the air of Ti electrodes used in electromodulation experiments for more than 30 h (14 nm), for 3 h (11 nm), and not used (6 nm) and calculated spectra (solid lines) assuming a TiO 2 surface oxide film with the respective thickness.

18 Figure 11 .
Figure 11.Measured reflection spectra (dashed lines) in Figure 2 at an angle of incidence of 5 degrees in the air of Ti electrodes used in electromodulation experiments for more than 30 h (14 nm), for 3 h (11 nm), and not used (6 nm) and calculated spectra (solid lines) assuming a TiO2 surface oxide film with the respective thickness.

Figure 12 .
Figure 12.Experimental (dashed line) and calculated (solid line) electroreflectance spectra.(a) Assuming refractive index change in the EDL of water (Δ > 0) and complex refractive index change in the TiO2 film (red-shift by 1.5 meV).(b) Assuming only the refractive index change (Δ > 0) in the EDL of water.(c) Assuming only complex refractive index change (red-shift by 1.5 meV) in TiO2 film.

Figure 12 .
Figure 12.Experimental (dashed line) and calculated (solid line) electroreflectance spectra.(a) Assuming refractive index change in the EDL of water (∆n > 0) and complex refractive index change in the TiO 2 film (red-shift by 1.5 meV).(b) Assuming only the refractive index change (∆n > 0) in the EDL of water.(c) Assuming only complex refractive index change (red-shift by 1.5 meV) in TiO 2 film.

Figure 13 .
Figure 13.Complex refractive index change due to 1.5 meV red shift of complex refractive index in TiO2 film assumed in the calculation of electroreflectance spectra in Figure 12.

Figure 13 .
Figure 13.Complex refractive index change due to 1.5 meV red shift of complex refractive index in TiO 2 film assumed in the calculation of electroreflectance spectra in Figure 12.

Table 1 .
The values of each element in the equivalent circuit in Figure8are determined by fitting in Figure7.The meaning of each fitting parameter is described in Appendix B.

Table 1 .
The values of each element in the equivalent circuit in Figure8are determined by fitting in Figure7.The meaning of each fitting parameter is described in Appendix B.