# Pockels Effect at the Interface between Water and Ti Electrode
## 5 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 \(n_{2}=1.9\times 10^{-20}\) 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 \(I=\frac{1}{2}\epsilon_{0}E^{2}c\), we obtain \(n_{2}^{*}=2.4\times 10^{-23}\)m\({}^{2}\)/V\({}^{2}\). Then, if the DC voltage 1 V all falls on the 1 nm thick EDL of water, \(E_{\rm DC}=10^{9}\) V/m, so the DC electric-field induced Pockels coefficient is \(n_{2}^{*}E_{\rm DC}=2.4\times 10^{-14}\) m/V \(=2.4\times 10^{-2}\) 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; \(n_{\rm{2 eff}}=14\times 10^{-20}\) 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.