#
Electric-Field Induced Shift in the Plasmon Resonance Due to the Interfacial Pockels Effect of Water on a Silver Surface^{ †}

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

_{3}, which is in practical use [2,3] (see also [4,5] and reference therein). Since then, it has been reported that the magnitude of the Pockels coefficient depends on the electrode material (about 1/3 for GaN electrodes compared to Indium Tin Oxide, ITO, electrodes) [6], and that liquids other than water also exhibit the Pockels effect [7]. However, the microscopic physical mechanism is still unknown, and there is no theory that can predict the magnitude and sign of the Pockels coefficient. For metal electrodes, there is only an evaluation on the order of the Pockels coefficient for platinum being two orders of magnitude smaller than that of ITO [8], and a precise quantitative evaluation has not yet been performed. The reason for this is that the $\mathsf{\Delta}n$ of interfacial water on the transparent electrode was estimated from the shift of interference fringes in the transmission spectrum of the thin transparent electrode film [2,3], while the same method cannot be used for metals because it is difficult to observe interference fringes even in thin films due to their large extinction coefficient [8]. If we can evaluate the Pockels coefficient of water at the interface of noble metals such as silver (Ag) and platinum (Pt), it will be the key to understand the mechanism. Therefore, the purpose of this paper is to establish a method to evaluate the Pockels coefficient of water on metal surfaces.

## 2. Materials and Methods

## 3. Results and Discussion

#### 3.1. Results

#### 3.2. Evalation of Energy Shift of the Plasmon Resonance

#### 3.3. Evaluation of the Refractive Index Change in the Interfacial Water

^{2}(water) for ${\epsilon}_{1}$. It was confirmed that the experimental results agree fairly well with the known SPP dispersion relation.

#### 3.4. Evaluation of the Pockels Coefficient of the Interfacial Water

#### 3.4.1. Thickness of the Electric Double Layer of Water

#### 3.4.2. Penetration Depth of Surface Plasmon Polaritons

- A.
- 300 nm, 1.331 (0.001),
- B.
- 100 nm, 1.333 (0.003), and
- C.
- 30 nm, 1.34 (0.01),

#### 3.4.3. Magnitude and Phase of Voltage Distributed in the Electric Double Layer of Water

- It may be a unique effect of the plasmon. However, to the best of our knowledge, there have been no experimental and theoretical reports about the additional phase of the plasmon in response to the dynamical refractive index change. It is unlikely that the plasmon does not instantaneously respond to the refractive index change at the interfacial dielectric around this low frequency range.
- The $\mathsf{\Delta}n$ of the interfacial water on Ag surface rises with the additional phase (nearly $\pm \frac{\pi}{2}$) in response to the electric field falling in the EDL. As shown in Figure 11, however, as long as the surface on ITO and Pt electrodes are concerned, the Pockels effect of interfacial water nearly instantaneously responds to the field around this low frequency range.
- The equivalent circuit was not correctly determined due to the imperfect impedance measurement. As shown in Figure 10, the present parameters reproduce the overall decaying behavior of the experimental signal magnitude with frequency, but the phase is inconsistent and there is discrepancy in the ratio of $X/Y$ even after adjusted by $\pm \frac{\pi}{2}$ phase. We used an Au electrode for the impedance measurement, because with the Ag electrode, the Cole–Cole plot showed anomalous behavior for lower frequencies, and it is difficult to be fit by the usual equivalent circuit. One of the possible reasons is the effect of the electrode reaction with electrolyte ions. The result for Ag is shown in Figure 12, where the same equivalent circuit is used for fitting. However, even in this case, since all the data points in the Cole–Cole plot reside in the Re$Z$ > 0 and Im $Z$ < 0 region, similarly to Figure 9, it should show such behavior that $X$ dominates for the low frequencies and $-Y$ grows with increasing frequency, as usual.

#### 3.5. Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Experimental setup with a cooled Spectrometric CCDs for measurement of reflection spectra and with a multi lock-in amplifier for measurement of electromodulation spectra ΔR using the function generator. R for normalization of ΔR was measured by intensity-modulationg the reflected probe with a chopper (not shown).

**Figure 2.**Reflection spectra of Ag in contact with (

**a**) air and (

**b**) water. The incidence angle $\theta $ in the prism was calculated as $\theta =45\xb0+{\mathrm{sin}}^{-1}\left[\mathrm{sin}\left({\theta}_{\mathrm{a}}-45\xb0\right)/1.47\right]$ from the incidence angle ${\theta}_{\mathrm{a}}$ in air [12] with the quartz refractive index 1.47. (For example, $\theta =$ 70.3° when ${\theta}_{\mathrm{a}}=$ 84°).

**Figure 3.**Normalized electromodulation spectra $\mathsf{\Delta}X/Rs$ and $\mathsf{\Delta}Y/Rs$ at 222 Hz, 333 Hz, and 444 Hz.

**Figure 4.**(

**a**) Reflection spectrum and (

**b**) its first derivative with respect to the photon energy, measured with the cooled spectrometric CCD.

**Figure 5.**The results of fitting $\frac{\left(\frac{d{R}_{p}}{dE}\right)\mathsf{\Delta}E}{{R}_{s}}$ (red curves) to $\frac{\mathsf{\Delta}{R}_{p}}{{R}_{s}}$ at 222 Hz (black curves) with the peak applied voltage of (

**a**) 0.4 V, (

**b**) 0.8 V, (

**c**) 1.2 V, (

**d**) 1.6 V, and (

**e**) 2.0 V. Here, the $\frac{\mathsf{\Delta}{R}_{p}}{{R}_{s}}$ is phase rotated from the raw data in Figure 3 such that the $X$ signal dominates.

**Figure 7.**Experimental data compared with calculated dispersion relations (Equation (3)) of SPP for Ag (${\epsilon}_{2}$ from [23] in contact with air and water $\left({\epsilon}_{1}=1\mathrm{and}{1.33}^{2}\right)$.

**Figure 8.**(

**a**) Penetration depth of SPP as a function of photon energy. (

**b**) Enlarged graph for the penetration depth into the metal side. (

**c**) SPP resonance spectra calculated by the transfer matrix method under the same Kretschmann configuration as in the experiment with an incident angle of 70.3°.

**Figure 9.**(

**a**) Cole–Cole plot ($-$Im $Z$ against Re $Z$). The green circle shows the impedance at 224 Hz, closest to 222 Hz. (

**b**) Equivalent circuit assumed for the electrolyte bulk solution and the electric double layer (EDL).

**Figure 10.**Frequency dependence of (

**a**) $X$ and (

**b**) $Y$ components in the electro-modulation spectra and in the calculation from Equation (12) with phase advanced by $\frac{\pi}{2}$. For both $X$ and $Y$, the magnitude is normalized to 24 Hz. (

**c**) Frequency dependence of $X$ in the electro-modulation spectra and in the calculation from Equation (12) with phase advanced by $\frac{\pi}{2}$, normalized to the magnitude of $Y$ at 24 Hz.

**Figure 11.**(

**a**)Typical data for raw electromodulation transmission change spectra of normal incidence on 330-nm thick Indium Tin Oxide (ITO) electrode in 0.1 M LiCl aqueous solution with an AC voltage of 1 V (ampliude) at 210 Hz. The $X$ signal is due to blue shift of the transmission spectrum. (

**b**) Raw electromodulation reflection change spectra of $87\xb0$ incidence on 400-nm thick TCO electrode in 0.1 M NaCl aqueous solution with an AC voltage of 2 V (ampliude) at 30 Hz. The $X$ signal is due to blue shift of the reflection spectrum [21]. (

**c**) Raw electromodulation transmission change spectra of normal incidence on 20-nm thick Pt electrode in 0.1 M NaCl aqueous solution with an AC voltage of 2 V (ampliude) at 21 Hz. The $X$ signal is characterized by red shift of the transmission spectrum [8].

**Figure 12.**Cole–Cole plot from the impedance measurement for Ag electrode with the applied voltage of 2 V. The green circle shows the impedance at 224 Hz, closest to 222 Hz. The same equivalent circuit as in Figure 9b is assumed for fitting.

**Table 1.**The background dielectric constant ${\epsilon}_{b}$ of Ag, experimentally determined from the fit of the observed surface plasmon polariton (SPP) resonance wavelength to Equation (5) with $\hslash {\omega}_{p}=3.82\mathrm{eV}$.

$\mathbf{Incidence}\text{}\mathbf{Angle}\text{}\mathit{\theta}$ | Experiment Figure 2b | $\mathbf{Calculation}\text{}\mathbf{Equation}\text{}\left(5\right)\text{}\mathbf{with}\text{}{\mathit{\epsilon}}_{\mathit{b}}=5.03$ | $\mathbf{Calculation}\text{}\mathbf{Equation}\text{}\left(5\right)\text{}\mathbf{with}{\mathit{\epsilon}}_{\mathit{b}}=5.94$ |
---|---|---|---|

67.4° | 1.58 eV | 1.72 eV | 1.84 eV |

69.2° | 1.88 eV | 1.88 eV | 2.00 eV |

70.3° | 2.08 eV | 1.95 eV | 2.08 eV |

**Table 2.**The energy shift of the SPP resonance from that with n = 1.330 in Figure 8c.

${\mathit{d}}_{\mathit{w}}$ | $\mathsf{\Delta}\mathit{n}$ | $\mathsf{\Delta}\mathit{n}{\mathit{d}}_{\mathit{w}}$ | Energy Shift (eV) |
---|---|---|---|

300 | 0.001 | 0.3 | 0.022 |

100 | 0.003 | 0.3 | 0.025 |

30 | 0.01 | 0.3 | 0.028 |

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**MDPI and ACS Style**

Nishi, Y.; Watanabe, R.; Sasaki, S.; Okada, A.; Seto, K.; Kobayashi, T.; Tokunaga, E. Electric-Field Induced Shift in the Plasmon Resonance Due to the Interfacial Pockels Effect of Water on a Silver Surface. *Appl. Sci.* **2021**, *11*, 2152.
https://doi.org/10.3390/app11052152

**AMA Style**

Nishi Y, Watanabe R, Sasaki S, Okada A, Seto K, Kobayashi T, Tokunaga E. Electric-Field Induced Shift in the Plasmon Resonance Due to the Interfacial Pockels Effect of Water on a Silver Surface. *Applied Sciences*. 2021; 11(5):2152.
https://doi.org/10.3390/app11052152

**Chicago/Turabian Style**

Nishi, Yurina, Ryosuke Watanabe, Subaru Sasaki, Akihiro Okada, Keisuke Seto, Takayoshi Kobayashi, and Eiji Tokunaga. 2021. "Electric-Field Induced Shift in the Plasmon Resonance Due to the Interfacial Pockels Effect of Water on a Silver Surface" *Applied Sciences* 11, no. 5: 2152.
https://doi.org/10.3390/app11052152