Abstract

We report the development of a light modulator using the Pockels effect of water in a nanometer-thick electric double layer on an electrode surface. The modulator comprises a transparent-oxide electrode on a glass substrate immersed in an aqueous electrolyte solution. When an optical beam is incident such that it is totally reflected at the electrode-water interface, the light is modulated at a specific wavelength with a near-100% modulation depth synchronized with the frequency of the applied AC voltage. This result was reproduced by a calculation that assumes a change in the refractive index of −0.1 in a 2-nm electric double layer and of −0.0031 in a 30-nm space-charge layer formed at the interface between the electrolyte aqueous solution and the transparent electrode. This is the first report of an optical modulator that uses the interfacial Pockels effect of a material that does not allow for the Pockels effect in the bulk. The principle of giant optical modulation is explained by invoking the large Pockels coefficient of interfacial water and a Fabry–Perot-resonance effect in the transparent thin-film electrode.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Ferroelectric crystals such as LiNbO3 exhibit the Pockels effect [1,2,3], for which the change in refractive index is proportional to the applied electric field. The Pockels effect is used in optical communications to convert electrical signals to optical signals. However, the Pockels effect requires broken inversion symmetry, hence, a special single crystal is needed to satisfy this condition with a length on the order of cm (propagation distance necessary for accumulating the phase change of π during propagation), resulting in expensive devices. Therefore, extensive research has focused recently on alternative technologies to fabricate compact, high-speed light modulators. A typical example is silicon light modulators [4], which are being intensively studied in the hopes of extending the present silicon-based integrated circuits to optoelectronic hybrid integrated circuits [5]. Light modulators based on monolayer materials such as graphene [6,7] and those using surface-plasmon polaritons [8,9,10] have also been studied. However, all existing electro-optic light modulators use the optical response of the bulk solid material (even the surface-plasmon modulators are assisted by the Pockels effect of the bulk material).

In 2007, the Pockels effect in a liquid was first reported for water at the interface with a transparent electrode [11]. Several reports over the past decade have showed that water exhibits a huge Pockels effect when the macroscopic inversion symmetry is broken. In 2008, the Pockels coefficient of interfacial water at the surface of a transparent electrode was reported to be an order of magnitude larger than in LiNbO3 [12]. Two years later, the Pockels coefficient of the interfacial water at the electrode surface was found to depend on the electrode material [13]. In 2016, water at an air-water interface was found to have an extraordinarily large Pockels coefficient; several orders of magnitude larger than that at the water-electrode interface [14]. In 2017, polar organic solvents with hydrogen bonds were also found to behave similarly [15]. Finally, in 2012 and 2018, in the presence of a charged ionic distribution, the Pockels effect was also shown to exist even at macroscopic distances from an interface (the “anomalous” Pockels effect in bulk water) [16,17]. Currently, water has the largest known Pockels coefficient of all liquids: by exploring this reason, anomalous properties of water [18] might be further elucidated.

In water, the Pockels effect takes place in the electric double layer (EDL) [11,19]. The EDL is a capacitor-like layer that forms at the electrode interface by the migration of electrolyte ions of opposite sign with respect to the polarity of the electrode. The thickness of the EDL is on the order of nanometers, so applying a voltage as low as 1 V can create an electric field in the EDL as high as 109 V/m without causing discharge breakdown. Since the EDL also provides the arena where electrochemical reactions in solution occur, such as the electrolysis of water, understanding its properties is important. In addition, various devices have been proposed that exploit the properties of the EDL; in particular, its high electric field [20,21]. Various experiments have investigated the properties of water in the EDL, which differ from those of bulk water. One such property is the Pockels effect of water, which reflects the dielectric response to electromagnetic waves of visible frequency (or the change in the refractive index in response to an external electric field). The Pockels effect may be a key factor to elucidate the electronic properties of water in the EDL.

Although some details of the Pockels effect are well understood, it remains unknown at present what microscopic physical mechanisms actually contribute to the Pockels effect in water. If this can be clarified, we could predict the magnitude of the Pockels effect in water. Based on this motivation, further basic research is needed. For applications, on the other hand, modulating light on a macroscopic scale has been considered to be difficult. Particularly, because a large Pockels coefficient appears only in a thin nanoscale layer near the interface, a modulation can be detected only with highly sensitive measurement equipment such as a multichannel lock-in amplifier [11,15] or a Sagnac-interferometer deflection detector [16,17]. In fact, the modulation depth of an optical signal because of the Pockels effect is in the order of 1/1000 [12]. In this paper, we propose a new light modulator that uses the Pockels effect in the interfacial water and explain how to extract a large signal from a nanometer-thin interfacial layer.

The initial idea to enhance modulation was to capture the change in the refractive index localized in the EDL at the interface by using the evanescent wave associated with total reflection. If total reflection from the interface was repeated many times, the phase change should accumulate and generate a large signal. We therefore projected a white-light probe beam onto the thin glass substrate of a commercially available transparent electrode. We were surprised to obtain a huge signal from a single reflection. An analysis showed that the transparent-oxide electrode (with a thickness on the order of the wavelength of visible light) on the glass substrate served as a Fabry–Perot resonator, and our first trial happened to nearly satisfy the conditions for coherent perfect absorption (CPA) [22] at a specific wavelength. As a result, a sharp, deep absorption dip appeared in the total-reflection spectrum, and a large differential reflectance was obtained due to a shift in the resonance wavelength caused by the change in the refractive index in the interfacial layer.

In this paper, we report these experimental methods and results, as well as calculations based on a multilayer-film model. Furthermore, we discuss the mechanism behind giant optical modulation and the features and prospects of the method compared with competitive methods of optical modulation. The calculation uses the Pockels coefficient of water and other relevant parameters determined in previous work [12].

2. Experimental method

Figures 1(a) and 1(b) show schematic diagrams of the conventional and proposed optical configuration, respectively, for detecting the Pockels effect in the EDL. Transparent conductive-oxide electrodes substrates (ITO/TCO) were immersed in aqueous electrolyte solution in a quartz cell with a platinum electrode as counter electrode. A white-light probe beam from a Xe lamp (Energetiq) was incident as shown in Fig. 1(c). Any change in the spectrum of the transmitted white light synchronized with an applied AC voltage between the electrodes was detected by using a polychromator (Acton SpectraPro-300i) with a 128-channel lock-in detection system [11,12,15] (with 128 avalanche photodiodes as photodetectors). All the measurements were performed at room temperature (∼300 K). To numerically simulate the experiment, we used the transfer-matrix method assuming a multiply layered dielectric structure, as shown in Figs. 1(a) and 1(b). The experimental parameters are given in Ref. [12].

 

Fig. 1. Schematic illustration of the optical configuration of relevant multilayer structure with and without electric field for (a) the conventional normal-incidence method and (b) the proposed total-reflection method. The ITO substrate comprised 330-nm ITO (In2O3 doped with SnO2) thin film on glass substrate (1.1-nm thick soda-lime glass); the TCO substrate was made of soda-lime glass (1.1 mm)/ITO (300 nm)/SnO2 (100 nm). The experimental systems in both panels (a) and (b) are properly modeled by three layers with the electric field off: a semi-infinite glass substrate, bulk ITO, and semi-infinite (bulk) water; and five layers with electric field on: a semi-infinite glass substrate, bulk ITO, SCL in ITO, EDL in water, and semi-infinite (bulk) water. (c) Definition of angle of incidence in experiment: the angle in air between the incident light beam with respect to the surface normal of the transparent conductive substrate in the water cell.

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Figure 2 shows a block diagram of the experimental setup. We used two types of commercially available transparent conductive-oxide electrodes on the glass substrates (Geomatec): One electrode consisted of an ITO substrate with 5 Ω/sq. made of 330-nm thick ITO (In2O3 doped with SnO2) thin film on a glass substrate (1.1-mm thick soda-lime glass), and the other electrode consisted of a TCO substrate made of soda-lime glass (1.1 mm)/ITO (300 nm)/SnO2 (100 nm) with 5 Ω/sq. ITO is an n-type semiconductor and is highly transparent in the visible. The thickness, resistivity, and carrier density of the ITO substrate were 330 nm, 1.2 × 10−4 Ω cm, and 1.0 × 1021 cm−3, respectively. Compared with ITO, TCO is highly resistive to acid and can withstand a higher applied voltage in electrolyte aqueous solution.

 

Fig. 2. Experimental setup: LDLS: Laser-driven light source (Xe lamp); SQ F50: 30-mm diameter, 50-mm focal-length synthetic quartz plano-convex lens; Pinhole: 40-µm diameter pinhole, Fiber: 1-mm core, 1.25-mm cladding multimode quartz fiber, Sample: aqueous electrolyte solution (NaCl) cell in which transparent conductive oxide and Pt electrodes are positioned as depicted.

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Rectangular plates of approximately 15 × 50 mm2 were cut from both the ITO and TCO substrates by using a diamond cutter, and the side faces of the plates were manually polished step-by-step with sandpapers #500, #1000, #2000, and then with abrasive powders #10 000 and #30 000.

For the proposed total internal reflection configuration, the ITO/TCO electrode plate was placed in parallel with a 36 × 12 × 0.3 mm3 platinum plate, interposing a 1.28-mm thick glass slide partially as a spacer between them. To apply the AC voltage, the electrodes were connected by using alligator clips to copper lead wires from a BNC cable connected to a function generator. Part of one end of the TCO/ITO electrode plate (15 × 15 × 1.1 mm3) was immersed in 0.1 M NaCl aqueous solution contained in a home-made open-top quartz cell measuring about 23 × 20 × 21 mm3. The platinum electrode was grounded and an AC voltage with a peak amplitude of 1 to 5 V was applied to the TCO/ITO electrode at a frequency F = 223 or 30 Hz. A collimated probe beam from a Xe lamp (see laser-driven light source, or LDLS in Fig. 2) was linearly polarized S or P and projected onto the ITO/TCO electrode in the NaCl solution in the quartz cell at various angles of incidence [see Fig. 1(c) for definition of angle of incidence].

To project the white-light beam from the Xe lamp onto a 1.1-mm thick edge of the glass plate with maximal coupling efficiency, the beam was focused onto the edge of the glass. This was done by focusing the collimated LDLS light with a 50-mm focal-length lens through a 40-µm pinhole and then loosely focusing the diverging output with a 10× objective lens (Plan Fluor, Nikon) so that a narrow beam was incident onto the edge of the glass plate. The convergence angle, beam size at the plate edge, and the focal spot size were approximately 1°, 0.4 mm, and 0.3 mm, respectively, and the focal spot was nearly circular. The beam transmitted through the sample was refocused to a spot size of approximately 0.5 mm on the input of a 1-mm core fiber connected to a polychromator.

For normal incidence (0°; conventional method), the two electrodes were displaced so as to overlap incompletely and thereby allow light transmitted through the ITO electrode to be detected. See Refs. [11,12,15] for a more detailed description of the experimental method.

3. Calculation method

To calculate the light transmitted through a multilayered dielectric structure, we use the transfer-matrix method [23,24], assuming constant refractive indexes for both the EDL and the space-charge layer (SCL). With no applied electric field, we modeled the system as three dielectric layers: semi-infinite (bulk) water, a bulk transparent thin-film electrode (330-nm thick ITO or 400-nm thick TCO), and a semi-infinite glass substrate [see Figs. 1(a) and 1(b), field off]. With the applied field on, the EDL and SCL form at the electrode-water interface to give five dielectric layers [see Figs. 1(a) and 1(b), field on]. The parameters are the refractive indexes nw = 1.33 for bulk water, nITO = n +  for bulk ITO (see Fig. 3), and nglass = 1.52 for glass. The thickness was dITO = 300 nm for bulk ITO, dSCL = 30 nm for SCL, and dEDL = 2 nm for EDL. The thickness dEDL (compact layer plus diffuse layer) was estimated based on the Debye–Hückel length for 0.1 M ionic strength, and dSCL was estimated from the saturation of the ultraviolet signal with increasing voltage [12]. For Δn and Δκ, we use the functions given in Fig. 6 of Ref. [15] and in Fig. 3 of the present work. Although the TCO substrate has a layered structure consisting of 300 nm of ITO coated with 100 nm of SnO2, it is modeled herein simply as 400 nm of ITO.

 

Fig. 3. (a), (b) Complex refractive index n +  of transparent electrode ITO and change in complex refractive index of SCL in ITO used for calculation (almost the same functions as used for simulating the experimental results in Refs. [11,12,15]).

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The incident light probes the SCL of ITO as a propagating wave, and the EDL of water as an evanescent wave, so it is affected by the refractive index of both layers. The voltages across the EDL and SCL for each modulation frequency were estimated based on the impedance of the experimental system, as determined in Ref. [12]. For a peak applied voltage of 2 V and a frequency of 1 Hz, each electrode has a potential drop of 1 V and the EDL and SCL have potential drops of 0.85 and 0.15 V, respectively. Similarly, the potential drop across the EDL and SCL is 0.81 and 0.16 V at 20 Hz and 0.33 and 0.07 V at 223 Hz. For simplicity, and to confirm that changes in the difference reflectance significantly differ for the different experimental arrangements (i.e., conventional configuration versus total internal reflection) even for the same change in refractive index, the thickness of the EDL and SCL and the change in refractive index in these two layers are all assumed to be the same in the calculation as that used in Ref. [12] for the application of 2 V at 1 Hz. Specifically, the EDL and SCL are 2- and 30-nm thick, respectively, and the change in refractive index is Δn = −0.1 (constant) in the EDL, and Δn = −0.0031 at 500 nm in the SCL (the spectrum of $\Delta n + i\Delta \kappa$ follows that given in Ref. [15] and shown in Fig. 3).

4. Results

Figures 4(a) and 4(b) show the experimental results for 330-nm thick ITO as obtained by the conventional method and the proposed total-reflection method, respectively. With the conventional method, the magnitude of ΔT/T in the visible region is on the order of 1/1000, whereas the new method gives a maximum magnitude for ΔT/T on the order of 0.2. The relative difference transmittance is thus enhanced by a factor of about 200. This result is quantitatively reproduced by the calculation, as shown in Figs. 4(c) and 4(d).

 

Fig. 4. Spectra of relative difference transmittance and reflectance for 330-nm thick ITO in 0.1-M NaCl aqueous solution. (a) Spectrum of relative difference transmittance obtained by using the conventional method with 0° incidence, 2 V, 20 Hz. (b) Spectra of relative difference reflectance obtained by using the new method with 85° incidence in air, 1–5 V, 223 Hz, S polarization. Calculated spectra for 330-nm thick ITO for (c) 0° incidence and for (d) 87° incidence in glass. For both calculations, $\Delta n ={-} 0.1$ in 2-nm thick EDL and $\Delta n ={-} 0.0031$ at 500 nm in 30-nm thick SCL, which corresponds to the experimental conditions of a peak AC voltage of 2 V at 1 Hz.

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Figures 5(a) and 5(b) show the experimental and calculated results for 400-nm-thick TCO, as obtained by the proposed total-reflection method. Under these conditions, the maximum difference transmittance obtained experimentally was ΔT/T = 0.5. The wavelength of the maximum ΔT/T depends on the thickness of the transparent electrode, which means that the wavelength that is strongly modulated (i.e., the resonance wavelength) can be adjusted by changing the film thickness. The slight discrepancy between the calculated and experimental resonance wavelengths may be due to the assumption that the refractive index of the SnO2 layer is the same as that of ITO.

 

Fig. 5. Relative difference reflectance for 400-nm thick TCO in 0.1-M NaCl aqueous solution, obtained by using the proposed method. (a) Experimental difference reflectance spectra for 87° incidence in air, with S polarization and peak voltages of 1–4 V at 223 Hz. (b) Calculated difference reflectance spectra for 89° incidence in glass assuming $\Delta n ={-} 0.1$ in 2-nm-thick EDL and $\Delta n ={-} 0.0031$ at 500 nm in 30-nm-thick SCL, which corresponds to the experimental condition of 2 V at 1 Hz.

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In the proposed total-reflection method, the incident light propagates through the SCL of ITO and then probes the EDL of water as an evanescent wave, so it is affected by changes in the refractive index of both layers. As discussed below in Sec. 5, we estimate that 60% of the difference reflectance in Figs. 4(b) and 5(a) comes from the Pockels effect in the EDL in water.

Figure 6 shows the reflectance and difference reflectance spectra from the electrode-water interface for S- and P-polarized light in the total-reflection configuration. Because 87° incidence in air corresponds to 88° incidence in the glass and because the incident optical beam was not collimated but converging, we calculated the reflectances for 87°, 88°, and 89° incidence and plot the average of the results in Fig. 6(b).

 

Fig. 6. Reflectance spectra and difference reflectance spectra (a) measured experimentally (87° incidence in air, 30 Hz, 2V) and (b) calculated (plot shows the average of results for 87°, 88°, and 89° incidence in glass) for S (black curves) and P (red curves) polarization in total-reflection configuration. The change in refractive index is the same as in Figs. 4 and 5.

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Finally, we also investigated how the maximum difference reflectance depends on the modulation frequency. Although the response time depends on the electrode geometry, ΔR/R is typically reduced by half in the frequency range 100–200 Hz compared with ΔR/R at 20 Hz, which is consistent with the results reported in Refs. [11,15,17].

5. Discussion

We now propose an explanation for the enhanced difference reflectance. From within the glass substrate (refractive index n0), light is incident at a large angle of incidence onto the ITO layer of thickness d and complex refractive index n1 = n + iκ such that light is totally reflected at the ITO-water interface. The light that enters the ITO layer finds itself in a resonator with 100% reflectance (total reflection) at the ITO-water interface and approximately 90% reflectance at the ITO-glass interface. In addition, because ITO has small but finite absorptivity [see Fig. 5(a) of Ref. [11] and Fig. 3 herein], a sharp absorption dip forms in the reflectance spectrum, as shown in Fig. 6, as the resonator mode at which the optical path length is effectively increased (to be precise, the condition for CPA is nearly satisfied, as discussed in Sec. 6). Here the total reflection at the ITO-water interface means that the evanescent wave probes the EDL of water and thereby senses changes in refractive index due to the Pockels effect in the EDL. Therefore, even a slight shift in the resonance wavelength due to a change in refractive index of the EDL of water at the ITO-water interface introduces a large change in the relative difference reflectance.

Note that the Pockels effect of water depends on the electrode material, and, compared with GaN and Pt [15,17], the EDL in the water at the ITO-water interface has the largest Pockels coefficient studied so far (r13 = 200 pm/V and r33 = 250 pm/V) [12]. Furthermore, the Pockels coefficient of ITO in the SCL is also sufficiently large to be compared with that of the EDL in water (160 pm/V at 500 nm) [12], as can be explained by the band-population effect [11,12,15]. Here, when calculating the giant difference reflectance signal, if zero change is assumed in refractive index of the SCL in ITO, then the difference reflectance is reduced to only 60%, which indicates that, in Figs. 4(b) and 5(a), 60% of the difference reflectance is due to the Pockels effect of water in the 2-nm thick EDL.

To see how the difference reflectance depends on EDL thickness dEDL, we assume zero change in refractive index in the SCL, so that any change in refractive index occurs only in the EDL. If dEDL = 10 nm and Δn = −0.02, the calculated ΔR/R is almost the same (95%) as for dEDL = 2 nm and Δn = −0.1. Here, Δn = −0.02 because, with the constant Pockels coefficient, the electric field is five times less than for the same applied voltage with dEDL = 2 nm and Δn = −0.1. By contrast, if we use dEDL = 100 nm and Δn = −0.002, then the calculated ΔR/R is reduced to 45%. These results make physical sense because the penetration depth of the evanescent wave into the EDL (1/k2z gives the depth at which the amplitude drops to 1/e of the initial amplitude) is about 130 nm at λ = 450 nm [Eq. (20) in Sec. 6.3], so that the evanescent light has sufficient amplitude in the EDL of thickness dEDL = 2 and 10 nm to undergo almost all phase change (φ = Δn · k · dEDL with Δn · dEDL = −0.2 nm in the layer) whereas the amplitude is significantly reduced at dEDL = 100 nm so that the phase change is only partially probed.

6. Theoretical details

The experimental results are well reproduced by a transfer-matrix calculation applied to the multiple dielectric layered structures shown in Fig. 1. However, to grasp the principle intuitively and to explain the phenomenon qualitatively, it suffices to consider a single layer of ITO/TCO film sandwiched between semi-infinite glass and water, as shown in Fig. 7. In reality, the refractive index changes only in the thin EDL and SCL at the ITO-water interface, but the essential features of the phenomenon may be explained by assuming a constant change in refractive index throughout the entire semi-infinite bulk water region. In this section, this situation is analyzed in detail, and the connection to CPA [22] and surface-plasmon resonance [25,26] is also discussed.

 

Fig. 7. Single-layer model to explain principle of giant optical modulation.

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6.1 Single-layer model and condition for multiple reflections

Consider a single-layer film (ITO layer) between semi-infinite glass and water layers, as shown in Fig. 7, with ${n_0} = 1.52$ for the glass, ${n_1} = n + i\kappa $ $(n = 2,\;\kappa = 0.005\;\textrm{at}\;\textrm{450}\;\textrm{nm)}$, and n2 = 1.33 for water.

The amplitude of the reflectance for multiple reflections in a single-layer film is [25]

$$r = \frac{{{r_{01}} + {r_{12}}{e^{2i\Phi }}}}{{1 + {r_{01}}{r_{12}}{e^{2i\Phi }}}},$$
with $\Phi = {k_{1z}}d = (n + i\kappa )kd\cos \theta_1 = p + iq$, where $k = {\omega \mathord{\left/ {\vphantom {\omega c}} \right.} c}$, $p \cong knd\cos x$, and $q \cong {{k\kappa d} \mathord{\left/ {\vphantom {{k\kappa d} {\cos x}}} \right.} {\cos x}}\;(\kappa \ll 1)$. Here, x (real) is determined from ${n_0}\sin {\theta _0} \cong n\sin x$, as shown below.

Assuming $\kappa \ll 1$, Snell’s law is given by:

$${n_0}\sin {\theta _0} = {n_1}\sin {\theta _1} = (n + i\kappa )\sin \theta_1,$$
with $\theta_1 = x + iy$ where $x \gg y.$ Then,
$$\begin{aligned}{n_0}\sin {\theta _0} &= (n + i\kappa )\sin (x + iy) = \frac{1}{2}\left\{[{\kappa ({e^{ - y}} - {e^y})\cos x + n({e^{ - y}} + {e^y})\sin x} ]\right. \\ & \quad \left.+ i[{\kappa ({e^{ - y}} + {e^y})\sin x - n({e^{ - y}} - {e^y})\cos x} ] \right\}.\end{aligned}$$
Since the imaginary part is zero, $\kappa ({e^{ - y}} + {e^y})\sin x = n({e^{ - y}} - {e^y})\cos x.$ Thus,
$${n_0}\sin {\theta _0} = \frac{1}{2}\left[ {\frac{{{n^2} + {\kappa^2}}}{n}({e^{ - y}} + {e^y})\sin x} \right] \cong n\sin x.$$
Note that first correction to this expression is a second-order infinitesimal.

In the following, the subscripts $z$ and $x$ denote direction normal and parallel to the interface, respectively, as shown in Fig. 7. Then, noting that $k = \omega /c\textrm{ }$ and $\kappa \ll 1,\;n,$,

$${k_{1x}} = (n + i\kappa )k\sin \theta_1 = {n_0}k\sin {\theta _0},$$
and
$$\begin{array}{l} {k_{1z}} = (n + i\kappa )k\cos \theta_1 = (n + i\kappa )k{(1 - {\sin ^2}\theta_1 )^{1/2}} = (n + i\kappa )k{\left[ {1 - {{\left( {\frac{{{n_0}}}{{n + i\kappa }}\sin {\theta_0}} \right)}^2}} \right]^{1/2}}\\ \quad = k{[{({n^2} - {\kappa^2} - {n_0}^2{{\sin }^2}{\theta_0}) + 2in\kappa } ]^{1/2}} \cong k{[{({n^2} - {n_0}^2{{\sin }^2}{\theta_0}) + 2in\kappa } ]^{1/2}}\\ \quad = k{({n^2} - {n_0}^2{\sin ^2}{\theta _0})^{1/2}}{\left[ {1 + \frac{{2in\kappa }}{{({n^2} - {n_0}^2{{\sin }^2}{\theta_0})}}} \right]^{1/2}} \cong k{({n^2} - {n_0}^2{\sin ^2}{\theta _0})^{1/2}}\left[ {1 + \frac{{in\kappa }}{{({n^2} - {n_0}^2{{\sin }^2}{\theta_0})}}} \right]\\ \quad = k\left[ {{{({n^2} - {n_0}^2{{\sin }^2}{\theta_0})}^{1/2}} + \frac{{in\kappa }}{{{{({n^2} - {n_0}^2{{\sin }^2}{\theta_0})}^{1/2}}}}} \right]\\ \quad \cong k\left( {n\cos x + \frac{{i\kappa }}{{\cos x}}} \right). \end{array}$$
Since $\kappa \ll 1$, $\kappa $ can be neglected in Fresnel’s equations. As seen later, if $\kappa = 0$ exactly, no dip appears in the reflection spectrum but R = 1, so that $\kappa \ne 0$ is necessary to obtain a sharp dip (we require $\kappa\;>\;0$ but as close as possible to zero, as discussed with respect to the width of the dip in Sec. 6.2).

As calculated below, for an angle of incidence as large as 89°, multiple reflections occur in the transparent electrode film, which acts as a Fabry–Perot resonator, but this is not the case for smaller angles of incidence (i.e., angles between normal incidence and the critical angle of incidence). For oblique incidence, Fresnel’s formulas [23] are

$${r_{01\textrm{S}}} = \frac{{{n_0}\cos {\theta _0} - {n_1}\cos {\theta _1}}}{{{n_0}\cos {\theta _0} + {n_1}\cos {\theta _1}}},\quad {r_{01\textrm{P}}} = \frac{{{n_1}\cos {\theta _0} - {n_0}\cos {\theta _1}}}{{{n_1}\cos {\theta _0} + {n_0}\cos {\theta _1}}},$$
$${r_{12\textrm{S}}} = \frac{{{n_1}\cos {\theta _1} - {n_2}\cos {\theta _2}}}{{{n_1}\cos {\theta _1} + {n_2}\cos {\theta _2}}},\textrm{ }\quad \textrm{ }{r_{12\textrm{P}}} = \frac{{{n_2}\cos {\theta_1} - {n_1}\cos {\theta_2}}}{{{n_2}\cos {\theta_1} + {n_1}\cos {\theta_2}}}.$$
For normal incidence, ${r_{01}} \cong \frac{{{n_0} - {n_1}}}{{{n_0} + {n_1}}} = \frac{{1.52 - 2}}{{1.52 + 2}} ={-} 0.136$ and ${r_{12}} \cong \frac{{{n_1} - {n_2}}}{{{n_1} + {n_2}}} = \frac{{2 - 1.33}}{{2 + 1.33}} = 0.201$, so that reflectance is low at both ITO interfaces.

For total reflection at the ITO-water interface, ${n_0}\sin {\theta _0} \cong {n_1}\sin x \ge {n_2}$ and ${r_{12}} = {e^{i{\Omega _\textrm{P}}}}\;\textrm{or}\;{e^{i{\Omega _\textrm{S}}}}$, where ${\Omega _\textrm{P}}\;\textrm{and }{\Omega _\textrm{S}}$ are polarization-dependent (P or S) phase shifts for total reflection.

The critical angle for light going from ITO to water is ${\theta _{1\textrm{C}}} = 41.68^\circ $ because $\sin {\theta _{1\textrm{C}}} = \sin {x_\textrm{C}} = {n_2}/{n_1} = 1.33/2 = 0.665$. The critical angle for light going from glass to water is ${\theta _{0\textrm{C}}} = 61.04^\circ $ because $\sin {\theta _{0\textrm{C}}} = {n_2}/{n_0} = 1.33/1.52 = 0.875.$ Then,

$${l} {r_{01\textrm{S}}} = \frac{{{n_0}\cos {\theta _0} - {n_1}\cos {\theta _1}}}{{{n_0}\cos {\theta _0} + {n_1}\cos {\theta _1}}} \cong \frac{{1.52\cos 61.04^\circ{-} 2\cos 41.68^\circ }}{{1.52\cos 61.04^\circ{+} 2\cos 41.68^\circ }} = \frac{{ - 0.758}}{{2.23}} ={-} 0.340\quad$$
$${r_{01\textrm{P}}} = \frac{{{n_1}\cos {\theta _1} - {n_0}\cos {\theta _1}}}{{{n_1}\cos {\theta _0} + {n_0}\cos {\theta _1}}} \cong \frac{{2\cos 61.04^\circ{-} 1.52\cos 41.68^\circ }}{{2\cos 61.04^\circ{+} 1.52\cos 41.68^\circ }} = \frac{{-0.167}}{{2.10}} = -0.0795$$
For total reflection at the critical angle at the ITO-water interface, reflectance is low at the glass-ITO interface.

For 89° incidence from glass to ITO, as demonstrated in the experiment reported herein, reflectance is high at the glass-ITO interface, as shown below:

$${n_0}\sin {\theta _0} = {n_1}\sin {\theta _1}\quad 1.52\sin 89^\circ \cong \textrm{2}\sin {\theta _1}\quad {\theta _1} = 49.5^\circ$$
$$1 \to 0\quad {r_{\textrm{10S}}} = \frac{{{n_1}\cos {\theta _1} - {n_0}\cos {\theta _0}}}{{{n_1}\cos {\theta _1} + {n_0}\cos {\theta _0}}} \cong \frac{{2\cos 49.5^\circ{-} 1.52\cos 89^\circ }}{{2\cos 49.5^\circ{+} 1.52\cos 89^\circ }} = \frac{{1.272}}{{1.325}} = 0.960,$$
$$1 \to 0\quad {r_{\textrm{10P}}} = \frac{{{n_0}\cos {\theta _1} - {n_1}\cos {\theta _0}}}{{{n_0}\cos {\theta _1} + {n_1}\cos {\theta _0}}} \cong \frac{{1.52\cos 49.5^\circ{-} 2\cos 89^\circ }}{{1.52\cos 49.5^\circ{+} 2\cos 89^\circ }} = \frac{{ - 0.952}}{{1.022}} = 0.932.$$

6.2 Condition for sharp dip in reflectance

The condition for zero reflectance dip $({R = {{|r |}^2} = 0} )$ can be found as follows:

$$r = \frac{{{r_{01}} + {e^{i(2\Phi + {\Omega _\textrm{X}})}}}}{{1 + {r_{01}}{e^{i(2\Phi + {\Omega _\textrm{X}})}}}} = \frac{{{r_{01}} + {e^{i(2(p + iq) + {\Omega _\textrm{X}})}}}}{{1 + {r_{01}}{e^{i(2(p + iq) + {\Omega _\textrm{X}})}}}} = \frac{{{r_{01}} + {e^{i(2p + {\Omega _\textrm{X}}) - 2q}}}}{{1 + {r_{01}}{e^{i(2p + {\Omega _\textrm{X}}) - 2q}}}}$$
Since ${r_{01}}$ is real in a good approximation and ${r_{01}}\;<\;0$, $r = 0$ if
$${r_{01}} ={-} {e^{i(2p + {\Omega _\textrm{X}}) - 2q}}\;\textrm{and}\;{e^{i(2p + {\Omega _\textrm{X}})}} = 1. $$
Therefore,
$$2p + {\Omega _\textrm{X}} = 2knd\cos x + {\Omega _\textrm{X}} = 2m\pi \quad m = 0,1,2 \cdots$$
and
$${r_{01}} ={-} {e^{ - 2q}}. $$
The width of the dip is determined by expanding R for small Δk around the bottom of the dip as follows:
$$\begin{array}{l} R = |r{|^2} = \frac{{{r_{01}} + {e^{ - 2q}}{e^{i(2p + {\Omega _\textrm{X}})}}}}{{1 + {r_{01}}{e^{ - 2q}}{e^{i(2p + {\Omega _\textrm{X}})}}}}\frac{{{r_{01}} + {e^{ - 2q}}{e^{ - i(2p + {\Omega _\textrm{X}})}}}}{{1 + {r_{01}}{e^{ - 2q}}{e^{ - i(2p + {\Omega _\textrm{X}})}}}} = \frac{{{r_{01}}^2 + {e^{ - 4q}} + 2{r_{01}}{e^{ - 2q}}\cos (2p + {\Omega _\textrm{X}})}}{{1 + {r_{01}}^2{e^{ - 4q}} + 2{r_{01}}{e^{ - 2q}}\cos (2p + {\Omega _\textrm{X}})}}\\ \quad \cong \frac{{4{r_{01}}^2}}{{{{(1 - {r_{01}}^2)}^2}}}({n^2} + {\kappa ^2}){d^2}\Delta {k^2}\quad \textrm{around}\;R = 0\quad \textrm{with}\;\textrm{the}\;\textrm{coefficient of finesse:}F = \frac{{4{r_{01}}^2}}{{{{(1 - {r_{01}}^2)}^2}}}\; \end{array}$$
For a sharp dip to appear (i.e., for a large coefficient of $\Delta {k^2}$), ${r_{01}}^2$ should be as close to unity as possible and n, d should be large. For $R = 0$ at the bottom of the dip to be satisfied simultaneously, $\kappa \gtrsim 0$ is necessary because we must satisfy ${r_{01}} ={-} {e^{ - 2q}}$ with $q = k\kappa d/\cos x$. The above expression for R also shows that $R = 1$ for $q = 0({\kappa = 0} )$.

As can be seen from the analysis above, R is always unity if $q = 0\;(\kappa = 0)$, so it is vital for κ to be finite even if it is small. A dip in the reflectance spectrum forms as follows: Visible light incident on a transparent conductive film (ITO, TCO) from within a glass substrate is reflected at nearly constant reflectance (i.e., no dependence on wavelength because the complex refractive indexes of the glass and of the transparent conductive film are almost constant in the visible range). We assume that amplitude of the reflected light is unity. The transmitted light undergoes multiple reflections within the transparent conductive film and is emitted from the surface of the film. If this light is completely out of phase with the initially reflected light and is attenuated by a finite amount to have an amplitude −1, then it completely cancels the initially reflected light, resulting in a drop in reflectance to exactly zero at its minimum.

For a physical interpretation, consider a thin transparent conductive film of water (100% reflector by total reflection) and bulk glass (10% output mirror) as the interfaces at the two ends of a Fabry–Perot resonator. Resonator modes that are in phase and constructively interfere after one round trip undergo selectively strong absorption (complete absorption). This process is exactly the opposite of light amplification in a laser oscillator filled with a gain medium with an inverted population, so it realizes CPA, as first introduced by Stone et al. [22].

The discussion above of the condition for a dip to zero reflectance based on a single-layer film is, in principle, the same as that for a reflectance dip generated by a surface-plasmon resonance in the Kretschmann or Otto configurations. The difference in the case of metal films is as follows: The film must be thinner (50−10 nm) due to the large $\kappa$ (typically 3−8) [27], and the resonance wavelength (i.e., wavelength of the dip) is determined by the dispersion relation of bulk metal and by the refractive index of the dielectric [26]. The result is the absence of multiple Fabry–Perot resonator modes, which differs from the present study.

6.3 Change in phase shift associated with total reflection induced by change in refractive index in zone of evanescent field

From the standard formulas [23], the polarization-dependent phase shift associated with total reflection is

$$r = \frac{{{r_{01}} + {e^{i{\Omega _\textrm{X}}}}{e^{2i\Phi }}}}{{1 + {r_{01}}{e^{i{\Omega _\textrm{X}}}}{e^{2i\Phi }}}}\quad \textrm{X} = \textrm{P}\;\textrm{or S}, $$
$$\tan \frac{{{\Omega _\textrm{P}}}}{2} ={-} \frac{{\sqrt {{{\sin }^2}{\theta _1} - {{({n_2}/{n_1})}^2}} }}{{{{({n_2}/{n_1})}^2}\cos {\theta _1}}}, $$
$$\tan \frac{{{\Omega _\textrm{S}}}}{2} ={-} \frac{{\sqrt {{{\sin }^2}{\theta _1} - {{({n_2}/{n_1})}^2}} }}{{\cos {\theta _1}}}, $$
when n2/n1 changes,
$$\begin{array}{l} \Delta {\Omega _\textrm{P}} ={-} \sin {\Omega _\textrm{P}}\left[ {\frac{{{n_2}/{n_1}}}{{{{\sin }^2}{\theta_1} - {{({n_2}/{n_1})}^2}}} + 2({n_1}/{n_2})} \right]\Delta ({n_2}/{n_1})\\ \quad \quad = 2{\cos ^2}\frac{{{\Omega _\textrm{P}}}}{2}\frac{{\Delta ({n_2}/{n_1})}}{{({n_2}/{n_1})\cos {\theta _1}{{[{{\sin }^2}{\theta _1} - {{({n_2}/{n_1})}^2}]}^{1/2}}}} - 2({n_1}/{n_2})\sin {\Omega _\textrm{P}}\Delta ({n_2}/{n_1}) \end{array}$$
and
$$\Delta {\Omega _\textrm{S}} ={-} \sin {\Omega _\textrm{S}}\left[ {\frac{{{n_2}/{n_1}}}{{{{\sin }^2}{\theta_1} - {{({n_2}/{n_1})}^2}}}} \right]\Delta ({n_2}/{n_1}) = 2{\cos ^2}\frac{{{\Omega _\textrm{S}}}}{2}\frac{{\Delta ({n_2}/{n_1})}}{{({n_2}/{n_1})\cos {\theta _1}{{[{{\sin }^2}{\theta _1} - {{({n_2}/{n_1})}^2}]}^{1/2}}}}. $$

These equations show that the phase change due to the Pockels effect in water is a maximum at the critical angle, which is consistent with the intuitive picture that the evanescent wave penetrates deepest into the water at the critical angle (the penetration length diverges to infinity at the critical angle) to maximally probe the change in refractive index in water. Recall that we assume that the change in refractive index is uniform throughout the semi-infinite water (although the equation of phase change is derived to satisfy the boundary condition between evanescent light and propagating light at the interface). However, at the critical angle the spectral dip is neither deep nor sharp and thus does not contribute to the normalized difference reflectance spectrum ΔR/R, as shown in Fig. 8. ΔR/R is largest at the dip when R = 0, which is not satisfied near the critical angle.

 

Fig. 8. Calculated reflectance and difference reflectance spectra (62°incidence, nearly critical angle, in glass) for S- and P-polarized light in total-reflection configuration. We assume the same change in refractive index as in Figs. 4, 5, and 6.

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In this experiment, the change in refractive index occurs only in the EDL in the water, which is much less than a wavelength thick. In the matrix method for calculating the results in Fig. 8, this thin layer is therefore taken into account by including the reflection condition for a multilayer film. In this case, because the evanescent light reaches the bulk water region beyond the EDL, incidence at the critical angle may not lead to the largest phase change.

The penetration depth of the evanescent light in water is estimated as follows:

By assuming $\;{\theta _1} = x$, ${n_1}\sin {\theta _1} = {n_2}\sin {\theta _2}$ (good approximation) with ${n_1} = 2,\textrm{ }{n_2} = 1.33,\textrm{ and }{\theta _1} \ge {\theta _{1C}}$, where ${n_1}\sin {\theta _{1C}} = {n_2}$. Since $\sin {\theta _2} = \frac{{{n_1}}}{{{n_2}}}\sin {\theta _1} \ge 1,$

$$\cos {\theta _2} = {(1 - {\sin ^2}{\theta _2})^{1/2}} = {(1 - {(\frac{{{n_1}}}{{{n_2}}})^2}{\sin ^2}{\theta _1})^{1/2}} ={\pm} i{[{(\frac{{{n_1}}}{{{n_2}}})^2}{\sin ^2}{\theta _1} - 1]^{1/2}}.$$
Then, using $k = \omega /c = 2\pi /\lambda $, the evanescent field as a function of $z$ (normal to the surface) is given by
$$\exp (i{k_{2z}}z) = \exp (ik\cos {\theta _2}z) = \exp ( - k{[{(\frac{{{n_1}}}{{{n_2}}})^2}{\sin ^2}{\theta _1} - 1]^{1/2}}z)$$
so that the penetration depth is
$${k_{2z}}^{ - 1} = \frac{\lambda }{{2\pi }}{[{(\frac{{{n_1}}}{{{n_2}}})^2}{\sin ^2}{\theta _1} - 1]^{ - 1/2}}.$$
For the critical angle ${\theta _{1\textrm{C}}} = 41.68^\circ ,$ ${k_{2z}}^{ - 1} \to \infty \;\textrm{nm}$ from ${\left[ {{{\left( {\frac{2}{{1.33}}} \right)}^2}{{\sin }^2}41.68^\circ{-} 1} \right]^{ - 1/2}} = {0^{ - 1/2}}$, whereas in the present experiment ${k_{2z}}^{ - 1} = \textrm{129}\;\textrm{nm}\;\textrm{@450}\;\textrm{nm }$ at ${\theta _1} = 49.5^\circ $ from ${\left[ {{{\left( {\frac{2}{{1.33}}} \right)}^2}{{\sin }^2}49.5^\circ{-} 1} \right]^{ - 1/2}} = 1.8$

7. Comparison with other electro-optic modulators

Let us compare the present electro-optic modulator with conventional ones. The Pockels crystal LiNbO3 has a high-speed response (over 10 GHz [28]) but is expensive (several thousand USD as a device). To obtain a half-wave phase shift (which is the condition for 100% intensity modulation) with a voltage of several volts requires a large-volume single crystal several centimeters in length with a cross section of several microns squared. Liquid crystals [2,3,29] used in displays or spatial light modulators [30] have a response speed of about 100 Hz, and birefringence is induced in response to the square of the applied electric field to generate a phase difference between an ordinary ray and an extraordinary ray (in the case of a vertically aligned nematic liquid crystal cell). A half-wavelength phase shift that changes the transmittance by 100% with the help of combined polarizer and analyzer plates requires the thickness of the liquid crystal layer to be 2 to 3 µm and a bias of several volts for the case of visible light.

Both of these systems use the volume effect and can modulate light over a wide range of wavelengths. The proposed total-reflection modulator, by contrast, uses interface effects, operates on the nano scale, has wavelength selectivity, and is extremely inexpensive (in the case of Geomatec, it costs 0.25 USD for a 1-cm-square ITO substrate, which is a polycrystalline film on a glass substrate manufactured by sputtering). The active volume where the change in refractive index occurs may be estimated as the square of the relevant optical wavelength multiplied by the thickness of the EDL layer, which is less than 10 nm, giving a volume less than 1 × 1 × 0.01 µm3. The entire modulator is composed simply of a transparent electrode substrate dipped in an aqueous electrolyte solution with a counter electrode. The wavelength range to be modulated is narrow and directional in the wave vector. The modulation wavelength can be adjusted by changing the angle of incidence of the light and/or changing the ITO-film thickness. This modulator is also unique because it can modulate light deep in to the ultraviolet region (to 170 nm), where water is transparent.

8. Future prospects

The principle of enhanced optical modulation is well explained by the micro-resonator effect of a stratified medium [23], so that the present results open the possibility of optical modulators using the ubiquitous interfacial Pockels effect at any interface. It is thus important to find interfaces with large Pockels coefficients and to elucidate the physical mechanisms that determine the magnitude of the Pockels coefficient.

The size of the Pockels coefficient of interfacial water depends on the electrode material, with oxide electrode > nitride electrode >> metal electrode [13,17]. This is consistent with a report that the Pockels coefficient is larger for solvents with stronger hydrogen bonding [15]. Thus, transparent conductive oxides other than ITO [31] may provide an even larger signal. Furthermore, if the Pockels effect of a solid-gas or solid-solid interface is available, any material can be used as a light modulator, and a fast response can also be expected. The problem is to concentrate an intense electric field at an interface without inducing dielectric breakdown.

Note that a liquid-solid interface sacrifices the high-speed response (due to the formation time of the EDL) for a highly concentrated electric field. In this respect, the present modulator is the first EDL light modulator of the many EDL applications, such as EDL capacitors [20], EDL transistors, and electric-field-induced superconductors [21], all of which benefit from a high electric field within the EDL in electrolyte solutions, including ionic liquids.

If the goal of future research on the proposed device is to replace existing light modulators for optical communication, the problem to overcome is the response speed. The response speed is currently on the order of 100 Hz [11,12,15,17], which is equivalent to that of liquid crystals and is limited by the rate at which electrolyte ions move through water (i.e., the rate of EDL formation). Note that water molecules should have faster response time than the bulky molecules of liquid crystals because the rotation of water molecules has a GHz response. The problem is how to use high-speed responsivity. One possible solution is to scale down of the system to micron size, as evident from the RC time constant, where R is the resistance and C is the capacitance of an equivalent circuit of the experimental system, both of which are size dependent. In particular, it might be effective to reduce the size to sub-micron order because the proton conductivity or mobility is remarkably enhanced (orders of magnitude) in nanochannels or extended nanospaces where the EDL occupies a significant volume [32,33]. Aside from this problem, numerous applications have yet to be investigated in depth because this is the first device that uses the Pockels effect at the liquid-solid interface. One promising application is a sensitive probe of the nature of surfaces or interfaces [34].

9. Conclusion

By exploiting the loss of inversion symmetry at a water-electrode interface, we obtained a large Pockels coefficient in an interfacial layer of water of nanometer-order thickness and used it to significantly modulate an optical beam. From a glass substrate, the optical beam is incident at an oblique angle on the transparent electrode such that total reflection occurs at the electrode-water interface. Thus, the electrode serves as a Fabry–Perot resonator because the reflectivity at both interfaces (electrode-water and electrode-glass) are increased. The condition for CPA can thus be nearly realized to generate sharp absorption dips in the reflectance spectra at specific wavelengths (for CPA, it is essential that the transparent electrode is not completely transparent).

Biasing the electrode produces an electric field in the interfacial electrode-water layer, which changes the refractive index in this layer and thereby changes the resonance condition for CPA, causing a shift in the wavelength of the resonance absorption. Here, the role of the EDL is to concentrate a strong electric field at the interface without causing dielectric breakdown and to generate a large change in the refractive index at the interface where it can be thoroughly probed by the evanescent field of the incident optical beam.

Fortunately, inexpensive mass-produced transparent electrodes almost completely satisfy the conditions for CPA when light is incident onto a thin glass substrate of the electrode. In the present experiment, to project white light onto the 1.1-mm thick substrate, we used a slightly convergent beam instead of a parallel beam. Thus, the angle of incidence had a spread of ± 0.5° and the polarization was not perfect, both of which reduced the maximum modulation with respect to the calculated result. Given a transparent conductive film with a thickness such that the CPA resonance matches the wavelength of a commercially available semiconductor laser on a sufficiently thick substrate (at least 3 mm), a modulation depth of near 100% can be expected under nearly ideal conditions.

Funding

Grant in Aid for Scientific Research(C) (Grant Number JP15K05134); Japan Society for the Promotion of Science (JSPS); Murata Science Foundation.

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References

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  1. A. Yariv, Quantum Electronics (Wiley, 1989).
  2. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).
  3. R. W. Boyd, Nonlinear Optics (Elsevier, 2008).
  4. Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
    [Crossref]
  5. C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y.-H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
    [Crossref]
  6. M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
    [Crossref]
  7. V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. V. Campenhout, C. Huyghebaert, I. Goykhman, A. K. Ott, A. C. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12(1), 40–44 (2018).
    [Crossref]
  8. A. Melikyan, L. Alloatti, A. Muslija, D. Hillerkuss, P. C. Schindler, J. Li, R. Palmer, D. Korn, S. Muehlbrandt, D. Van Thourhout, B. Chen, R. Dinu, M. Sommer, C. Koos, M. Kohl, W. Freude, and J. Leuthold, “High-speed plasmonic phase modulators,” Nat. Photonics 8(3), 229–233 (2014).
    [Crossref]
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2018 (3)

V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. V. Campenhout, C. Huyghebaert, I. Goykhman, A. K. Ott, A. C. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12(1), 40–44 (2018).
[Crossref]

C. Haffner, D. Chelladurai, Y. Fedoryshyn, A. Josten, B. Baeuerle, W. Heni, T. Watanabe, T. Cui, B. Cheng, S. Saha, D. L. Elder, L. R. Dalton, A. Boltasseva, V. M. Shalaev, N. Kinsey, and J. Leuthold, “Low-loss plasmon-assisted electro-optic modulator,” Nature 556(7702), 483–486 (2018).
[Crossref]

S. Yukita, Y. Suzuki, N. Shiokawa, T. Kobayashi, and E. Tokunaga, “Mechanisms of the anomalous Pockels effect in bulk water,” Opt. Rev. 25(2), 205–214 (2018).
[Crossref]

2017 (2)

K. Takagi, S. V. Nair, R. Watanabe, K. Seto, T. Kobayashi, and E. Tokunaga, “Surface Plasmon Polariton Resonance of Gold, Silver, and Copper Studied in the Kretschmann Geometry: Dependence on Wavelength, Angle of Incidence, and Film Thickness,” J. Phys. Soc. Jpn. 86(12), 124721 (2017).
[Crossref]

H. Kanemaru, S. Yukita, H. Namiki, Y. Nosaka, T. Kobayashi, and E. Tokunaga, “Giant Pockels effect of polar organic solvents and water in the electric double layer on a transparent electrode,” RSC Adv. 7(72), 45682–45690 (2017).
[Crossref]

2016 (1)

Y. Suzuki, K. Osawa, S. Yukita, T. Kobayashi, and E. Tokunaga, “Anomalously large electro-optic Pockels effect at the air-water interface with an electric field applied parallel to the interface,” Appl. Phys. Lett. 108(19), 191103 (2016).
[Crossref]

2015 (2)

C. Haffner, W. Heni, Y. Fedoryshyn, J. Niegemann, A. Melikyan, D. L. Elder, B. Baeuerle, Y. Salamin, A. Josten, U. Koch, C. Hoessbacher, F. Ducry, L. Juchli, A. Emboras, D. Hillerkuss, M. Kohl, L. R. Dalton, C. Hafner, and J. Leuthold, “All-plasmonic Mach–Zehnder modulator enabling optical high-speed communication at the microscale,” Nat. Photonics 9(8), 525–528 (2015).
[Crossref]

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y.-H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
[Crossref]

2014 (4)

A. Melikyan, L. Alloatti, A. Muslija, D. Hillerkuss, P. C. Schindler, J. Li, R. Palmer, D. Korn, S. Muehlbrandt, D. Van Thourhout, B. Chen, R. Dinu, M. Sommer, C. Koos, M. Kohl, W. Freude, and J. Leuthold, “High-speed plasmonic phase modulators,” Nat. Photonics 8(3), 229–233 (2014).
[Crossref]

R. Burt, G. Birkett, and X. S. Zhao, “A review of molecular modelling of electric double layer capacitors,” Phys. Chem. Chem. Phys. 16(14), 6519–6538 (2014).
[Crossref]

K. Ueno, H. Shimotani, H. Yuan, J. Ye, M. Kawasaki, and Y. Iwasa, “Field-Induced Superconductivity in Electric Double Layer Transistors,” J. Phys. Soc. Jpn. 83(3), 032001 (2014).
[Crossref]

K. Mawatari, Y. Kazoe, H. Shimizu, Y. Pihosh, and T. Kitamori, “Extended-Nanofluidics: Fundamental Technologies, Unique Liquid Properties, and Application in Chemical and Bio Analysis Methods and Devices,” Anal. Chem. 86(9), 4068–4077 (2014).
[Crossref]

2012 (1)

S. Yukita, N. Shiokawa, H. Kanemaru, H. Namiki, T. Kobayashi, and E. Tokunaga, “Deflection switching of a laser beam by the Pockels effect of water,” Appl. Phys. Lett. 100(17), 171108 (2012).
[Crossref]

2011 (1)

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref]

2010 (2)

H. Kanemaru, Y. Nosaka, A. Hirako, K. Ohkawa, T. Kobayashi, and E. Tokunaga, “Electrooptic effect of water in electric double layer at interface of GaN electrode,” Opt. Rev. 17(3), 352–356 (2010).
[Crossref]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent Perfect Absorbers: Time-Reversed Lasers,” Phys. Rev. Lett. 105(5), 053901 (2010).
[Crossref]

2008 (1)

Y. Nosaka, M. Hirabayashi, T. Kobayashi, and E. Tokunaga, “Gigantic optical Pockels effect in water within the electric double layer at the electrode-solution interface,” Phys. Rev. B 77(24), 241401 (2008).
[Crossref]

2007 (2)

E. Tokunaga, Y. Nosaka, M. Hirabayashi, and T. Kobayashi, “Pockels effect of water in the electric double layer at the interface between water and transparent electrode,” Surf. Sci. 601(3), 735–741 (2007).
[Crossref]

H. Hosono, “Recent progress in transparent oxide semiconductors: Materials and device application,” Thin Solid Films 515(15), 6000–6014 (2007).
[Crossref]

2005 (2)

S. Liu, Q. Pu, L. Gao, C. Korzeniewski, and C. Matzke, “From Nanochannel-Induced Proton Conduction Enhancement to a Nanochannel-Based Fuel Cell,” Nano Lett. 5(7), 1389–1393 (2005).
[Crossref]

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[Crossref]

1999 (1)

G. E. Brown, V. E. Henrich, W. H. Casey, D. L. Clark, C. Eggleston, A. Felmy, D. W. Goodman, M. Grätzel, G. Maciel, M. I. McCarthy, K. H. Nealson, D. A. Sverjensky, M. F. Toney, and J. M. Zachara, “Metal Oxide Surfaces and Their Interactions with Aqueous Solutions and Microbial Organisms,” Chem. Rev. 99(1), 77–174 (1999).
[Crossref]

1983 (1)

1971 (1)

E. Kretschmann, “Die Bestimmung optischer Konstanten von Metallen durch Anregung von Oberflachenplasmaschwingungen,” Z. Phys. A: Hadrons Nucl. 241(4), 313–324 (1971).
[Crossref]

Alexander, R. W.

Alloatti, L.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y.-H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
[Crossref]

A. Melikyan, L. Alloatti, A. Muslija, D. Hillerkuss, P. C. Schindler, J. Li, R. Palmer, D. Korn, S. Muehlbrandt, D. Van Thourhout, B. Chen, R. Dinu, M. Sommer, C. Koos, M. Kohl, W. Freude, and J. Leuthold, “High-speed plasmonic phase modulators,” Nat. Photonics 8(3), 229–233 (2014).
[Crossref]

Asanovic, K.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y.-H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
[Crossref]

Asselberghs, I.

V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. V. Campenhout, C. Huyghebaert, I. Goykhman, A. K. Ott, A. C. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12(1), 40–44 (2018).
[Crossref]

Atabaki, A. H.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y.-H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
[Crossref]

Avizienis, R. R.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y.-H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
[Crossref]

Baeuerle, B.

C. Haffner, D. Chelladurai, Y. Fedoryshyn, A. Josten, B. Baeuerle, W. Heni, T. Watanabe, T. Cui, B. Cheng, S. Saha, D. L. Elder, L. R. Dalton, A. Boltasseva, V. M. Shalaev, N. Kinsey, and J. Leuthold, “Low-loss plasmon-assisted electro-optic modulator,” Nature 556(7702), 483–486 (2018).
[Crossref]

C. Haffner, W. Heni, Y. Fedoryshyn, J. Niegemann, A. Melikyan, D. L. Elder, B. Baeuerle, Y. Salamin, A. Josten, U. Koch, C. Hoessbacher, F. Ducry, L. Juchli, A. Emboras, D. Hillerkuss, M. Kohl, L. R. Dalton, C. Hafner, and J. Leuthold, “All-plasmonic Mach–Zehnder modulator enabling optical high-speed communication at the microscale,” Nat. Photonics 9(8), 525–528 (2015).
[Crossref]

Bell, R. J.

Bell, R. R.

Bell, S. E.

Bhatia, A. B.

M. Born, E. Wolf, A. B. Bhatia, P. C. Clemmow, D. Gabor, A. R. Stokes, A. M. Taylor, P. A. Wayman, and W. L. Wilcock, “Principles of Optics by Max Born,” /core/books/principles-of-optics/D12868B8AE26B83D6D3C2193E94FFC32.

Birkett, G.

R. Burt, G. Birkett, and X. S. Zhao, “A review of molecular modelling of electric double layer capacitors,” Phys. Chem. Chem. Phys. 16(14), 6519–6538 (2014).
[Crossref]

Boltasseva, A.

C. Haffner, D. Chelladurai, Y. Fedoryshyn, A. Josten, B. Baeuerle, W. Heni, T. Watanabe, T. Cui, B. Cheng, S. Saha, D. L. Elder, L. R. Dalton, A. Boltasseva, V. M. Shalaev, N. Kinsey, and J. Leuthold, “Low-loss plasmon-assisted electro-optic modulator,” Nature 556(7702), 483–486 (2018).
[Crossref]

Born, M.

M. Born, E. Wolf, A. B. Bhatia, P. C. Clemmow, D. Gabor, A. R. Stokes, A. M. Taylor, P. A. Wayman, and W. L. Wilcock, “Principles of Optics by Max Born,” /core/books/principles-of-optics/D12868B8AE26B83D6D3C2193E94FFC32.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Elsevier, 2008).

Brown, G. E.

G. E. Brown, V. E. Henrich, W. H. Casey, D. L. Clark, C. Eggleston, A. Felmy, D. W. Goodman, M. Grätzel, G. Maciel, M. I. McCarthy, K. H. Nealson, D. A. Sverjensky, M. F. Toney, and J. M. Zachara, “Metal Oxide Surfaces and Their Interactions with Aqueous Solutions and Microbial Organisms,” Chem. Rev. 99(1), 77–174 (1999).
[Crossref]

Burt, R.

R. Burt, G. Birkett, and X. S. Zhao, “A review of molecular modelling of electric double layer capacitors,” Phys. Chem. Chem. Phys. 16(14), 6519–6538 (2014).
[Crossref]

Campenhout, J. V.

V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. V. Campenhout, C. Huyghebaert, I. Goykhman, A. K. Ott, A. C. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12(1), 40–44 (2018).
[Crossref]

Cao, H.

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent Perfect Absorbers: Time-Reversed Lasers,” Phys. Rev. Lett. 105(5), 053901 (2010).
[Crossref]

Casey, W. H.

G. E. Brown, V. E. Henrich, W. H. Casey, D. L. Clark, C. Eggleston, A. Felmy, D. W. Goodman, M. Grätzel, G. Maciel, M. I. McCarthy, K. H. Nealson, D. A. Sverjensky, M. F. Toney, and J. M. Zachara, “Metal Oxide Surfaces and Their Interactions with Aqueous Solutions and Microbial Organisms,” Chem. Rev. 99(1), 77–174 (1999).
[Crossref]

Chelladurai, D.

C. Haffner, D. Chelladurai, Y. Fedoryshyn, A. Josten, B. Baeuerle, W. Heni, T. Watanabe, T. Cui, B. Cheng, S. Saha, D. L. Elder, L. R. Dalton, A. Boltasseva, V. M. Shalaev, N. Kinsey, and J. Leuthold, “Low-loss plasmon-assisted electro-optic modulator,” Nature 556(7702), 483–486 (2018).
[Crossref]

Chen, B.

A. Melikyan, L. Alloatti, A. Muslija, D. Hillerkuss, P. C. Schindler, J. Li, R. Palmer, D. Korn, S. Muehlbrandt, D. Van Thourhout, B. Chen, R. Dinu, M. Sommer, C. Koos, M. Kohl, W. Freude, and J. Leuthold, “High-speed plasmonic phase modulators,” Nat. Photonics 8(3), 229–233 (2014).
[Crossref]

Chen, Y.-H.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y.-H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
[Crossref]

Cheng, B.

C. Haffner, D. Chelladurai, Y. Fedoryshyn, A. Josten, B. Baeuerle, W. Heni, T. Watanabe, T. Cui, B. Cheng, S. Saha, D. L. Elder, L. R. Dalton, A. Boltasseva, V. M. Shalaev, N. Kinsey, and J. Leuthold, “Low-loss plasmon-assisted electro-optic modulator,” Nature 556(7702), 483–486 (2018).
[Crossref]

Chong, Y. D.

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent Perfect Absorbers: Time-Reversed Lasers,” Phys. Rev. Lett. 105(5), 053901 (2010).
[Crossref]

Clark, D. L.

G. E. Brown, V. E. Henrich, W. H. Casey, D. L. Clark, C. Eggleston, A. Felmy, D. W. Goodman, M. Grätzel, G. Maciel, M. I. McCarthy, K. H. Nealson, D. A. Sverjensky, M. F. Toney, and J. M. Zachara, “Metal Oxide Surfaces and Their Interactions with Aqueous Solutions and Microbial Organisms,” Chem. Rev. 99(1), 77–174 (1999).
[Crossref]

Clemmow, P. C.

M. Born, E. Wolf, A. B. Bhatia, P. C. Clemmow, D. Gabor, A. R. Stokes, A. M. Taylor, P. A. Wayman, and W. L. Wilcock, “Principles of Optics by Max Born,” /core/books/principles-of-optics/D12868B8AE26B83D6D3C2193E94FFC32.

Contestabile, G.

V. Sorianello, M. Midrio, G. Contestabile, I. Asselberghs, J. V. Campenhout, C. Huyghebaert, I. Goykhman, A. K. Ott, A. C. Ferrari, and M. Romagnoli, “Graphene–silicon phase modulators with gigahertz bandwidth,” Nat. Photonics 12(1), 40–44 (2018).
[Crossref]

Cook, H. M.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y.-H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
[Crossref]

Cui, T.

C. Haffner, D. Chelladurai, Y. Fedoryshyn, A. Josten, B. Baeuerle, W. Heni, T. Watanabe, T. Cui, B. Cheng, S. Saha, D. L. Elder, L. R. Dalton, A. Boltasseva, V. M. Shalaev, N. Kinsey, and J. Leuthold, “Low-loss plasmon-assisted electro-optic modulator,” Nature 556(7702), 483–486 (2018).
[Crossref]

Dalton, L. R.

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Y. Nosaka, M. Hirabayashi, T. Kobayashi, and E. Tokunaga, “Gigantic optical Pockels effect in water within the electric double layer at the electrode-solution interface,” Phys. Rev. B 77(24), 241401 (2008).
[Crossref]

E. Tokunaga, Y. Nosaka, M. Hirabayashi, and T. Kobayashi, “Pockels effect of water in the electric double layer at the interface between water and transparent electrode,” Surf. Sci. 601(3), 735–741 (2007).
[Crossref]

Toney, M. F.

G. E. Brown, V. E. Henrich, W. H. Casey, D. L. Clark, C. Eggleston, A. Felmy, D. W. Goodman, M. Grätzel, G. Maciel, M. I. McCarthy, K. H. Nealson, D. A. Sverjensky, M. F. Toney, and J. M. Zachara, “Metal Oxide Surfaces and Their Interactions with Aqueous Solutions and Microbial Organisms,” Chem. Rev. 99(1), 77–174 (1999).
[Crossref]

Ueno, K.

K. Ueno, H. Shimotani, H. Yuan, J. Ye, M. Kawasaki, and Y. Iwasa, “Field-Induced Superconductivity in Electric Double Layer Transistors,” J. Phys. Soc. Jpn. 83(3), 032001 (2014).
[Crossref]

Ulin-Avila, E.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref]

Van Thourhout, D.

A. Melikyan, L. Alloatti, A. Muslija, D. Hillerkuss, P. C. Schindler, J. Li, R. Palmer, D. Korn, S. Muehlbrandt, D. Van Thourhout, B. Chen, R. Dinu, M. Sommer, C. Koos, M. Kohl, W. Freude, and J. Leuthold, “High-speed plasmonic phase modulators,” Nat. Photonics 8(3), 229–233 (2014).
[Crossref]

Wade, M. T.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y.-H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
[Crossref]

Wang, F.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref]

Ward, C. A.

Watanabe, R.

K. Takagi, S. V. Nair, R. Watanabe, K. Seto, T. Kobayashi, and E. Tokunaga, “Surface Plasmon Polariton Resonance of Gold, Silver, and Copper Studied in the Kretschmann Geometry: Dependence on Wavelength, Angle of Incidence, and Film Thickness,” J. Phys. Soc. Jpn. 86(12), 124721 (2017).
[Crossref]

Watanabe, T.

C. Haffner, D. Chelladurai, Y. Fedoryshyn, A. Josten, B. Baeuerle, W. Heni, T. Watanabe, T. Cui, B. Cheng, S. Saha, D. L. Elder, L. R. Dalton, A. Boltasseva, V. M. Shalaev, N. Kinsey, and J. Leuthold, “Low-loss plasmon-assisted electro-optic modulator,” Nature 556(7702), 483–486 (2018).
[Crossref]

Waterman, A. S.

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y.-H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
[Crossref]

Wayman, P. A.

M. Born, E. Wolf, A. B. Bhatia, P. C. Clemmow, D. Gabor, A. R. Stokes, A. M. Taylor, P. A. Wayman, and W. L. Wilcock, “Principles of Optics by Max Born,” /core/books/principles-of-optics/D12868B8AE26B83D6D3C2193E94FFC32.

Wilcock, W. L.

M. Born, E. Wolf, A. B. Bhatia, P. C. Clemmow, D. Gabor, A. R. Stokes, A. M. Taylor, P. A. Wayman, and W. L. Wilcock, “Principles of Optics by Max Born,” /core/books/principles-of-optics/D12868B8AE26B83D6D3C2193E94FFC32.

Wolf, E.

M. Born, E. Wolf, A. B. Bhatia, P. C. Clemmow, D. Gabor, A. R. Stokes, A. M. Taylor, P. A. Wayman, and W. L. Wilcock, “Principles of Optics by Max Born,” /core/books/principles-of-optics/D12868B8AE26B83D6D3C2193E94FFC32.

Xu, Q.

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[Crossref]

Yariv, A.

A. Yariv, Quantum Electronics (Wiley, 1989).

Ye, J.

K. Ueno, H. Shimotani, H. Yuan, J. Ye, M. Kawasaki, and Y. Iwasa, “Field-Induced Superconductivity in Electric Double Layer Transistors,” J. Phys. Soc. Jpn. 83(3), 032001 (2014).
[Crossref]

Yin, X.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref]

Yuan, H.

K. Ueno, H. Shimotani, H. Yuan, J. Ye, M. Kawasaki, and Y. Iwasa, “Field-Induced Superconductivity in Electric Double Layer Transistors,” J. Phys. Soc. Jpn. 83(3), 032001 (2014).
[Crossref]

Yukita, S.

S. Yukita, Y. Suzuki, N. Shiokawa, T. Kobayashi, and E. Tokunaga, “Mechanisms of the anomalous Pockels effect in bulk water,” Opt. Rev. 25(2), 205–214 (2018).
[Crossref]

H. Kanemaru, S. Yukita, H. Namiki, Y. Nosaka, T. Kobayashi, and E. Tokunaga, “Giant Pockels effect of polar organic solvents and water in the electric double layer on a transparent electrode,” RSC Adv. 7(72), 45682–45690 (2017).
[Crossref]

Y. Suzuki, K. Osawa, S. Yukita, T. Kobayashi, and E. Tokunaga, “Anomalously large electro-optic Pockels effect at the air-water interface with an electric field applied parallel to the interface,” Appl. Phys. Lett. 108(19), 191103 (2016).
[Crossref]

S. Yukita, N. Shiokawa, H. Kanemaru, H. Namiki, T. Kobayashi, and E. Tokunaga, “Deflection switching of a laser beam by the Pockels effect of water,” Appl. Phys. Lett. 100(17), 171108 (2012).
[Crossref]

Zachara, J. M.

G. E. Brown, V. E. Henrich, W. H. Casey, D. L. Clark, C. Eggleston, A. Felmy, D. W. Goodman, M. Grätzel, G. Maciel, M. I. McCarthy, K. H. Nealson, D. A. Sverjensky, M. F. Toney, and J. M. Zachara, “Metal Oxide Surfaces and Their Interactions with Aqueous Solutions and Microbial Organisms,” Chem. Rev. 99(1), 77–174 (1999).
[Crossref]

Zentgraf, T.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref]

Zhang, X.

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref]

Zhao, X. S.

R. Burt, G. Birkett, and X. S. Zhao, “A review of molecular modelling of electric double layer capacitors,” Phys. Chem. Chem. Phys. 16(14), 6519–6538 (2014).
[Crossref]

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Y. Suzuki, K. Osawa, S. Yukita, T. Kobayashi, and E. Tokunaga, “Anomalously large electro-optic Pockels effect at the air-water interface with an electric field applied parallel to the interface,” Appl. Phys. Lett. 108(19), 191103 (2016).
[Crossref]

S. Yukita, N. Shiokawa, H. Kanemaru, H. Namiki, T. Kobayashi, and E. Tokunaga, “Deflection switching of a laser beam by the Pockels effect of water,” Appl. Phys. Lett. 100(17), 171108 (2012).
[Crossref]

Chem. Rev. (1)

G. E. Brown, V. E. Henrich, W. H. Casey, D. L. Clark, C. Eggleston, A. Felmy, D. W. Goodman, M. Grätzel, G. Maciel, M. I. McCarthy, K. H. Nealson, D. A. Sverjensky, M. F. Toney, and J. M. Zachara, “Metal Oxide Surfaces and Their Interactions with Aqueous Solutions and Microbial Organisms,” Chem. Rev. 99(1), 77–174 (1999).
[Crossref]

J. Phys. Soc. Jpn. (2)

K. Ueno, H. Shimotani, H. Yuan, J. Ye, M. Kawasaki, and Y. Iwasa, “Field-Induced Superconductivity in Electric Double Layer Transistors,” J. Phys. Soc. Jpn. 83(3), 032001 (2014).
[Crossref]

K. Takagi, S. V. Nair, R. Watanabe, K. Seto, T. Kobayashi, and E. Tokunaga, “Surface Plasmon Polariton Resonance of Gold, Silver, and Copper Studied in the Kretschmann Geometry: Dependence on Wavelength, Angle of Incidence, and Film Thickness,” J. Phys. Soc. Jpn. 86(12), 124721 (2017).
[Crossref]

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[Crossref]

A. Melikyan, L. Alloatti, A. Muslija, D. Hillerkuss, P. C. Schindler, J. Li, R. Palmer, D. Korn, S. Muehlbrandt, D. Van Thourhout, B. Chen, R. Dinu, M. Sommer, C. Koos, M. Kohl, W. Freude, and J. Leuthold, “High-speed plasmonic phase modulators,” Nat. Photonics 8(3), 229–233 (2014).
[Crossref]

C. Haffner, W. Heni, Y. Fedoryshyn, J. Niegemann, A. Melikyan, D. L. Elder, B. Baeuerle, Y. Salamin, A. Josten, U. Koch, C. Hoessbacher, F. Ducry, L. Juchli, A. Emboras, D. Hillerkuss, M. Kohl, L. R. Dalton, C. Hafner, and J. Leuthold, “All-plasmonic Mach–Zehnder modulator enabling optical high-speed communication at the microscale,” Nat. Photonics 9(8), 525–528 (2015).
[Crossref]

Nature (4)

C. Haffner, D. Chelladurai, Y. Fedoryshyn, A. Josten, B. Baeuerle, W. Heni, T. Watanabe, T. Cui, B. Cheng, S. Saha, D. L. Elder, L. R. Dalton, A. Boltasseva, V. M. Shalaev, N. Kinsey, and J. Leuthold, “Low-loss plasmon-assisted electro-optic modulator,” Nature 556(7702), 483–486 (2018).
[Crossref]

Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon electro-optic modulator,” Nature 435(7040), 325–327 (2005).
[Crossref]

C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, S. Lin, B. R. Moss, R. Kumar, F. Pavanello, A. H. Atabaki, H. M. Cook, A. J. Ou, J. C. Leu, Y.-H. Chen, K. Asanović, R. J. Ram, M. A. Popović, and V. M. Stojanović, “Single-chip microprocessor that communicates directly using light,” Nature 528(7583), 534–538 (2015).
[Crossref]

M. Liu, X. Yin, E. Ulin-Avila, B. Geng, T. Zentgraf, L. Ju, F. Wang, and X. Zhang, “A graphene-based broadband optical modulator,” Nature 474(7349), 64–67 (2011).
[Crossref]

Opt. Rev. (2)

S. Yukita, Y. Suzuki, N. Shiokawa, T. Kobayashi, and E. Tokunaga, “Mechanisms of the anomalous Pockels effect in bulk water,” Opt. Rev. 25(2), 205–214 (2018).
[Crossref]

H. Kanemaru, Y. Nosaka, A. Hirako, K. Ohkawa, T. Kobayashi, and E. Tokunaga, “Electrooptic effect of water in electric double layer at interface of GaN electrode,” Opt. Rev. 17(3), 352–356 (2010).
[Crossref]

Phys. Chem. Chem. Phys. (1)

R. Burt, G. Birkett, and X. S. Zhao, “A review of molecular modelling of electric double layer capacitors,” Phys. Chem. Chem. Phys. 16(14), 6519–6538 (2014).
[Crossref]

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Y. Nosaka, M. Hirabayashi, T. Kobayashi, and E. Tokunaga, “Gigantic optical Pockels effect in water within the electric double layer at the electrode-solution interface,” Phys. Rev. B 77(24), 241401 (2008).
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Figures (8)

Fig. 1.
Fig. 1. Schematic illustration of the optical configuration of relevant multilayer structure with and without electric field for (a) the conventional normal-incidence method and (b) the proposed total-reflection method. The ITO substrate comprised 330-nm ITO (In2O3 doped with SnO2) thin film on glass substrate (1.1-nm thick soda-lime glass); the TCO substrate was made of soda-lime glass (1.1 mm)/ITO (300 nm)/SnO2 (100 nm). The experimental systems in both panels (a) and (b) are properly modeled by three layers with the electric field off: a semi-infinite glass substrate, bulk ITO, and semi-infinite (bulk) water; and five layers with electric field on: a semi-infinite glass substrate, bulk ITO, SCL in ITO, EDL in water, and semi-infinite (bulk) water. (c) Definition of angle of incidence in experiment: the angle in air between the incident light beam with respect to the surface normal of the transparent conductive substrate in the water cell.
Fig. 2.
Fig. 2. Experimental setup: LDLS: Laser-driven light source (Xe lamp); SQ F50: 30-mm diameter, 50-mm focal-length synthetic quartz plano-convex lens; Pinhole: 40-µm diameter pinhole, Fiber: 1-mm core, 1.25-mm cladding multimode quartz fiber, Sample: aqueous electrolyte solution (NaCl) cell in which transparent conductive oxide and Pt electrodes are positioned as depicted.
Fig. 3.
Fig. 3. (a), (b) Complex refractive index n +  of transparent electrode ITO and change in complex refractive index of SCL in ITO used for calculation (almost the same functions as used for simulating the experimental results in Refs. [11,12,15]).
Fig. 4.
Fig. 4. Spectra of relative difference transmittance and reflectance for 330-nm thick ITO in 0.1-M NaCl aqueous solution. (a) Spectrum of relative difference transmittance obtained by using the conventional method with 0° incidence, 2 V, 20 Hz. (b) Spectra of relative difference reflectance obtained by using the new method with 85° incidence in air, 1–5 V, 223 Hz, S polarization. Calculated spectra for 330-nm thick ITO for (c) 0° incidence and for (d) 87° incidence in glass. For both calculations, $\Delta n ={-} 0.1$ in 2-nm thick EDL and $\Delta n ={-} 0.0031$ at 500 nm in 30-nm thick SCL, which corresponds to the experimental conditions of a peak AC voltage of 2 V at 1 Hz.
Fig. 5.
Fig. 5. Relative difference reflectance for 400-nm thick TCO in 0.1-M NaCl aqueous solution, obtained by using the proposed method. (a) Experimental difference reflectance spectra for 87° incidence in air, with S polarization and peak voltages of 1–4 V at 223 Hz. (b) Calculated difference reflectance spectra for 89° incidence in glass assuming $\Delta n ={-} 0.1$ in 2-nm-thick EDL and $\Delta n ={-} 0.0031$ at 500 nm in 30-nm-thick SCL, which corresponds to the experimental condition of 2 V at 1 Hz.
Fig. 6.
Fig. 6. Reflectance spectra and difference reflectance spectra (a) measured experimentally (87° incidence in air, 30 Hz, 2V) and (b) calculated (plot shows the average of results for 87°, 88°, and 89° incidence in glass) for S (black curves) and P (red curves) polarization in total-reflection configuration. The change in refractive index is the same as in Figs. 4 and 5.
Fig. 7.
Fig. 7. Single-layer model to explain principle of giant optical modulation.
Fig. 8.
Fig. 8. Calculated reflectance and difference reflectance spectra (62°incidence, nearly critical angle, in glass) for S- and P-polarized light in total-reflection configuration. We assume the same change in refractive index as in Figs. 4, 5, and 6.

Equations (26)

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r = r 01 + r 12 e 2 i Φ 1 + r 01 r 12 e 2 i Φ ,
n 0 sin θ 0 = n 1 sin θ 1 = ( n + i κ ) sin θ 1 ,
n 0 sin θ 0 = ( n + i κ ) sin ( x + i y ) = 1 2 { [ κ ( e y e y ) cos x + n ( e y + e y ) sin x ] + i [ κ ( e y + e y ) sin x n ( e y e y ) cos x ] } .
n 0 sin θ 0 = 1 2 [ n 2 + κ 2 n ( e y + e y ) sin x ] n sin x .
k 1 x = ( n + i κ ) k sin θ 1 = n 0 k sin θ 0 ,
k 1 z = ( n + i κ ) k cos θ 1 = ( n + i κ ) k ( 1 sin 2 θ 1 ) 1 / 2 = ( n + i κ ) k [ 1 ( n 0 n + i κ sin θ 0 ) 2 ] 1 / 2 = k [ ( n 2 κ 2 n 0 2 sin 2 θ 0 ) + 2 i n κ ] 1 / 2 k [ ( n 2 n 0 2 sin 2 θ 0 ) + 2 i n κ ] 1 / 2 = k ( n 2 n 0 2 sin 2 θ 0 ) 1 / 2 [ 1 + 2 i n κ ( n 2 n 0 2 sin 2 θ 0 ) ] 1 / 2 k ( n 2 n 0 2 sin 2 θ 0 ) 1 / 2 [ 1 + i n κ ( n 2 n 0 2 sin 2 θ 0 ) ] = k [ ( n 2 n 0 2 sin 2 θ 0 ) 1 / 2 + i n κ ( n 2 n 0 2 sin 2 θ 0 ) 1 / 2 ] k ( n cos x + i κ cos x ) .
r 01 S = n 0 cos θ 0 n 1 cos θ 1 n 0 cos θ 0 + n 1 cos θ 1 , r 01 P = n 1 cos θ 0 n 0 cos θ 1 n 1 cos θ 0 + n 0 cos θ 1 ,
r 12 S = n 1 cos θ 1 n 2 cos θ 2 n 1 cos θ 1 + n 2 cos θ 2 ,     r 12 P = n 2 cos θ 1 n 1 cos θ 2 n 2 cos θ 1 + n 1 cos θ 2 .
l r 01 S = n 0 cos θ 0 n 1 cos θ 1 n 0 cos θ 0 + n 1 cos θ 1 1.52 cos 61.04 2 cos 41.68 1.52 cos 61.04 + 2 cos 41.68 = 0.758 2.23 = 0.340
r 01 P = n 1 cos θ 1 n 0 cos θ 1 n 1 cos θ 0 + n 0 cos θ 1 2 cos 61.04 1.52 cos 41.68 2 cos 61.04 + 1.52 cos 41.68 = 0.167 2.10 = 0.0795
n 0 sin θ 0 = n 1 sin θ 1 1.52 sin 89 2 sin θ 1 θ 1 = 49.5
1 0 r 10S = n 1 cos θ 1 n 0 cos θ 0 n 1 cos θ 1 + n 0 cos θ 0 2 cos 49.5 1.52 cos 89 2 cos 49.5 + 1.52 cos 89 = 1.272 1.325 = 0.960 ,
1 0 r 10P = n 0 cos θ 1 n 1 cos θ 0 n 0 cos θ 1 + n 1 cos θ 0 1.52 cos 49.5 2 cos 89 1.52 cos 49.5 + 2 cos 89 = 0.952 1.022 = 0.932.
r = r 01 + e i ( 2 Φ + Ω X ) 1 + r 01 e i ( 2 Φ + Ω X ) = r 01 + e i ( 2 ( p + i q ) + Ω X ) 1 + r 01 e i ( 2 ( p + i q ) + Ω X ) = r 01 + e i ( 2 p + Ω X ) 2 q 1 + r 01 e i ( 2 p + Ω X ) 2 q
r 01 = e i ( 2 p + Ω X ) 2 q and e i ( 2 p + Ω X ) = 1.
2 p + Ω X = 2 k n d cos x + Ω X = 2 m π m = 0 , 1 , 2
r 01 = e 2 q .
R = | r | 2 = r 01 + e 2 q e i ( 2 p + Ω X ) 1 + r 01 e 2 q e i ( 2 p + Ω X ) r 01 + e 2 q e i ( 2 p + Ω X ) 1 + r 01 e 2 q e i ( 2 p + Ω X ) = r 01 2 + e 4 q + 2 r 01 e 2 q cos ( 2 p + Ω X ) 1 + r 01 2 e 4 q + 2 r 01 e 2 q cos ( 2 p + Ω X ) 4 r 01 2 ( 1 r 01 2 ) 2 ( n 2 + κ 2 ) d 2 Δ k 2 around R = 0 with the coefficient of finesse: F = 4 r 01 2 ( 1 r 01 2 ) 2
r = r 01 + e i Ω X e 2 i Φ 1 + r 01 e i Ω X e 2 i Φ X = P or S ,
tan Ω P 2 = sin 2 θ 1 ( n 2 / n 1 ) 2 ( n 2 / n 1 ) 2 cos θ 1 ,
tan Ω S 2 = sin 2 θ 1 ( n 2 / n 1 ) 2 cos θ 1 ,
Δ Ω P = sin Ω P [ n 2 / n 1 sin 2 θ 1 ( n 2 / n 1 ) 2 + 2 ( n 1 / n 2 ) ] Δ ( n 2 / n 1 ) = 2 cos 2 Ω P 2 Δ ( n 2 / n 1 ) ( n 2 / n 1 ) cos θ 1 [ sin 2 θ 1 ( n 2 / n 1 ) 2 ] 1 / 2 2 ( n 1 / n 2 ) sin Ω P Δ ( n 2 / n 1 )
Δ Ω S = sin Ω S [ n 2 / n 1 sin 2 θ 1 ( n 2 / n 1 ) 2 ] Δ ( n 2 / n 1 ) = 2 cos 2 Ω S 2 Δ ( n 2 / n 1 ) ( n 2 / n 1 ) cos θ 1 [ sin 2 θ 1 ( n 2 / n 1 ) 2 ] 1 / 2 .
cos θ 2 = ( 1 sin 2 θ 2 ) 1 / 2 = ( 1 ( n 1 n 2 ) 2 sin 2 θ 1 ) 1 / 2 = ± i [ ( n 1 n 2 ) 2 sin 2 θ 1 1 ] 1 / 2 .
exp ( i k 2 z z ) = exp ( i k cos θ 2 z ) = exp ( k [ ( n 1 n 2 ) 2 sin 2 θ 1 1 ] 1 / 2 z )
k 2 z 1 = λ 2 π [ ( n 1 n 2 ) 2 sin 2 θ 1 1 ] 1 / 2 .

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