Active electrochemical high-contrast gratings as on/off switchable and color tunable pixels

To be viable for display applications, active structural colors must be electrically tunable, on/off switchable, and reversible. Independently controlling the first two functions, however, is difficult because of causality that ties the real and imaginary parts of the optical constants or changing overlap of fields during structural variations. Here, we demonstrate an active reflective color pixel that encompasses separate mechanisms to achieve both functions reversibly by electrochemically depositing and dissolving Cu inside the dielectric grating slits on a Pt electrode with ΔV < 3 V. Varying the modal interference via Cu occupancy in the slits changes the CIE space coverage by up to ~72% under cross-polarized imaging. In the same pixel, depolarization and absorption by the dissolving porous Cu switches the color off with a maximum contrast of ~97%. Exploiting these results, we demonstrate an active color-switching display and individually addressable on/off pixel matrix that highlights their potential in reflective display applications.

To calculate the dispersion and modal profile of the waveguide-array modes in a bare HCG, we used the modal formalism developed by the Chang-Hasnain group. 1 We note that the dispersion and modal profile only depend on the lateral dimension (defined as the direction) and optical constants of the HCG bar and slit, in contrast to the reflection, which additionally depends on the HCG height and material above and below the HCG. Here, our treatment focuses on s-pol light under normal incidence, which restricts our solution to even modes.
In  where 0 , and 0 are the vacuum permeability, and vacuum permittivity, respectively. s , a , and 0 are the lateral wavenumbers inside the grating bars, slits, and vacuum, respectively. m is the propagating constant in the longitudinal direction ( ). The modal profile in the HCG can be found from equations (1).
By matching the boundary conditions, the characteristic equation is found as: s,m tan ( s,m 2 ) = − a,m tan ( a,m 2 ).
We can then find m from m 2 = ( 2 slit ) 2 − a,m 2 = ( 2 bar ) 2 − s,m 2 , where slit and bar are the refractive indices of slit and grating bar, respectively.
To calculate the waveguide-array modes in a Cu-filled HCG, we implemented surface impedance boundary conditions (SIBC) first proposed by Lochbihler et al. 2,3 The SIBC treatment was previously used to understand the effect of extraordinary optical transmission through sub-wavelength slits in metals. [3][4][5][6] Similarly, here, the modes in a Cu-filled HCG can be easily found by ignoring the field inside the Cu and assuming that the tangential components of the electric and magnetic fields are related as follows.
, where Cu , and n are the Cu permittivity and normal unit vector, respectively. Here, the spol lateral electric field can be expressed as follows.
We can find s,m as follows (8): Using these set of equations, we calculated the modal profiles of the bare and Cu-filled HCG at λ=550 nm.  Unlike the bare and Cu-filled HCGs where the s-pol response dominates the optical properties, the partially Cu-filled HCG (a) is affected by both s-pol and p-pol responses.

Supplementary
The fundamental p-pol waveguide-array mode, propagating within the bare parts of the HCG, carries field concentrated at the slit sidewalls, and is therefore reflected by Cu accumulated inside the slit. This means that for thicker Cu, the mode wavelength must be shorter to accumulate the same phase over the propagation length. The calculated p-pol 0 th order reflection phase spectra plotted over Cu thickness up to the grating height confir m that the characteristic phase at zero radians blueshifts with increasing Cu thickness (c). On the other hand, the s-pol phase at 0 radians is relatively unaffected by the Cu thickness in the adjacent slits (b) due to its field concentrated inside the HCG bar (Fig. 1b). The two distinct s and p-pol phase dependences on the Cu thickness, respectively, result in a ~π phase difference and 45º elliptical polarization tilt angle over a range of wavelengths and Cu thicknesses (d, e). This translates to a cross-polarized reflection peak (f) much broader than that of the bare or Cu-filled HCG because both s and p-pol responses contribute to the reflected field vector rotation, rather than just the s-pol response. These properties are also confirmed with a bare HCG on Cu substrate whose p-pol response mimics the partially Cufilled HCG (g). Here, an increasing Cu thickness for a partially Cu-filled HCG gives a ppol response similar to a bare HCG on Cu substrate with decreasing HCG bar height since both scenarios describe a decreasing propagation length for the p-pol mode in the bare part of the HCG. Indeed, for the bare HCG on Cu substrate, the phase transition across 0 radians blueshifts with decreasing HCG bar height (i). Electric field distributions under p-pol illumination also confirm similar interference fields concentrated at the bare part of the slit sidewalls at the phase transition, for both partially Cu-filled (j) and bare HCG on Cu substrate (k). This field pattern is clearly distinct from those at non-resonant conditions (1,3,4, and 6) shown in (j) and the surface plasmonic resonances (9 and 12) shown in (k). The |Ex| field is not observable for the bare HCG, as expected, but is strong for the Cu-dissolving HCG due to the morphological disorder inherent in the Cu that scrambles the incident polarization.

Supplementary
, where , , and indicate reflection spectrum, time, and wavelength, respectively.
The maximum contrast is defined as the contrast between the state of maximum brightness and the off state as follows. field. The simulated pixel size was 50 × 50 μm 2 . The grating spacing was 500 nm and the period was 1 μm. A 1 M Cu 2+ concentration with 50 % Cu + ion conversion efficiency was used. The diffusivity of the electrolyte was 10 −10 m 2 /s. Equilibrium potentials were estimated from the measured CV curve. As shown in Fig. (a, left), the simulated results for a voltage of −1.9 V applied for 5 s reveal more electrodeposited metal along the edge of the pixel than in the center.
Electrodepositing for longer durations (30 s) at a lower potential −1.7 V improves the uniformity of the Cu thickness as shown in Fig. (a, right). The simulated results can be qualitatively verified with measurements as shown in Fig. (b). At large applied voltages applied for short durations (Fig.   (b, left)), one notices darker edges appearing over time, indicative of thicker Cu at the edges. On the other hand, for smaller voltages applied for longer durations (Fig. (b, right)), the colors remain spatially uniform over the pixel area, in agreement with the simulated results. The spatial nonuniformity found during dissolution can be explained in a similar manner, where the pixel edges appear brighter than the center, suggesting faster dissolution at the edges than at the center.
We note that the spatial inhomogeneity of the deposited metal over the pixel area is not unique to our pixel, but a general phenomenon for electrodeposition on a resistive electrode. Previous research (ACS Energy Lett. 3, 2823−2828 (2018)) on dynamic windows using metal electrodeposition on a square ITO electrode derived the potential drop (∆ ) with side length 2 as a function of position, where is current density, is the thickness, and is the resistivity respectively.
This analytical equation can be plotted as follows, which is qualitatively similar to the COMSOL distribution of Fig. (a, left). For electrodeposition, the current density is negative ( < 0), meaning < . This means that more metal is deposited at the edge, giving rise to a darker edge.
For dissolution, the current density is positive ( > 0), meaning > . This implies that dissolution occurs faster at the edge which gives the appearance of a brighter edge as observed experimentally. We note that the potential drop decreases for lower J and thicker , implying that lower voltages and longer durations result in less potential differences over the pixel and thus more uniform coverage, in agreement with the simulation results. Note 1: The on/off contrast is calculated as, where Ron and Roff are the reflection spectra for the on and off state, respectively. The wavelength range of interest is the visible range. All values were calculated from data extracted from the reported figures.
Note 2: The peak wavelength shift is calculated as the shift between two given peak wavelengths in the visible range, achievable in a single pixel. For reports providing more than one pixel, a band of wavelengths is provided.
Note 3: The applied voltage is a complex function of extrinsic factors such as the effective electrode size, distance between electrodes, electrolyte concentration, etc, and is therefore only used here to provide a ballpark range rather than a precise measure for comparison.
where , , , , , , and are the weight of the deposit, density of metal, atomic weight, total charge, number of electrons, faraday constant, and current, respectively. As a result, = where α represents the constant . For the case of electrodeposition, we assume, to a first approximation, that the deposit area, , does not change with time such that / = Cu / . Therefore, where the −0.5 dependence is found from the Cottrell plot. From this relation, the time dependence of Cu can be expressed as Cu ∝ √ . For the case of dissolution, the current decays exponentially. Therefore, the Cu volume has an exponential dependence on time. To control the 3×5 pixel matrix, a customized voltage controller was manufactured on a printed circuit board. The above photos show a picture of the voltage controller (left) and the corresponding blueprint (right). The controller was designed to precisely control the amplitude and time duration of bidirectional (+/−) DC voltage using a PC program. DC power (5V/1A) was supplied using an external adapter. The supplied voltage was adjusted to a setting-voltage using a multi-channel D/A converter and the impedance was reduced using a voltage buffer. The reference voltage was precisely adjusted using a trimmer. The controller was operated by a computer through a USB connection. Each pixel in the 3×5 pixel matrix was addressed by sourcing a potential through the respective WE output