Trans-reflective tunable color filter using electro-optic material

Ayesha Kanwal; Ahsan Sarwar Rana; Ahsan Sarwar Rana; Sadia Noureen; Khaled A. Aljaloud; Ali H. Alqahtani; Rifaqat Hussain; Akram Alomainy; Muhammad Qasim Mehmood

doi:10.1364/OME.514260

1. Introduction

Metasurfaces are nanostructures that can modify the phase and amplitude of light waves, opening up a new paradigm for creating optical devices. Color filters based on metasurfaces have drawn considerable attention in recent years due to their unique features, such as high efficiency, polarization insensitivity, and flexibility in design [1–4]. Further advancements in metasurface technologies have led to the development of color filters for high-resolution displays and imaging applications [5–9]. Moreover, metasurface color filters have been explored for many other applications, such as sensing, cryptography, and decorative photovoltaics. The operating concept of metasurface-based filtering depends on light-matter interaction, in which radiation interacts with nanoscale formations, allowing color screening through light diffraction, dispersion, refraction, reflection, and transmission on resonant wavelengths [10,11].

Since the early demonstrations of color filters, many new and efficient designs have been explored to enhance color filtering capabilities further. Transmission-based color filters were designed to filter out additive colors (red, blue, and green) [12]. The angle sensitivity of 1D grating was helpful in a dielectric-based guided mode resonant color filter design with angle tunability for additive color filters. It showed approximately 94%, 96%, and 99% efficiencies with green and red color filters, respectively [13]. Reflective color filters also gained significant attention due to the selectivity of subtractive colors (Cyan, Magenta, and yellow) of light while transmitting or absorbing others, offering various applications for precise color manipulation in displays, imaging, and optical signal processing [14]. Using a-Si-Al hybrid nanodisk metasurfaces onto Si substrate, a subtractive CMY color filter demonstrated good efficiency and color quality [15]. An ultra-thin hexagonal nanodisk-nanohole hybrid framework array produced excellent gamut, high color brightness, and polarization-independent subtractive colors with a resolution of 77,000 dpi [16]. An arrangement with two-dimensional randomized silver nanodisks onto a glass substrate possessed increased angle insensitivity of up to 60° for reflected color filters. Angle insensitivity increased to 70° by fabricating randomly dispersed nanodisks nanoholes onto a silicon substrate using hydrogen silsesquioxane (HSQ) Ag films [17]. Another research presented an asymmetrical Fabry Perot-based reflective color filter [18]. It employed a lossless metal, i.e., nickel (Ni) thin film for anti-reflection coating on the highest point of the cavity, and a thick Aluminium (AI) coating at the bottom, allowing for zero transmission.

Trans-reflective filters are innovative optical devices that yield color filters in transmission and reflection, realizing many exciting applications, including holography, microscopy with fluorescence, charge-coupled devices (CCD) imaging, and so on [19–22]. A trans-reflective color filter that uses a phase-corrected etalon (PCE) powered nano-resonator to provide a changeable bandwidth on a uniform resonant wavelength was also demonstrated [19]. Each filter is made up of a silver-titania-silver (Ag-TiO₂-Ag) structure combined with a titania dielectric functional layer (DFL), resulting in a (metal-dielectric-metal-dielectric) MDMD configuration. In an all-dielectric polarization-tailored trans-reflective structured multicolored pixel design, a hydrogenated amorphous silicon (a-Si: H) grating was employed to achieve a transmission efficiency of 95% and 90% in TM & TE mode, respectively [23]. In this case, the angle tolerance was increased to 35.

Tunable color filters were also presented as an advancement in color filtering technology, and several methods have been used to metasurface-based color filters to attain excellent tunability and compactness [24–28]. Compared to other techniques for providing outside stimulation, including chemical treatment and mechanical reconfiguration, electro-optic (EO) technology has become more popular because of its reliability benefits, minimal power use, and quick switching [29]. The applied electric field alters the refractive index simultaneously across the two optical planes, namely ordinary and exceptional axes, due to negative birefringence, eventually resulting in tunability. The refractive index varies linearly when exposed to an electric field. It begins to change proportionately to the square of the electric field [30] until it hits a limit known as the Pockels effect [31]. Because of its affinity-producing oxide substrates, barium titanate (BTO) is an excellent choice for a strong Pockels effect. Its application in thin films increases the material's relevance for on-chip electronics. Recently, an Indium Tin Oxide (ITO)-based metasurface color filter with electrical tunability was demonstrated by modifying the carrier concentration and plasma frequency through a Metal-Oxide-Semiconductor (MOS) capacitor configuration and focused ion beam milling of cylindrical pillars [32]. The ITO can also be combined with other metal oxides to enhance color purity through nanoscale pillar patterning [33].

Classical optimization methods, such as gradient-based topology optimization and the evolution algorithm, have been extensively used to perform inverse design of various photonic structures gadgets over the past few years. At the same time, neural networks have only recently become known as an effective instrument for the same reason [34–36]. Because NNs can correctly forecast the optical reaction once the geometrical parameters of the material distributions are supplied, properly trained Neural Networks (NN) can replace the traditional time-consuming numerical simulation for forward prediction [37]. In the inverse design, NNs perform the opposite function. In a nutshell, NN can find the best structure to accomplish specified goal answers or functionality [38–40].

This research focuses on designing an electrically tunable trans-reflective color filter using Barium Titanate (BTO) and optimizing its performance through an artificial intelligence (AI) based inverse design model. By carefully considering the tunable optical characteristics and high transmission efficiency of BTO, we can competently achieve transmission and reflection spectra and provide a broad range of vibrant and customizable colors. The color filter's specific configuration and structural dimensions are meticulously engineered by an inverse design model composed of two individual NN blocks. The first is the parametric optimization block (POB), which employs two deep neural networks (DNNs) in the forward and inverse directions to achieve the optimized dimensional values of the proposed meta-atom geometry. The second one is the voltage tuning block (VTB), which predicts optimal input voltage that gives the refractive index to achieve the desired trans-reflective colors. These predictions are based on the learned relationships between the electrical stimuli and the desired color output. Thus, the proposed device can be optimized to give any desired color within a fraction of a second. The design encompasses transmissive and reflective characteristics, yielding a trans-reflective color filter of unprecedented versatility. This design is also polarization insensitive and covers a large color gamut with spatial resolution of 74,700 dpi. This electrically tunable trans-reflective color filter holds great promise for applications in displays, imaging devices, and other areas that require accurate and customizable color indication. By leveraging the tunable properties of BTO and the optimization capabilities of DNNs, this research opens up new possibilities for advanced color filtering technologies.

2. Methodology

The geometrical structure of the proposed electrically tunable color filter’s meta-atom incorporating an electro-optic material is demonstrated in Fig. 1(a). A Barium Titanate (BTO) layer is laid over an Indium tin oxide substrate, providing additional freedom for designing the metasurface optical mode profile. A cylindrical nanostructure of ITO is placed on top of the BTO layer. The periodic boundary conditions in the x and y direction and a perfectly matched layer throughout the propagating axis, or z-axis. A light beam with linear polarization is emitted from 350 nm above the structure. Two monitors are positioned for reflection and transmission, above the source and below the structure respectively. Electric potential is applied between the ITO substrate and the ITO cylinder, acting as an electrode. Compared with various EO materials, BTO exhibits an exceptionally high Pockel’s coefficient [25], making it a standout choice. By adjusting different bias voltages across the two ITO structures, the EO effect can be used to change the refractive index of BTO, as illustrated by the following equation:

(1)$$\delta {n_l} ={-} \frac{1}{2}{n^3}{r_{lk}}{E_k}$$

Where r_lk denotes the electro-optic coefficient, n represents the index of refraction in the absence of an electric field, E denotes the electric field (E = V/d), and d is the measurement of the height of the BTO layer. The equation above shows that variations in the electric field or the applied voltage linearly affect the refractive index, allowing us to transmit different colors. The Fig. 1(a(iii)) depicts the linear relationship between n and V. The International Commission on Illumination (CIE) chromaticity diagram 1931 evaluates the color filter’s tunability and purity for reflective and transmissive colors.

Fig. 1. (a): Structure of Proposed Unit Cell: (i) Perspective view, (ii) top view, (iii) Voltage vs Refractive index of BTO, (b) Illustration of the methodology to design color filtering meta-atoms.

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An artificial intelligence (AI) based inverse design model rapidly optimizes the meta-atom’s structural dimensions and tunes the bias voltage applied to the meta-atom’s BTO layer, as shown in Fig. 1(b). This model comprises two sub-blocks. The first is the parametric optimization block (POB), followed by the Voltage tuning block (VTB) as the second. POB contains two individual deep neural networks (DNNs), referred to as optimization neural networks (ONN) and simulator neural network (SNN). ONN is used to find the optimum values of the meta-atoms geometrical parameters, i.e., ITO cylinder’s radius (r), ITO cylinder’s thickness (t₃), BTO layer thickness (t₂), and periodicity (P). SNN follows ONN, pre-trained to verify whether the optimized parameter values (generated by the ONN) provide the desired response. The ONN and SNN are deployed to ensure the geometric parameters are optimized for maximum tunability and color purity in both the transmission and reflection directions. Once the optimal parameters are achieved, the next block, i.e., VTB, is employed to map specific colors onto the refractive index or the applied voltage of the BTO layer. This block is composed of another DNN, and it takes the x y coordinates of the target colors as input and outputs the refractive index of BTO and the bias voltage to be applied between the two ITO structures.

To train the POB and VTB blocks, a dataset is collected via FTDT simulations of the proposed meta-atom over the wavelength range 400 nm to 700 nm. The substrate ITO’s thickness (t₁) is fixed in all the simulations at t₁ = 130 nm. In contrast, the rest of the parameters are varied in the ranges: t₂ = 90 nm to 140 nm, t₃ = 100 nm to 150 nm, r = 30 nm to 100 nm, and the refractive index (varied by the applied voltage) n = 2.45 to 5.5. Taking different combinations of these parameters within the mentioned range, 2000 meta-atom simulations were performed to collect a dataset of 2000 samples. Each simulation’s transmission and reflection results are converted into x y color coordinates of the CIE 1931 plot. These two coordinates and the corresponding four geometrical parameters, r, t₂, t₃, and P, are stored in the datasets.

The dataset for the ONN is defined as D_ONN = [(I_ONN,_i, O_ONN,_i), i = 0, 1, 2, …, N], where input I_ONN consists of three x,y color coordinates for three different values of n along transmission and three other x,y color coordinates for different values of n along reflection. Thus, I_ONN,i = [x₁t,_i, y₁t,_i ; x₂t,_i, y₂t,_i ; x₃t,_i, y₃t,_i ; x_1r,_i, y_1r,_i ; x_2r,_i, y_2r,_i ; x_3r,_i, y_3r,_i], is a [ 6 × 2 ] vector, used to ensure maximum tunability with n along transmission as well as reflection while optimizing the structural parameters. Choosing three color coordinates for each mode ensures the realization of the CMY (cyan, magenta, and yellow) and RGB (red, green, and blue) colors along transmission and reflection, respectively. The output O_ONN, _i = [r_i, t_2i, t_3i, and P_i], is a [4 × 1] vector representing the four geometrical parameters intended to be tuned. This dataset is then used to train the ONN, having seven hidden layers with several neurons (6–50 – 200–600 – 800–600 – 200–50 – 4). Relu is the activation function at the hidden layers to prevent a vanishing gradient. This network is trained for 500 epochs with an Adam optimizer. Since the values of the output parameters are continuous, ONN is dealt with as a regression-based network and acquainted with the mean square error (MSE) between the predicted and the ground truth parameters given as:

(2)$$MSE = \; \frac{1}{N}\mathop \sum \limits_{i = 1}^N {({P_i^{\prime} - \; {P_i}} )^2}$$

Here, N is the total number of samples, Pi’ represents the set of predicted parameters for ith input sample, and Pi is the set of ground truth parameters.

The dataset for pre-training the SNN is the same as that for the ONN, with the order of the inputs and outputs reversed. D_SNN = [(I_SNN,_i, O_SNN,_i), i = 0, 1, 2, …, N], where I_SNN,_i = O_ONN,_i = [r_i, t₂,_i, t₃,_i, and P_i] is a [4 × 1] vector of geometrical parameters, and O_SNN,i = I_ONN,_i = [x₁t,_i, y₁t,_i ; x₂t_,i, y₂t,_i ; x₃t,_i, y₃t,_i ; x_1r,_i, y_1r,_i ; x_2r,_i, y_2r,_i ; x_3r,_i, y_3r,_i], is a [ 6 × 2 ] vector of corresponding x, y color coordinates for different values of n along transmission and reflection. The architecture of the SNN is the same as that of the ONN. The pre-trained SNN works as the forward simulator, taking ONN’s optimized set of parameter values to generate the corresponding color coordinates. Since the output values are continuous, SNN is also dealt with as a regression-based network and trained with the mean square error (MSE) between the predicted and the ground truth x,y color coordinates along transmission and reflection given as,

(3)$$MSE = \frac{1}{N}\mathop \sum \limits_{i = 1}^N [{{{({Ti_{x,y}^\mathrm{^{\prime}} - {\; }T{i_{x,y}}} )}^2} + {\; }{{({Ri_{x,y}^\mathrm{^{\prime}} - {\; }R{i_{x,y}}} )}^2}} ]$$

where,

Ti_{x,y}^\mathrm{^{\prime}} = [{({x_{1t,i}^\mathrm{^{\prime}}{\; },{\; }y_{1t,i}^\mathrm{^{\prime}}{\; }} ),({x_{2t,i}^\mathrm{^{\prime}}{\; },{\; }y_{2t,i}^\mathrm{^{\prime}}{\; }} ),({x_{3t,i}^\mathrm{^{\prime}}{\; },{\; }y_{3t,i}^\mathrm{^{\prime}}{\; }} )} ]{\; \; }and{\; }

T{i_{x,y}} = [{({{x_{1t,i}},{y_{1t,i}}{\; }} ),({{x_{2t,i}},{y_{2t,i}}{\; }} ),({{x_{3t,i}},{y_{3t,i}}{\; }} )} ]

Ri_{x,y}^\mathrm{^{\prime}} = [{({x_{1r,i}^\mathrm{^{\prime}}{\; },{\; }y_{1r,i}^\mathrm{^{\prime}}{\; }} ),({x_{2r,i}^\mathrm{^{\prime}}{\; },{\; }y_{2r,i}^\mathrm{^{\prime}}{\; }} ),({x_{3r,i}^\mathrm{^{\prime}}{\; },{\; }y_{3r,i}^\mathrm{^{\prime}}{\; }} )} ]{\; \; }and{\; \; }

Rix,y = [{({{x_{1r,i}},{y_{1r,i}}{\; }} ),({{x_{2r,i}},{y_{2r,i}}{\; }} ),({{x_{3r,i}},{y_{3r,i}}{\; }} )} ]

The Fig. 1(a(i)) shows a perspective image of the developed meta-atom with the optimized parameters predicted by the POB as P = 340 nm, t₁ = 130 nm, t₂ = 110 nm, t₃ = 120 nm, and r = 50 nm, which operates in the visible range. An electric potential is applied to both the ITO substrate and the ITO cylinder to modify the BTO layer's refraction index between them. The second block, VTB, is then utilized to map specified target colors onto the BTO layer's index of refraction. This block is composed of another DNN with five hidden layers with several neurons: 2–50 – 300–600 – 300–50 – 2. Relu is the activation function at the hidden layers to prevent a vanishing gradient. This network takes the x y coordinates of the target color as input and outputs the refractive index of BTO and the corresponding bias voltage to be applied between the two ITO structures. The dataset used for training this network is defined as D_VTB = [(I_VTB,i, O_VTB,i), i = 0, 1, 2, …, N], where I_VTB,i= [x_i, y_i] and O_VTB,i= [V_i, n_i]. Here (x_i,y_i) are the color coordinates of the target color, and Vi, ni represents the corresponding refractive index and the bias voltage. The geometrical parameters are kept constant (with optimized values given by POB) while collecting all the samples. This network is trained for 500 epochs with an Adam optimizer. MSE for this network is defined as,

(4)$$MSE = \; \frac{1}{N}\mathop \sum \limits_{i = 1}^N [{{{({V_i^{\prime} - \; {V_i}} )}^2} + \; {{({n_i^{\prime} - \; {n_i}} )}^2}} ]$$

Thus, the AI-based inverse design model composed of POB and VTB blocks provides an ample solution for rapidly optimizing the proposed color filter meta-atom and tuning its applied voltage to obtain the desired colors along the transmission and reflection modes. Figure 2 provides a detailed pictorial depiction of the suggested AI model. The NN takes 2.7 minutes, and the traditional method takes 730 minutes to generate a result. The NN design process is about 270 times faster than the conventional method, proving that it is more efficient and effective and minimizes design challenges. The tunable color filter can be fabricated by a nanofabrication procedure that contains electron beam lithography (EBL) patterning, mask deposition and reactive-ion etching (RIE). Firstly 90 nm BTO coated on the ITO substrate by e-beam evaporation, E-beam lithography patterning is used to create the nanostructures on top of the BTO surface. Poly methyl methacrylate (PMMA) is used as the e-beam lithography resist, and the final ITO nanocylinders are created by a lift-off process [41,42].

Fig. 2. Detailed pictorial depiction of the proposed inverse design AI model.

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3. Results

The two components of the proposed AI-based inverse design model, i.e., POB and VTB, are trained with an Adam optimizer and 10⁻³ learning rate to minimize their respective MSEs given by Eqs. (3) and 4. The average test MSE achieved for POB is 6.5 × 10^−3, and VTB is 2 × 10⁻¹. Once the VTB is optimally trained, it takes an additive and a subtractive color (in transmission and reflection, respectively) as the target input. It outputs a specific voltage and refractive index that, when applied to the proposed meta-device, results in maximum color purity for the target colors. Table 1 shows the input and output of VTB for CMY and RGB colors. If our target colors are cyan in reflection and red in transmission, then the predicted applied voltage to the unit cell is 20.13, and the refractive index of BTO is 4.77. The predicted voltage and refractive indexes for other pairs of colors are also given in Table No. 1. When these predicted voltages are applied to the device, its spectrum response is measured and analyzed, as shown in Fig. 3(a). When plotted in the CIE 1931 diagram, the result is presented in Fig. 3(b). When the input voltage ranges from 0 to 30 volts, the index of refraction of BTO fluctuates from 2.50 to 5, and the CIE plot for both modes show a wide range of colors reflected and transmitted, as depicted in Fig. 3(c) and 3(d).

Fig. 3. (a) Transmittance for CMY and RGB, (b) CIE 1931 plot of CMY and RGB, (c) CIE 1931 plot of Reflection, (d) CIE 1931 plot of Transmission.

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Table 1. Input colors of VTB and corresponding predicted outputs.

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The Fig. 4 depicts the reflection of different-sized metasurfaces. The reflection of the single unit cell, simulated with periodic boundary condition (PBC), is not similar to that of the unit cell, which is simulated using a perfectly matched layer (PML). Therefore, various supercells are tested (i.e., 2 × 2 unit cells or greater), which can give a similar reflection to PBC with PML boundary conditions. Figure 4(a) shows the unit cell's reflection intensity with periodic boundary conditions. The percentage difference between the reflection intensities of different-sized metasurfaces and the actual unit cell values is demonstrated in Fig. 4(e). As the dimension of the metasurface expanded, the disparity shrank. The reflection intensity of a 4 × 4 metasurface is roughly equivalent to that of an actual unit cell. As a result, the metasurface pixel size is 4 × 4. An 8 × 8 metasurface is designed and divided into four 4 × 4 parts, each fed with a different voltage to verify the pixel size. As seen in Fig. 5, One color is transmitted, and one is reflected at a single voltage. In this case, if 20.13 V is applied, red is transmitted and cyan is reflected. In Fig. 5, a box with the word “cyan” indicates a pixel that transmits red and reflects cyan. A distinct set of colors is reflected and transmitted, and they are indicated in the box labeled “other color,” if the applied voltage differs from the voltages mentioned in Table 1.

Fig. 4. Reflection of different sized metasurface (a) Unit cell with PBC (b) 2 × 2 metasurface, (c) 4 × 4 metasurface, (d) 8 × 8 metasurface, (e) % difference of different sized metasurface with unit cell.

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Fig. 5. XY plane E-fields at (a) 425.532 nm, (b) 509,.091 nm, (c) 472.973 nm, (d) 600.858, (e) 429.448 nm, (f) 578.512 nm.

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After selecting the pixel size, a 15 × 15 pixel metasurface is designed, as shown in Fig. 6, where each pixel has 4 × 4 unit cells, and a separate voltage is applied to each pixel. C/R denotes that the voltage applied to this pixel reflects cyan and transmits red, M/G denotes that the voltage applied to this pixel reflects magenta and transmits green, and Y/B denotes that the voltage applied to this pixel reflects yellow and transmits blue. The applied voltages for C/R, M/G, and Y/B are 20.13 V, 25.776 V and 10.65 V respectively. The Fig. 7 illustrates the electric field intensity at various wavelengths.

Fig. 6. Metasurface layout (C for Cyan, R for Red, M for magenta, G for Green, Y for Yellow, and B for Blue)

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Fig. 7. XY plane E-fields of metasurface at (a) 425.532 nm, (b) 509.091 nm, (c) 472.973 nm, (d) 600.858 nm (e) 429.448 nm (f), 578.512 nm.

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To calculate the spatial resolution (SR) of the device in dots per inch (DPI), the following formula is used;

(5)$$S{R_{dpi}} = N/{L_{in}}$$

where L is the length of the metasurface in inches, and N is the number of pixels. The 4 × 4 metasurface is approximately 53.54 inches long, with a resolution of around 74,700 dpi. To compare color purity, the relative distance.

(6)$$RD = \sqrt {{{({C{p_x} - {C_x}} )}^2} + {{({C{p_y} - {C_y}} )}^2}} $$

where Cp_x & Cp_y are clear color coordinates on the CIE plot. Cx and C_y are the coordinates on the CIE plot for the specific color obtained by the proposed design. The lesser the RD, the higher the color purity [36]. Table 2 shows the relative distance of RGB and CMY. The colors on the reflection side are purer than those on the transmission side.

Table 2. Relative Distance of CMY and RGB.

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A flexible design of the color filter is also desired for angle insensitivity and independence of direction of polarisation of incident light, whether it is x-polarized or y-polarised. The Fig. 8 shows angle tolerance with polarisation independence in both the reflection and transmission sides. Similarly, reflection and transmission color filtering achieve an angle insensitivity of up to 50°. The overall performance parameters of the proposed design are shown in Fig. 9.

Fig. 8. (a) Reflection at different incident angles, (b) Reflection at different polarization angles, (c) Transmission at different incident angles, (d) Transmission at different polarization angles.

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Fig. 9. Key Performance Parameters.

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4. Conclusion

This study presents an electrically tunable, trans-reflective color filter utilizing Barium Titanate (BTO). The performance of the design has been improved using an artificial intelligence-based inverse design methodology. The design has a broad color gamut, a high spatial resolution of 74,700 dpi, and is polarization insensitive. The efficiency of the designed metasurface has increased by 5%. This tunable trans-reflective color filter has improved tunability and efficiency, which can be employed in displays and imaging systems applications. Moreover, using the AI-based design process and BTO layer, the color filter can be designed faster with tunable colors of high purity. Lastly, BTO has the additional advantage of growing epitaxially on the silicon substrate, which boosts its CMOS fabrication compatibility.

Funding

King Saud University, Riyadh, Saudi Arabia (RSP2024R474).

Acknowledgement

The authors would like to acknowledge the support provided by Researchers Supporting Project number (RSP2024R474), King Saud University, Riyadh, Saudi Arabia.

Disclosures

There is no conflict of interest to declare by the authors.

Data availability

The data supporting this study’s findings are available from the corresponding author upon reasonable request.

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Trans-reflective tunable color filter using electro-optic material

Abstract

1. Introduction

2. Methodology

3. Results

4. Conclusion

Funding

Acknowledgement

Disclosures

Data availability

References

Data availability

Cited By

Figures (9)

Tables (2)

Equations (10)

Optical Materials Express

Input Target Color		Output
Reflected Color	Transmitted Color	Voltage (v)	Refractive index (n)
Cyan	Red	20.13	4.77
Magenta	Green	25.776	5.40
Yellow	Blue	10.65	3.70