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Abstract
This study provides a comprehensive investigation of dye-doped super twisted nematic liquid crystal (DDSTNLC) with the aim of uncovering its potential applications. Using design of experiments (DoE) techniques, we elucidated the relationships between physical variables and constructed a transmission model. We then used Monte Carlo simulations to demonstrate the potential applications of DDSTNLC in various optical performances, including high light transmittance and contrast ratio. The investigation combining the modeling and DoE paves the way for advancing progress in the development of DDSTNLC-based light valves.
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1. Introduction
Light valves (LVs) are devices that can be used to control the amount of light that passes through them or to protect privacy. They include a material that can be switched between transparent and opaque states by applying an electric field. The switching can be based on light reflection, absorption, or scattering. Light-absorbing LVs are a promising technology that is currently under development based on light dimming from a transparent state. There are many types of LVs, including the electrochromic (EC) [1–3], suspended particle (SP) [4,5], and liquid crystal (LC) [6–20] devices. The ECLV is an advanced optical device that achieves light modulation by manipulating the coloration of electrochromic materials using electric fields. However, the conventional inorganic ECLV may be limited in terms of switching speed due to the inherent time requirements of the color change process. In addition, the cost of ECLVs can be relatively high due to their intricate technological complexity, potentially limiting their scalability in large-scale applications. The SPLVs use suspended nanoparticles in a liquid or gel as the light modulating material and laminated between two transparent conductive substrates. By applying an electric field, the SPLV can be switched from a transparent state to an opaque state. The SPLVs encounter challenges including device lifetime in practical applications. For instance, suspended particles can sediment or aggregate over time, affecting the overall performance of the devices. Moreover, producing high-quality SPs can require complicated manufacturing processes, potentially leading to an increase in production costs. Both ECLVs and SPLVs have similar issues, such as slow switching speeds and high switching voltages. Additionally, they all require complicated manufacturing processes and high costs. The LC is an ideal material for use in light-dimming LVs. The LCLVs have combined properties of light dimming and light scattering of EC liquids and SP solids, respectively. LCLVs offer several advantages over ECLVs and SPLVs, including low power consumption, fast response time, and matured mass production process. They are commonly used in display technologies that use electric fields to manipulate the orientation of LC molecules, thereby facilitating light modulation.
The functionality of LC modulation often requires the use of polarization components to maximize the field-driven optical effect, which selectively filter light along specific axes, causing a partial loss of light energy. In response to the challenges associated with polarization components, researchers have explored the integration of polymers or dyes into LCLVs for scattering or dimming types of devices, respectively. These approaches aim to improve the efficiency of light modulation. In polymer-doped LCLVs, polymers are introduced to modify the alignment of the LCs, potentially improving contrast ratio (CR) and response speed. Examples of these approaches include polymer dispersed LCs (PDLCs) [21–24] and polymer stabilized LCs (PSLCs) [23,25–27]. However, incorporating polymers without matching refractive indices between the guest and host can cause light scattering, which can affect optical clarity. Additionally, precise control of the polymerization process is essential for PDLCs and PSLCs. This is compounded by the limited selection of suitable component of polymers and LCs, surface alignment and with the external applied field to mediate a specific alignment configuration. Dye-doped LCs (DDLCs) use dichroic dye molecules in the LC host to adjust light propagation and attenuate the amount of light passage, reduce the dependence on polarization components and potentially improving light transmission.
A super twisted nematic liquid crystal display (STNLCD) comprises a chiral-doped nematic liquid crystal layer with tilted boundaries and a twist angle of about 270°. It operates in a birefringent optical mode between two non-conventionally oriented polarizers – neither parallel nor orthogonal. Performance characteristics include a low driving voltage of about 1.75 V, a response time of about 300 milliseconds, and a contrast ratio of 10:1 at normal incidence and ≥4:1 within a viewing cone of 45° from the normal direction [28]. The twist angle of the STNLCD is determined by the chiral dopant and the angle of the director near the alignment layer, which depends on the rubbing direction of the alignment layers of the top and bottom substrates. The orientation of the LC molecules twists in the direction of the azimuth angle to form a helical structure. The chiral pitch of the STNLCD is the distance required for the LC molecules to undergo a full 360° twist and can also be determined by the ratio of thickness to twist angle multiplied by 360°. In this study, we depart from the conventional STNLCD mechanism by opting for the dichroic dye instead of polarizers, presenting a different approach named dye-doped STNLC (DDSTNLC). The doping of dichroic dye has negligible effect on the twist structure in STNLCs because of low concentration of dichroic dye and strong surface anchoring in our experiments. The long axes of the dichroic dye molecules align with that of the LC molecules due to the guest-host effect via van der Waals interactions. The anchoring force induced by the antiparallel rubbed polyimide alignment layer coating on the substrates fixes the twist angles at multiples of 180°, such as 0°, 180°, 360°, and 720°. In a 0° dye-doped nematic LC system (DDNLC), the viewing angle is approximately 120° at a 10:1 contrast ratio and 150° at a 5:1 contrast ratio [29]. The DDSTNLC can be thought of as DDNLC with an additional twist of 180° to 720°, having the potential for a wider and more uniform viewing angle than the 0° DDNLC due to the rotational symmetry of the DDSTNLC.
As shown in Fig. 1, in the absence of an electric field, the dichroic dye molecules, with higher absorbance along its long axis, follow the liquid crystal (LC) molecules in a helical structure, causing absorption of all polarizations of incident light. This results in a lower transmittance in the haze-free dark state. When an electric field is applied to the DDSTNLC, the dye molecules reorient parallel to the LC molecules and perpendicular to the light propagation direction. This causes the DDSTNLC to switch to a transparent state with higher transmittance. This is called a guest-host system [30]. As a result, the DDSTNLC with homogeneous alignment at zero voltage can be switched between a haze-free dark state and a transparent state. And vice versa, a DDSTNLC with a vertical alignment at zero voltage can be switched between a transparent state and a dark state in response to an applied voltage. While the driving voltage required for these DDSTNLC samples is only about 10 V at 1 kHz, which is sufficient to unwind the helical twist, a voltage of 24 V at 1 kHz gives a higher contrast ratio.
The response time for the DDSTNLC sample with a 360° twist angle is 180 milliseconds. The haze is less than 3% for all samples in both the on and off states.
Active smart window technology allows various forms of light to be controlled with electricity. When electricity is applied, the smart window undergoes a transition from a dark state to a transparent state, allowing for dynamic light control. If the DDSTNLC were applied to window applications, it would be difficult to perceive that approximately half of the light was absorbed in the transparent state because the human eye is not very sensitive to the difference between 50% and 90% transmittance. Until now, DDSTNLC devices have not been commercialized because it was limited by two main issues: insufficient CR and transparent state transmittance. Design of experiment (DoE) is a scientific method for planning and conducting experiments to improve the quality of products and processes by identifying and understanding the relationships between variables. By efficiently collecting relevant data and extracting maximum information from experiments, DoE enables decision making based on empirical data. It provides a systematic and controlled approach to understanding how various factors affect results. In this research, we utilized DoE to optimize the configuration of DDSTNLC, a method that has never been used for this purpose. This optimization is expected to yield significant improvements, including highly improved the CR, reduced voltage requirements, maintained haze-free performance in both dark and transparent states, simplified fabrication processes, and shortened the response time.
2. Design of experiment
2.1 Identification of five factors
Due to the insufficient high transmittance in the transparent state and low transmittance in the dark state of DDSTNLC, coupled with a limited CR, its application is limited. Therefore, we conducted a comprehensive analysis of the five factors that potentially affect the performance of DDSTNLC, including LC birefringence (Δn), dye concentration (c, measured in weight percent, wt%), cell gap (d, measured in micrometers, µm), twist angle (A, measured in degrees, °), and rubbing strength (R, measured in times). The goal was to identify methods to optimize the performance of DDSTNLC. Each of the five factors has the potential to affect the performance of the device. While each factor may have its own optimal independent result, it does not necessarily represent a global maximum under the condition that other factors are fixed. In addition, there may be interactions between the factors. Therefore, in order to determine the globally optimal conditions, it is imperative to consider all factors simultaneously, merge them, and formulate a theoretical model that includes all factors.
2.2 Design of experiment
As shown in Table 1, we used two common LCs, TMS83700 (HCCH) and HTG135200-100 (HCCH), with optical birefringence values of 0.1 and 0.21, respectively, to investigate the influence of LC on the device,. The optical transmittance of the device is mainly due to the absorption capacity of the dichroic dye. To improve the performance of the device, we used a commercially available highly soluble black dichroic dye M1012 (Mitsui Chemicals). The selected c were 5, 8 and 10 wt% of the total mixture. The d also affects the total amount of dye molecules in the device and the degree of the light dimming effect. Therefore, we selected three separate d of 3.0, 4.9, and 9.7 µm. This range covers and exceeds the highest and lowest thicknesses of LC displays. Due to the guest-host relationship, dichroic dyes twist with the orientation of the LC. To broaden the applicability of the device, we used natural light, which is unpolarized light consisting of polarizations from all directions and types. Three A of 180°, 360°, and 720° were selected by adding the appropriate concentration of chiral dopant R811 (HCCH) to the mixtures. The twisted orientation of the LC molecules allows the dye to absorb polarizations from a wider range of directions. Twist angles beyond this range lead to hysteresis and haze during the electrical switching process and are beyond the scope of this discussion, commonly referred to as cholesteric LCs. To address the boundary conditions (i.e., LC anchoring energy and pretilt angle), we selected three R of 2, 5, and 10 times.
Table 1. Number of variables and level of values for each factor in DDSTNLC
The solubility of the dichroic dye M-1012 in STNLCs with a twist angle of 720° using LC HTG135200-100 was measured to be at least 20 wt% at room temperature. The absence of visible dye crystallization under the microscopic observation at 0°C provides assurance of the unsaturated state. For large-angle STNLCs (>720°), the solubility of the dichroic dye may be limited. The small-angle STNLCs (<720°) behave similarly to the TNLC with a smooth optical response to voltage with a weak hysteresis effect (haze is less than 3% for all samples in both the on and off states in this study), while the large-angle STNLCs (>720°) behave more like cholesteric LCs, exhibiting a strong hysteresis effect with haze in the focal conic texture during voltage application. The decision to use only small-angle STNLCs in the study is based on the negligible hysteresis effect in this range and the prominence of hysteresis in large-angle STNLCs.
2.3 Fractional factorial design
To comprehensively analyze the effect of these five factors on the device, there would be a total of 2 × 3 × 3 × 3 × 3 = 162 combinations in the DoE. Running experiments for all these combinations would be time-consuming and resource-intensive, which is not feasible with the limited resources and time frame. Therefore, we apply statistical methods and use fractional factorial design to select 18 mutually orthogonal subsets. By analyzing these 18 experimental results, we can calculate the results for all 162 combinations. This approach allows the construction of a theoretical model which then facilitates the evaluation of the optical characteristics of the device. With this information, we can design a corresponding device based on customized-specific conditions.
Table 2 presents 18 experimental DDSTNLC combinations selected by an orthogonal experimental design. The left section outlines the five specified independent variables, or factors, while the right section represents the dependent variables, or experimental results. After the fabrication of the 18 samples, transmittance spectra were measured under both no electric field (0 V) and applied electric field (24 V) conditions. The transmittances at the photopic peak of 550 nm were measured under two conditions: 24 V at 1 kHz and 0 V at 1 kHz, referred to as the maximum transmittance (Tmax) and minimum transmittance (Tmin), respectively. The CR was then determined as the ratio of Tmax divided by Tmin.
Table 2. Orthogonal experimental design and results for 18 DDSTNLC combinations
2.4 Optical properties of 13th experimental sample
As shown in Fig. 2(a), we performed spectral measurements of the 13th experimental sample and took corresponding sample images in transparent state 2(b) and dark state 2(c). When an electric field is applied, the sample is in the transparent state. From the sample images, a bright and clear background pattern with a transmittance of 47.5% at a wavelength of 550 nm can be clearly observed. When no electric field is applied, the sample is in the dark state. At this point, the transmittance at a wavelength of 550 nm is 5.2%. Although the background becomes very dark, careful observation shows that the background remains clear and not hazy. This indicates that the dark state of the DDSTNLC cell is due solely to dye absorption and not to other scattering phenomena. It is worth noting that the CR for this sample is as high as 9.1:1, which is very high for a DDLC mode. Moreover, the color of the DDSTNLC cells was analyzed using visible light spectra in Fig. 2(a). Both the transparent and dark states exhibit flat and featureless curves with no discernible color peaks, indicating uniform absorption of all colors of visible light by the black dichroic dye. This uniformity results in a consistent black and transparent appearance with no specific colors, and the DDSTNLC cells exhibit minimal to no observable color variation between the transparent and dark states. In window applications such as automotive window tinting, the 5.2% transmittance makes it almost impossible to see the background behind the window. With the push of a button, it can be quickly adjusted to a transparent state with 47.5% transmittance, as clear as a window without solar control film.
Fig. 2. (a) Transmission spectra without polarizers of 13th experimental DDSTNLC sample and corresponding sample images in (b) transparent state and (c) dark state.
3. Moodel of transmittance for DDSTNLC cells
3.1 Correlation matrix
To explore the relationships between the factors and the results, we used Python to compute the correlation matrix for 18 experimental DDSTNLC combinations, as shown in Fig. 3. The correlations between Δn, c, d, A, and R are all 0, indicating that they are independent variables. Tmax is primarily affected by c and d, while Tmin is primarily affected by Δn, c, d, and A. R has a minimal effect on both Tmax and Tmin. This indicates that the surface anchoring provided by the polyimide coating is sufficient for the LC to achieve a uniform and planar alignment after two rubbings. In addition, the pretilt angle remains constant. Since the rubbing strength has a minimal effect on the device performance, we chose to exclude this factor. The CR is calculated by dividing Tmax by Tmin. Therefore, there is no need to analyze CR separately. Once the models for Tmax and Tmin are established, the CR can be calculated directly.
3.2 Transmittance models
Dichroic dyes exhibit two different absorption coefficients when observed at different angles: the higher absorption coefficient is observed along the long axis (α∥) and the relatively lower absorption coefficient is observed along the short axis (α⊥). Due to the guest-host effect via van der Waals interactions, dichroic dye molecules are aligned with the direction of long axis of LC molecules. The transmittances of a dichroic dye-doped and homogeneously-aligned nematic LC cell for polarization parallel and perpendicular to the long axis of the dye molecules can be described as:
where T‖ and T⊥ are the transmittances of a dye-doped nematic LC cell for polarization parallel and perpendicular to the long axis of the dye molecules, respectively. T0 is the transmittance of a homogeneously aligned LC cell without a dye. c is the dye concentration and d is the cell gap [31,32].In the DDSTNLC cell, the dye molecules are aligned parallel to the substrates and absorb most of incident light regardless of the polarization direction so that this inactivated state is tint. In the transparent state, the dye molecules are aligned perpendicular to the substrates and absorb only a little amount of incident light so that this inactivated state is transparent. The transmittance of an unpolarized light in the transparent state and dark state can be expressed as:
3.3 Transmittance minimum in dark state
Without an applied electric field, the dichroic dye aligns within the STNLC in a helical structure. Both the long axes of the LC and the dye molecules are parallel to the glass substrate. At this point, the transmittance of the device is affected not only by the long axis absorption coefficient α∥ and the amount of dye in the LC cell, but also by the A and the Δn of the LC. The effective absorption coefficient is maximized. The fitting result of Tmin against the 18 experimental data points can be expressed by the following formula:
When the birefringence of the LC is zero, the polarization state of the incident light is not affected by the LC. The twist angle of the dye only needs to be greater than or equal to 90° to completely absorb all ambient light, since unpolarized light can be produced from the combination of vertical and horizontal linearly polarized light. However, due to the incident light is not only absorbed by the dye, but also has its polarization state and phase altered, delayed, and rotated by the LC. For example, when light passes through a 90° twisted nematic LC cell that satisfies the Mauguin condition of the Gooch–Terry theory [33], the polarization of the light is rotated by 90° an along with the twisted LC molecule. This means that the effective twist angle of dye is 0°, and the dye absorption effect is identical to that of a dye-doped and homogeneously-aligned nematic LC cell with a 0° twist angle. Therefore, LCs with smaller Δn, smaller d, and larger A will all reduce the optical effects of the LC, ultimately leading to an improvement in the dark state absorption coefficient of the device and a reduction in the Tmin. B is a fixed constant proportional to but not equal to α∥. This fitting has an R2 of 0.94, indicating that this theoretical model is in good agreement with experimental results. That is, knowing c, d, A, and Δn, the Tmin of the device can be calculated.
3.4 Transmittance maximum in transparent state
When a sufficient electric field is applied to the LC cell, both the long axis of the LC and the dye molecules rotate to align parallel to the electric field and perpendicular to the glass substrate. At this point, both the effective Δn and A are nearly equal to zero. The transmittance of the device is primarily affected by the short axis absorption coefficient of dye, α⊥, and the amount of dye in the LC cell. The effective absorption coefficient is minimized. The fitting result of Tmax against the 18 experimental data points can be expressed by the following formula:
Without considering dye absorption, the non-normalized Tmax of the device is 90.7%, which is equal to Tmax0 due to multiple interfaces between the glass substrate, LC, and air resulting in light reflection and scattering, as well as slight light absorption by the LC and glass. When αmax1 is 0.058, much smaller than 2.16 of αmax3, that means the effect of LC is very small in the transparent state. When αmin3 is 2.16, it directly serves as the α⊥, an indicator of the dye absorption capacity. The product of c and d represents the total amount of dye. This fitting shows an exceptionally high R2 of 0.99, indicating an excellent fitting between the theoretical model and experimental results. This means that it is possible to calculate the Tmax of a device by knowing the variables of DDSTNLC.
This design and modeling approach not only enables rapid result prediction and cost savings, but also helps to identify the theoretical limits of device performance, which is applicable in scientific research and technical production.
4. Monte Carlo simulation
4.1 Simulation
We have developed a theoretical model for predicting the transmittance of DDSTNLC. This model not only allows for fast and inexpensive computation of experimental results that would otherwise require 162 different experimental combinations, but also allows for arbitrary non-integer independent variables within the original experimental design range. However, it is worth noting that the reliability of the model decreases when extrapolating beyond the original experimental range.
To demonstrate the robust capability of the DDSTNLC model, we conducted 2000 Monte Carlo simulations, each with specific parameter ranges for Δn ranging from 0.05 to 0.25, for c from 0% to 10%, for d ranging from 1 µm to 10 µm, and for A from 0° to 720°. Since we were interested in both CR and Tmax, we plotted the simulated results and experimental results as a graph of CR versus Tmax as shown in Fig. 4. It is clear from the graph that regions with high Tmax yield low CR results, and conversely, regions with high CR yield low Tmax results, indicating an inverse relationship between Tmax and CR. From these simulation results, we have identified three examples that warrant further discussion, which are detailed in Table 3.
Fig. 4. (a) The simulation (blue square dot) and the experiment (red circle dot) results as a graph of contrast ratio versus maximum transmittance. (b) the comparison between calculated and the experimental results as a graph of transmittance versus sample number.
Table 3. Three potential DDSTNLC examples from Monte Carlo simulations
The R2 values of 0.99 for Tmax and 0.94 for Tmin indicate a strong correlation between the model predictions and the actual experimental data. In addition, the fact that all 18 experimental data points are within the 2000 simulated data points calculated from the models as shown in the Fig. 4(a) further supports the idea that the simulation results closely match the experimental results. To better illustrate the agreement between experiments and calculations, Fig. 4(b) shows the maximum and minimum transmittance values for the 18 experimental samples, as well as the simulated maximum and minimum transmittance calculated from the experimental independent variables using the model. The experimental and simulated results are well matched. After the model developed from the non-optimized experimental data, three potential examples selected from 2000 Monte Carlo simulation but not calculated from the same experimental independent variables using the model. The potential examples should be verified.
4.2 High CR over 100:1
We present a possible pathway to achieve ultra-high CR in DDSTNLC devices. In Table 3, a simulation shows that a CR of up to 118:1 can be achieved with a carefully selected combination of dye concentration, LC thickness, Δn, and A. However, this high CR comes at the expense of low transmittance in both dark and transparent states. The result shows that a Tmax of only 14.4% can be achieved. While the low transmittance of this DDSTNLC sample limits its application in windows, it may be suitable for applications where high CR is more important than high transmittance, such as augmented reality and virtual reality displays.
4.3 High ΔT over 50%
To meet the requirements of high transmittance applications, we tried to look for another set of examples in the simulation. However, we found that simply seeking the highest Tmax is not enough, because if no dye is added, Tmax may reach 90%, but the Tmin will also be 90%, making it impossible to adjust. This also indirectly shows that neither too high nor too low a Tmax can provide a suitable adjustment range. Therefore, we chose another indicator: the difference between Tmax and Tmin, which is denoted by ΔT. As shown in the second example in Table 3, we found a set of examples in the simulation results with a ΔT of 55.3%, where Tmax is 70.2%, Tmin is 14.9%, and the CR is 4.7:1. This example not only has a high ΔT value, but also provides excellent high transmittance in the transparent state and a sufficiently low transmittance in the dark state. The only disadvantage is the relatively low CR.
This high ΔT example can be widely used in various scenarios, especially those with high transparent state transmittance requirements. Since this example has the largest ΔT value in the simulation, it means that the theoretical maximum ΔT value of the DDSTNLC device is approximately this much, regardless of how its factors are adjusted within the given constraints. Through this model, we can directly determine where the highest possible performance level can be achieved if we plan to design this type of device. This revelation enables an evaluation of the viability of research in this direction before embarking on its development.
4.4 Tmax over 50% and CR over 10:1
Previous guest-host LC devices have been limited by two main issues in applications: insufficient CR and transparent state transmittance. To demonstrate that DDSTNLC devices can overcome these limitations, we found a possible solution in the simulation results shown in the third example in Table 3 with a Tmax and Tmin of 50.4% and 4.30%, respectively, resulting in a CR of 11.7:1 and a ΔT of 46.1%.
The previously fabricated 13th sample was very close to achieving the goal of high CR and high transparent state transmittance. By simply increasing the twist angle, we were able to reduce the Tmin and improve the CR to meet the target. We believe that this DDSTNLC device will open another valuable venue in the development and production of window applications.
4.5 Analysis
In Table 3 we observe similar characteristics in the independent variables of these three examples. They have relatively smaller Δn of LC, higher A and c. In addition, the d varies from low to high. The smaller Δn is due to the fact that in the dark state of DDSTNLC, the absorption efficiency of the dye is affected by the LC. The polarization state and phase of the incident light are altered, retarded, and rotated by the LC, which counteracts the effective twist effect of the dye, thereby increasing the transmittance in the dark state. Therefore, as Δn of LC decreases, the CR increases, resulting in improved device performance. The Δn is a fundamental property of LC materials. To achieve high performance DDSTNLC, it is essential to select an LC host with a lower Δn value. The higher A is advantageous because it allows the dye to absorb polarized light from a wider range of directions. However, in the DDSTNLC system, the inherent counteraction of the LC never reaches zero. Therefore, having a larger A reduces the degree of effective counteraction, thereby increasing the performance of the DDSTLNC. The higher c increases the light absorption, thereby contributing to an improved CR. However, it also reduces both the Tmax and Tmin. According to the Tmax model, when the other independent variables are fixed, the product of d and c represents the total amount of dye in the device, which is a critical factor in determining the Tmax. Therefore, a high c must be coupled with a low d to achieve an increase in CR without compromising Tmax.
5. Conclusion
This study demonstrated the application potential of DDSTNLC devices. We developed a mathematical model for transmittance that included four factors including c, d, A, and Δn. The model had a fitting accuracy (R2) of 0.99 and 0.94 for Tmax and Tmin, respectively. We obtained three key insights through the model of experiments: first, the product of c and d is inversely proportional to Tmax and Tmin, while being directly proportional to CR; second, a DDSTNLC with lower Δn LC, higher A, higher c, and lower d can increase CR; and third, there is an inverse relationship between Tmax and CR. We also discovered three potential applications for DDSTNLC through Monte Carlo simulations: first, a high CR over 100:1; second, a wide tuning range over 50%; and third, simultaneous high Tmax over 50% and high CR over 10:1 are achievable. Nevertheless, we are aware of some potential limitations of the device, for example, achieving a high CR device by increasing c can be challenging due to difficulties in obtaining dichroic dyes with high solubility, a DDSTNLC with a large A can lead to hysteresis problems during the driving process, thinner DDSTNLC cells can also be challenging in maintaining uniformity of cell gap during the fabrication of large size panels. Overall, the model developed in this study provides new insights into DDSTNLC-based light valves and opens up new possibilities for their further development and application. Future research will focus on validating these results and, if necessary, refining the model for increased accuracy.
Funding
National Science and Technology Council (NSTC 112-2223-E-110-004).
Acknowledgments
C.-T.H. and L.-C.C. acknowledge the financial support from Corning Incorporated, USA. C.-T.H. and T.-H.L. acknowledge the support from the National Science and Technology Council of Taiwan under the grant number NSTC 112-2223-E-110-004.
Disclosures
The authors declare no conflict of interests.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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