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Twisted nematic liquid crystal polymer-based multi-layer composite polarizer with low azimuthal transmittance variation

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Abstract

The polarizer is an indispensable element in modern displays, but the azimuthal transmittance variation of the polarizer also affects the display quality, and it is hard to eliminate the azimuthal transmittance variation because of the polarizer’s structure. In this paper, we propose a multi-layer composite polarizer with polarizing layer – twisted nematic liquid crystal polymer layer – polarizing layer structure. An iodide molecule distribution model is introduced to explain the azimuthal transmittance variation of the normal polarizer and guide the design of the multi-layer composite polarizer. The azimuthal transmittance variation of the multi-layer composite polarizer and normal polarizer is measured and calculated, and the results show that the azimuthal transmittance variation of the multi-layer composite polarizer is only about one-fifth of that of the normal polarizer. Except for the most uniform transmittance distribution, the transmittance distribution of the multi-layer composite polarizer can be adjusted to meet different requirements. The potential concerns about low transmittance and color shift are also discussed, and they can be solved by reducing the polarization degree of the polarizing layers and increasing the thickness of the liquid crystal polymer layer. The results show that the multi-layer composite polarizer can replace the normal polarizer to reduce the viewing angle defects of the emissive displays.

© 2021 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

Polarizer, an indispensable element in modern displays, has been widely applied in various different kinds of displays to obtain different functions, and its performance is a key parameter that impacts the display quality [14]. In liquid crystal displays (LCD), two polarizers, crossed polarizer and analyzer, are the basis of the optical switching function. The polarizer converts the light emitted by backlight into linearly polarized light, whose polarization state is modulated in the liquid crystal layer, and the analyzer blocks or passes through the output polarized light of the liquid crystal layer. At dark-state, the liquid crystal layer has no rotating effect, and the analyzer blocks the linearly polarized light produced by the polarizer. At bright-state, the linearly polarized light is modulated by the liquid crystal layer and can go through the analyzer [59]. In the emissive display, such as the organic light-emitting diodes (OLED), the circular polarizer consisting of a polarizer and a quarter waveplate is used to obtain high ambient contrast ratio and keep the display luminance [10,11]. While the ambient light shines onto the OLED, the ambient light transforms into right (or left) circularly polarized light by the circular polarizer, then transforms into left (or right) circularly polarized light after reflecting by the reflector on the substrate, and blocked by the circular polarizer [12,13]. Only one polarizer is used in the structure of the emissive display [14], so the transmittance variation of the polarizer will affect the performance of the emissive display. The research on the polarizer in displays focused on the light leakage of the crossed polarizers [1517], yet the optical defect of the single polarizer has not been appreciated enough.

To date, the most polarizer applied in displays is the iodine type polarizer, and the polarization selecting effect of the polarizer is based on the alignment of iodine molecules. The iodine type polarizer is fabricated by stretching the iodine-stained polyvinyl alcohol (PVA) film, and the iodine molecule directionally arranges on the stretched PVA film [18,19]. The iodine molecule can absorb the input light whose polarization vector parallels to the orientation of the iodine molecule, so the output light is polarized. Because of the anisotropic structure, the polarizer has obvious azimuthal transmittance variation at the oblique viewing direction. In LCD, the crossed polarizers are used to obtain the display function, and the azimuthal transmittance variation of the display is strongly dependent on the arrangement of liquid crystal, so the azimuthal transmittance variation of the polarizers is not important. However, there is only one polarizer in the emissive displays, so the transmittance variation of the polarizer affects the display quality. The transmittance variation, especially the azimuthal transmittance variation of the polarizer, further enlarges the luminance mura caused by the cavity in the emissive displays. Reducing the azimuthal transmittance variation can improve the display quality.

In this paper, a multilayer composite polarizer with polarizing layer - twisted nematic liquid crystal polymer (TN-LCP) layer - polarizing layer structure is proposed. Firstly, a three-dimensional model is introduced to explain the transmittance variation of the normal polarizer. Next, the structure and the polarization changing process of light in the multi-layer composite polarizer are shown. Then, the transmittance variation of the multi-layer composite polarizer is measured and analyzed, and the comparison with the normal polarizer shows the obvious improvement in the azimuthal transmittance variation. After that, the influence of structure on transmittance variation is investigated, and the multi-layer composite polarizers with different transmittance variations are designed to fit different requirements. Finally, the potential concerns about transmittance and color shift are discussed, and solutions are given.

2. Transmission principle of polarizer

In the iodide type polarizer, the distribution of iodine molecules in the polarizer is not completely uniform due to the stretching in the fabrication process, and the distribution of the iodide molecules is directional [18,19]. Thus, the transmittance variation with polar angles shows different tendencies at different azimuth angles, and the azimuthal transmittance is non-uniform at a polar angle. To explain the transmittance variation, we introduce a simplified three-dimensional model of iodide molecule distribution. Figure 1(a) shows the schematic diagram of the iodide molecule distribution in the polarizer and the definition of viewing angles. The iodide molecules alternately distribute in different layers, and they cover the whole plane of the polarizer at the normal viewing direction. The anisotropic distribution of iodide molecules leads to the transmittance variation. Figures 1(b)–1(d) show the schematic diagram of normal incidence and oblique incidence at 0° azimuth angle (parallel to the absorption axis). When the incident light deviates from the normal direction, there are longer light paths that induce the absorption of the polarizer stronger, so the transmittance is decreased. Figures 1(e)–1(g) show the schematic diagram of normal incidence and oblique incidence at 90° azimuth angle (perpendicular to the absorption axis). When the incident light deviates from the normal direction, there are longer light paths, but a small part of light can go through the interspace between the iodide molecules layers as the polar angle is at an appropriate range, so the transmittance is increased slightly (Fig. 1(f)); when the incident light deviates to a large polar angle, the interspace is blocked by the projection of the iodide molecules (Fig. 1(g)), so the transmittance is decreased. Generally, the maximum polar transmittance variation of the polarizer appears at 0° azimuth angle, and the minimum polar transmittance variation appears at 90° azimuth angle. Thus, the polarizer has a serious azimuthal transmittance variation at the oblique viewing direction because of the different varied tendencies.

 figure: Fig. 1.

Fig. 1. Model of iodide molecule distribution in the polarizer. (a) Schematic diagram of the iodide molecule distribution. The blue cuboids are the space where the iodide molecules exist, the black double-headed arrow is the absorption axis, the xyz coordinate system is the observer coordinate, the orange dash line shows the viewing direction, θ is the polar angle, ϕ is the azimuth angle. (b)-(g) Schematic diagram of iodide molecule distribution in the light path, the blue lines represent the iodide molecule distribution, and the orange lines represent the beam. The incident angles are: (b) θ=0°, ϕ=0°; (c) θ=45°, ϕ=0°; (d) θ=75°, ϕ=0°; (e) θ=0°, ϕ=90°; (f) θ=45°, ϕ=90°; (g) θ=75°, ϕ=90°.

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3. Multi-layer composite polarizer

To reduce the azimuthal transmittance variation, a multi-layer composite polarizer is proposed. Figure 2(a) shows the optical configuration of the multi-layer composite polarizer, which consists of the 1st polarizing layer, TN-LCP layer and 2nd polarizing layer. The absorption axis of the 1st polarizing layer is in the 0° direction (x-axis), and the absorption axis of the 2nd polarizing layer is in the 90° direction (y-axis). The liquid crystal molecules twist from 0° to 90° in the TN-LCP layer. Figure 2(b) shows the changing process of polarization state in the multi-layer composite polarizer. When a natural light going through the multi-layer composite polarizer, the polarization state changes three times by the three parts of the multi-layer composite polarizer. Firstly, the incident light is converted into linearly polarized light with 0° azimuthal direction by the 1st polarizing layer. Then, the polarization direction of the linearly polarized light is rotated 90° azimuthal direction by the TN-LCP layer. Finally, the light is converted into linearly polarized light with 90° azimuthal direction by the 2nd polarizing layer.

 figure: Fig. 2.

Fig. 2. Multi-layer composite polarizer. (a) Optical structure of the multi-layer composite polarizer. (b) Polarization changing process in the multi-layer composite polarizer.

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There are two polarizing layers in the multi-layer composite polarizer, so the transmittance depends on both the distributions of iodine molecules in the 1st and 2nd polarizing layers, and it is different from that of a single polarizer. Figure 3(a) shows the change of absorption axis in the beam of the normal polarizer. The length of the absorption axis becomes longer while the polar angle changes at the azimuth angle parallel to the absorption axis, and the length of the absorption axis doesn't change while the polar angle changes at the azimuth angle perpendicular to the absorption axis. At an oblique polar angle, the lengths of absorption axis in the beam are different at different azimuth angles, so the transmittance is obviously varied. Figure 3(b) shows the change of absorption axes in the beam of the multi-layer composite polarizer. The changes of lengths of absorption axes in two polarizing layers are opposite, so the total lengths of absorption axes of the crossed polarizing layers have a little change at different azimuth angles. Thus, the azimuthal transmittance variation of the multi-layer composite polarizer is far less than that of the normal polarizer. As shown in Figs. 3(a) and 3(b), the change of absorption axes of the normal polarizer and multi-layer composite polarizer at different azimuth angles are both symmetric, and the biggest and smallest changes appear at some certain azimuth angles (0°, 45°, 90° and 135°). Thus, the azimuthal transmittance variation of the normal polarizer and multi-layer composite polarizer can be analyzed by measuring the transmittance at a few azimuth angles.

 figure: Fig. 3.

Fig. 3. Schematic diagram of the change of absorption axis in the beam at different viewing directions. The brown lines represent the absorption axes of the normal polarizer and polarizing layer in the multi-layer composite polarizer, and the yellow circles represent the beam. (a) Normal polarizer. (b) multi-layer composite polarizer.

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4. Result

We fabricate the multi-layer composite polarizer by using liquid crystal polymer (HCM021, HCM020 and HCM009 from Jiangsu Hecheng Display Technology Co., Ltd.) and two normal polarizers (from LG chem. Ltd.), and the structural formulas of monomers are shown in Fig. 4(a). Firstly, the precursor is configured with the monomers and photo-initiator Irgacure 651, and it is heated to 85 °C to become isotropic. Then, the isotropic precursor is filled into the 8 μm gap between two substrates with crossed rubbing directions. After that, the precursor is cooled to 63° C to become nematic phase, and the liquid crystal molecules twist 90° between the substrates. Then, the precursor is cured by ultraviolet (UV) light for 1 minute, and the substrates are removed, and the TN-LCP layer is fabricated [20]. Finally, the multi-layer composite polarizer is fabricated by combining the polarizers and the TN-LCP layer. The birefringence of the liquid crystal polymer is shown in Fig. 4(b).

 figure: Fig. 4.

Fig. 4. Fabrication of the multi-layer composite polarizer. (a) Structural formulas of monomers. (b) Birefringence of the liquid crystal polymer.

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We measure the transmittance curves and calculate the azimuthal transmittance variation ratio of the normal polarizer and multi-layer composite polarizer. The transmittance is measured while the polar angle varies from 0° to 75° with 15° intervals, and the azimuth angle varies from 0° to 135° with 45° intervals. Figure 5(a) shows the transmittance curves and azimuthal transmittance variation ratio of the normal polarizer with its absorption axis at 0° azimuth angle, the transmittance generally decreases with the increasing polar angle, but there is an abnormal variation at 90° azimuth angle. At 90° azimuth angle, the transmittance increases first and then decreases sharply with the increasing polar angle; at 0° azimuth angle, the transmittance decreases with the increasing polar angle, and the decrease is more obvious than that at other azimuth angles. The different transmittance curves lead to the azimuthal transmittance variation, and the azimuthal transmittance variation increases with the increasing polar angle. We define the azimuthal transmittance variation ratio as:

$$\Delta {\textrm{T}_\textrm{A}} = \frac{{{T_{\max }} - {T_{\min }}}}{{{T_{\min }}}} \times 100\%,$$
where Tmax and Tmin are the maximum and minimum azimuthal transmittances at a certain polar angle, respectively. For the normal polarizer, the azimuthal transmittance variation ratio is 21% at 45° polar angle and 84% at 75° polar angle. Figure 5(b) shows the transmittance curves and azimuthal transmittance variation ratio of the multi-layer composite polarizer. The transmittance curves at different azimuth angles have similar shapes, and the azimuthal transmittance variation ratio is 5% at 45° polar angle and 16% at 75° polar angle. The azimuthal transmittance variation ratio of the multi-layer composite polarizer is only about one-fifth of that of the normal polarizer, and the non-uniform transmittance can be improved more.

 figure: Fig. 5.

Fig. 5. Transmittance curves and azimuthal transmittance variation ratio of (a) Normal polarizer. (b) Multi-layer composite polarizer. The color lines are the transmittance curves at different azimuth angles, the cyan columns are the azimuthal transmittance variation ratio at different polar angles.

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Further, we calculate the optical properties of the normal polarizer and multi-layer composite polarizer by a commercial software TechWiz LCD (Sanayi Systems, Korea) to analyze the improvement of the multi-layer composite polarizer in more detail. In the simulations, the birefringence of the liquid crystal is set as 0.126, the thickness of the TN-LCP layer is set as 8 μm, and the parameters of the polarizer (G1220DU) are set as follow: the refractive index is n=1.5, the complex refractive index are ke=0.001929 and ko=0.000045 at 550 nm, and the thickness is 230 μm. Figure 6(a) shows the iso-transmittance contour of the normal polarizer, the graph is axisymmetric about the absorption axis. The abnormal transmittance variation appeared nearby 90° and 270° azimuth angles (the direction of the transmittance axis). Figure 6(b) shows the azimuthal transmittance variation of the normal polarizer at a few polar angles, the most abnormal transmittance variation appears at 90° and 270° azimuth angles, and the largest transmittance variation appears at 0° and 180° azimuth angles (the direction of the absorption axis). The azimuthal transmittance variation of the normal polarizer is obvious at large polar angle, which means that an obvious luminance mura appears at large polar angle. Figure 6(c) shows the iso-transmittance contour of the multi-layer composite polarizer, there is no abnormal transmittance variation, and the transmittance variations at different azimuth angles are similar. Figure 6(d) shows the azimuthal transmittance variation of the multi-layer composite polarizer at a few polar angles, the transmittance is uniform when the polar angle is less than 60°. The azimuthal transmittance variation ratio also remains at a low level even at 75° polar angle. From the calculated results, the azimuthal transmittance variation of both normal polarizer and multi-layer composite polarizer is periodic, the period of the normal polarizer is 180°, and the period of the multi-layer composite polarizer is 90°. The calculated results agree with the measured results well.

 figure: Fig. 6.

Fig. 6. Transmittance variation of the normal polarizer and multi-layer composite polarizer. (a) Iso-transmittance contour of the normal polarizer. (b) Azimuthal transmittance variation of the normal polarizer. (c) Iso-transmittance contour of the multi-layer composite polarizer. (d) Azimuthal transmittance variation of the multi-layer composite polarizer.

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5. Discussion

5.1 Influence of structure

For some special applications, like television and vehicle displays, the change of viewing angle is mainly at a few azimuth angles, so the high transmittance in a certain direction is needed in the polarizer. The transmittance distribution as shown in Fig. 6(c) offers uniform transmittance at all azimuth angles, but it is not the most wanted transmittance distribution in these special applications. Fortunately, the transmittance distribution of the multi-layer composite polarizer can be controlled by changing the structure. In the multi-layer composite polarizer, the absorption axes of the polarizing layers are consistent with the direction of the adjacent liquid crystal polymer molecules, and the twist angle of the liquid crystal polymer layer is the same as the angle between the absorption axes of the polarizing layers. Here, we define the twist angle of the liquid crystal polymer layer and the angle between absorption axes of the polarizing layers as α, and we calculate the transmittance distribution of the multi-layer composite polarizer with serval α values while keeping the absorption axis of the 1st polarizing layer at 0°. Figure 7(a) shows the iso-transmittance contour of the multi-layer composite polarizer while α=30°. The transmittance at 105° and 285° azimuth angles are obviously higher than that at other azimuth angles, and the transmittance variation is still smaller than that of the normal polarizer. Figure 7(b) shows the iso-transmittance contour of the multi-layer composite polarizer while α=60°. The transmittance at 120° and 300° azimuth angles are obviously higher than that at other azimuth angles, and the transmittance distribution is more uniform than that in Fig. 7(a). Figure 7(c) shows the iso-transmittance contour of the multi-layer composite polarizer while α=-30°. The transmittance distribution is similar to Fig. 7(a), but the azimuth angles with high transmittance become 75° and 255°. Figure 7(d) shows the iso-transmittance contour of the multi-layer composite polarizer while α=-60°. The transmittance distribution is similar to Fig. 7(b), but the azimuth angles with high transmittance become 60° and 240° azimuth angles. The azimuth angles with high transmittance equal to α/2 + 90° and α/2 + 270°. The transmittance distribution of the multi-layer composite polarizer depends on the angle α, and the transmittance distribution is more uniform as α tends to 90°. The multi-layer composite polarizer can meet different requirements by adjusting α from -90° to 90°. Moreover, the light intensity can be controlled to uniform using a proper structure if the emitting display has a non-uniform light emission intensity.

 figure: Fig. 7.

Fig. 7. Iso-transmittance contour of the multi-layer composite polarizer with different values of α. (a) α=30°. (b) α=60°. (c) α= -30°. (d) α= -60°.

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5.2 Transmittance

One of the potential concerns about the multi-layer composite polarizer is the low transmittance caused by the additional polarizing layer, and it can be solved by reducing the degree of polarization of each polarizing layer. For the normal polarizer and the multi-layer composite polarizer, the transmittance is connected to the degree of polarization of the polarizing layer, the higher degree of polarization means the lower transmittance. The proposed multi-layer composite polarizer is mainly used in emissive displays, so it is combined with the quarter waveplate to form the circular polarizer to reduce the reflectance [21]. The degree of polarization of the polarizing layers in the multi-layer composite polarizer can be reduced to increase the transmittance while keeping the reflex-suppressing effect. Here we calculate the influence of the degree of polarization on the transmittance and reflex-suppressing effect, only the reflected light from the back reflector (its reflectance is assumed as 1.0) is considered, and the reflectance of the polarizer’s surface and the interfaces is ignored in the calculation. Figure 8(a) shows the influence of degree of polarization on transmittance and reflex-suppressing effect of a normal polarizer when it is used in the OLED. The reflectance is less than 0.00005 when the degree of polarization is larger than 0.9995, and the transmittance is 0.3669. Figure 8(b) shows the influence of degree of polarization on transmittance and reflex-suppressing effect of the multi-layer composite polarizer when it is used in the OLED. If keeping the reflectance is less than 0.00005, the needed degree of polarization of the polarizing layer is 0.96545, and the transmittance of the multi-layer composite polarizer is 0.3622. Compared with the normal polarizer, the transmittance of the multi-layer composite polarizer only decreases a little (1.3%).

 figure: Fig. 8.

Fig. 8. Influence of the degree of polarization on transmittance and reflectance. (a) Normal polarizer. (b) Multi-layer composite polarizer. The green dash lines show the degrees of polarization while the reflectance is less than 0.00005, and the gray dash lines show the corresponding transmittance.

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5.3 Color shift

Another potential concern is the color shift caused by the multi-layer composite polarizer. Different from the normal polarizer, the transmittance of the multi-layer composite polarizer is not consistent at different wavelengths because of the added TN-LCP layer, and the transmittance curves are different at different viewing angles. The normalized transmittance of the multi-layer composite polarizer can be written as [22]:

$$\textrm{T} = \textrm{k}\left( {1 - {{{{\sin }^2}\left( {\phi \sqrt {1 + {\tau^2}} } \right)} / {({1 + {\tau^2}} )}}} \right),$$
where k is the transmittance of the polarizing layers, $\phi$ is the twist angle of the liquid crystal polymer layer, $\tau = \pi d\Delta n/\phi \lambda$, $\Delta n$ is the birefringence of the liquid crystal polymer, d is the thickness of the liquid crystal polymer layer, and $\lambda$ is the wavelength of light. From Eq. (2), the fluctuation of transmittance is dependent on τ, and the fluctuation decreases with the increasing of τ. Figure 9(a) shows the transmittance spectrum of the normal polarizer and multi-layer composite polarizers with different values of τ. When τ reaches 6 at 500 nm, the transmittance spectrum of the multi-layer composite polarizer is similar to that of the normal polarizer. Figure 9(b) shows the transmittance spectra of the multi-layer composite polarizer with τ=6 at different viewing angles. The obvious change of transmittance spectrum only appears at a large polar angle, and the variety of transmittance of the multi-layer composite polarizer at different azimuthal angles is not obvious at a small polar angle. We calculated the color shift caused by the multi-layer composite polarizer while it is applied in an OLED. Figure 9(c) shows the spectra of the OLED while it displays white, blue, green and red. Figure 9(d) shows the color shift caused by the multi-layer composite polarizer while the polar angle varied from 0° to 75° with 15° intervals and the azimuth angle varied from 0° to 315° with 45° intervals. In the CIE 1931-xy coordinates, the color shifts of white, blue, green and red caused by the multi-layer composite polarizer are (±0.00348, ±0.002085), (±0.00011, ±0.00027), (±0.00204, ±0.00152) and (±0.00026, ±0.000255), respectively, the color shift is so small that the color at arbitrary viewing angle can be regarded as the same color. Such a small color shift is far less than that caused by other factors [23,24].

 figure: Fig. 9.

Fig. 9. Color shift caused by the multi-layer composite polarizer. (a) Transmittance spectra of the multi-layer composite polarizers with different τ at 500 nm. (b) Transmittance spectra of the multi-layer composite polarizer at different viewing angles. (c) Spectra of the OLED. (d) Color shift caused by the multi-layer composite polarizer.

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6. Conclusion

In summary, we have proposed a multi-layer composite polarizer consisting of two polarizing layers and a TN-LCP layer, and the azimuthal transmittance variation ratio of the multi-layer composite polarizer is far less than that of the normal polarizer. The iodide molecules distribution model has been proposed to explain the reason why the normal polarizer has a serious azimuthal transmittance variation and the azimuthal transmittance variation of the multi-layer composite polarizer is so small. The experimental results show that the azimuthal transmittance variation ratio of the multi-layer composite polarizer is only about one-fifth of that of the normal polarizer, and the calculation results verify the experimental results. The further calculation shows that the transmittance distribution of the multi-layer composite polarizer is tunable to meet different requirements. The transmittance of the multi-layer composite polarizer is discussed, and the multi-layer composite polarizer can achieve the same level of transmittance as the normal polarizer by reducing the degree of polarization of the polarizing layers. The color shift of the emissive displays caused by the multi-layer composite polarizer is investigated, and it can be ignored when the appropriate value of the TN-LCP layer is used. The multi-layer composite polarizer can be used to replace the normal polarizer in the emissive displays to reduce the luminance mura without other defects.

Funding

National Key Research and Development Program of China (2018YFB0703701); National Natural Science Foundation of China (61475042).

Disclosures

The authors declare that there are no conflicts of interest related to this article.

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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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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Figures (9)

Fig. 1.
Fig. 1. Model of iodide molecule distribution in the polarizer. (a) Schematic diagram of the iodide molecule distribution. The blue cuboids are the space where the iodide molecules exist, the black double-headed arrow is the absorption axis, the xyz coordinate system is the observer coordinate, the orange dash line shows the viewing direction, θ is the polar angle, ϕ is the azimuth angle. (b)-(g) Schematic diagram of iodide molecule distribution in the light path, the blue lines represent the iodide molecule distribution, and the orange lines represent the beam. The incident angles are: (b) θ=0°, ϕ=0°; (c) θ=45°, ϕ=0°; (d) θ=75°, ϕ=0°; (e) θ=0°, ϕ=90°; (f) θ=45°, ϕ=90°; (g) θ=75°, ϕ=90°.
Fig. 2.
Fig. 2. Multi-layer composite polarizer. (a) Optical structure of the multi-layer composite polarizer. (b) Polarization changing process in the multi-layer composite polarizer.
Fig. 3.
Fig. 3. Schematic diagram of the change of absorption axis in the beam at different viewing directions. The brown lines represent the absorption axes of the normal polarizer and polarizing layer in the multi-layer composite polarizer, and the yellow circles represent the beam. (a) Normal polarizer. (b) multi-layer composite polarizer.
Fig. 4.
Fig. 4. Fabrication of the multi-layer composite polarizer. (a) Structural formulas of monomers. (b) Birefringence of the liquid crystal polymer.
Fig. 5.
Fig. 5. Transmittance curves and azimuthal transmittance variation ratio of (a) Normal polarizer. (b) Multi-layer composite polarizer. The color lines are the transmittance curves at different azimuth angles, the cyan columns are the azimuthal transmittance variation ratio at different polar angles.
Fig. 6.
Fig. 6. Transmittance variation of the normal polarizer and multi-layer composite polarizer. (a) Iso-transmittance contour of the normal polarizer. (b) Azimuthal transmittance variation of the normal polarizer. (c) Iso-transmittance contour of the multi-layer composite polarizer. (d) Azimuthal transmittance variation of the multi-layer composite polarizer.
Fig. 7.
Fig. 7. Iso-transmittance contour of the multi-layer composite polarizer with different values of α. (a) α=30°. (b) α=60°. (c) α= -30°. (d) α= -60°.
Fig. 8.
Fig. 8. Influence of the degree of polarization on transmittance and reflectance. (a) Normal polarizer. (b) Multi-layer composite polarizer. The green dash lines show the degrees of polarization while the reflectance is less than 0.00005, and the gray dash lines show the corresponding transmittance.
Fig. 9.
Fig. 9. Color shift caused by the multi-layer composite polarizer. (a) Transmittance spectra of the multi-layer composite polarizers with different τ at 500 nm. (b) Transmittance spectra of the multi-layer composite polarizer at different viewing angles. (c) Spectra of the OLED. (d) Color shift caused by the multi-layer composite polarizer.

Equations (2)

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Δ T A = T max T min T min × 100 % ,
T = k ( 1 sin 2 ( ϕ 1 + τ 2 ) / ( 1 + τ 2 ) ) ,
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