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Inner helical waveplate with angle-insensitive retardation

Chi Zhang, Rui Niu, Pengfei Sha, Xiaoshuai Li, Hongmei Ma, and Yubao Sun

Open Access Open Access

Abstract

The angle-sensitivity is a serious defect of birefringent waveplate, and it draws lots of interest from researchers. In this paper, an angle-insensitive waveplate with inner helix structure is proposed. The super-twisted nematic liquid crystal polymer is used to fabricate the inner helical waveplate, and the retardation-shift is measured and analyzed. In the measured result, the retardation-shift is in the range from -0.311% to 0.194% at 45° polar angle, which is 2 orders of magnitude lower than that of the conventional waveplate. Theoretically, the retardation-shift is less than 0.5% in the polar angle range from 0° to 60°, and it will be less if the material with high refractive index is used. The analysis of the self-compensation effect explains the principle of angle-insensitivity, and the influence of tilt angle on angle-sensitivity is also investigated to guide the better design. At last, the application of the inner helical waveplate in wide color gamut display is taken as an example to show the broad application prospects.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Waveplate is one of the most basic and important optical elements, which has been widely applied in optical observation, communication, displays, and other fields [1–3]. The application of waveplate dates back more than one hundred years ago, and it still plays an important role in modern optics [4,5]. The classic birefringent waveplate has many advantages including simple structure, high polarization modulated efficiency and clear principle. However, the defects of the classic waveplate are also considerable, and they block the further application of waveplate. The angle-sensitivity is a fatal defect of waveplate, which draws lots of interest from researchers. The polarization modulation of the conventional birefringent waveplate is based on the retardation caused by birefringence, and the retardation is connected with extraordinary refractive index (ne), ordinary refractive index (no) and thickness of waveplate (d) at the normal sightline [6,7]. While the sightline skews from the normal direction, the retardation is calculated by the projection of refractive index and the thickness of waveplate on the polarization plane and light path. The variation of retardation makes waveplate sensitive to the incident angle, and the application of the waveplate-based element, such as the Lyot filter, is limited by the angle-sensitivity of waveplate [8].

Angle-insensitivity is an important requirement of waveplate, and it is also the key point to the further application of waveplate. To break the limit of angle-sensitivity, many methods have been proposed. The nanofin array and field transformation methods have been used to fabricate angle-insensitive waveplate [9,10]. However, the retardation of these kinds of waveplates is still angle-sensitive at the large incident angle. The novel structure makes it more like a new element than a waveplate, and other characteristics are also changed. The compound waveplate with multi-materials has been designed to reduce the angle-sensitivity of waveplate [11]. The interaction between positive and negative birefringent material reduces the angle-sensitivity of the whole element, but there is still a large space to further reduce the angle-sensitivity of waveplate.

Liquid crystal is a special birefringent material, and it can be used to fabricate novel devices with unique optical characteristics [12,13]. The multilayer model is used to analyze the optical effect of twisted nematic liquid crystal, in which the nematic liquid crystal consists of many monolayers liquid crystal [14,15]. Thus, the liquid crystal layer can be seen as an optical system, and the arrangement of liquid crystal can be controlled by surface orientation and chiral dopant [16,17]. Usually, the liquid crystal is applied for polarization converting [14,15], and it also has the potential to improve the performance of the waveplate. Ravi K. Komanduri et al proposed the multi-twisted retarder based on the twist nematic liquid crystal to offer control of broadband polarization transformation in 2013 [18]. Lingshan Li et al proposed the super achromatic wide-angle quarter-waveplates and wide-viewing angle color filters based on the twist nematic liquid crystal in 2021 [19,20]. We have found that there is a compensation effect between the monolayers liquid crystal in the super twisted nematic liquid crystal, and it is helpful to reduce the angle-sensitivity of waveplate. A waveplate with inner helix structure could be angle-insensitivity, and the liquid crystal polymer can be used to obtain the stable helix structure [21,22].

In this work, the inner helical waveplate with angle-insensitive retardation is proposed. Firstly, we design an inner helical waveplate with 180° twisted helix structure, and we fabricate it with liquid crystal polymer. Then, we build a birefringent filter and introduce a calculation method to measure the retardation-shift of the inner helical waveplate at large incident angle. Next, we explain the principle of angle-insensitivity of the inner helical waveplate by analyzing the self-compensation effect, and the theoretical angle-sensitivity of the inner helical waveplate is given. Further, we investigate the influence of tilt angle and refractive index on the angle-sensitivity. At last, the inner helical waveplate is used to enhance the color gamut of liquid crystal displays (LCD), and an excellent color gamut is obtained.

2. Fabrication and measurement

2.1 Fabrication

In the experiment, three monomers, as shown in Fig. 1(a), including HCM021, HCM020 and HCM009 (from Jiangsu Hecheng Display Technology Co., Ltd.), and photo-initiator Irgacure 651 (from TCI Co., Ltd.) are used to fabricate the inner helical polymer waveplate, and the empty twisted nematic liquid crystal cell with an 8 μm cell gap was used as the mold of the liquid crystal polymer film. Figure 1(b) shows the fabricating progress. Firstly, we configured the precursor consisting of 39.75 wt.% HCM021, 20 wt.% HCM020, 39.75 wt.% HCM009, and 0.5 wt.% photo-initiator Irgacure 651. Next, we heated the precursor and liquid crystal cells to 85℃, and the precursor became isotropic. At 85℃, we filled the isotropic precursor into two liquid crystal cells. After that, we cooled the liquid crystal cells with the precursor to 63℃, and the precursor changed from isotropic to nematic phase. The liquid crystal molecules at the top and bottom substrates of the liquid crystal cell arranged orthogonally under the anchoring energy, and the tilt angle at the bottom and top surfaces were 1° and -1°, respectively. The liquid crystal molecules uniformly twisted 90° in the liquid crystal cells. Then, we cured the precursor by ultraviolet (UV) light, and two twisted nematic liquid crystal polymer films were fabricated in the liquid crystal cells. Finally, we combined the two liquid crystal cells to obtain the inner helical waveplate. During the combination process, the liquid crystal directors at the interface of the two liquid crystal cells were parallel, thus, the liquid crystal molecules twisted 180° in the inner helical waveplate, as shown in Fig. 1(c). The slow axis of the inner helical waveplate is in the direction of the liquid crystal director at the surface.

 figure: Fig. 1.

Fig. 1. Fabrication of the inner helical waveplate. (a) Structural formulas of monomers. (b) Schematic diagram of fabricating progress. (c) Schematic diagram of the double-deck structure of the inner helical waveplate.

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2.2 Measurement

In order to measure the retardation of the inner helical waveplate at a large incident angle (45°), we built a birefringent filter with the inner helical waveplate and two polarizers [23,24]. The inner helical waveplate was located between two parallel polarizers, and the angle between the slow axis of the inner helical waveplate and the transmission axes of the polarizers was 45°, as shown in Fig. 2(a). The different wavelengths of light have different changes of polarization state, so the transmittance of different wavelengths is different. The normalized transmittance of the birefringent filter conforms to the formula:

$$\textrm{T = }{\cos ^2}({{\raise0.7ex\hbox{$\Gamma $} \!\mathord{\left/ {\vphantom {\Gamma 2}} \right.}\!\lower0.7ex\hbox{$2$}}} ),$$
where Γ is the retardation of the waveplate. Thus, the retardation can be calculated by the measured transmittance. In the inner helical waveplate, the twist of liquid crystal molecules leads to additional retardation [25,26], and the retardation of the inner helical waveplate at the normal incident angle is
$$\Gamma \textrm{ = }\sqrt {{{({{\raise0.7ex\hbox{${2\pi \Delta \textrm{nd}}$} \!\mathord{\left/ {\vphantom {{2\pi \Delta \textrm{nd}} \lambda }} \right.}\!\lower0.7ex\hbox{$\lambda $}}} )}^2} + 4{\pi ^2}} .$$

 figure: Fig. 2.

Fig. 2. Measurement of the inner helical waveplate. (a) Schematic diagram of measuring light path. (b) Schematic diagram of incident angle. The orange line is the incident direction, the blue dash line is the slow axis of the inner helical waveplate, θ is the polar angle, ϕ is the azimuth angle.

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Figure 2(b) is the schematic diagram of incident angle. In the measurement, we set the direction of the polarizers’ transmission axes at 0° azimuth angle (in the x-axis direction), and the slow axis of the inner helical waveplate was at 45° azimuth angle. While the incident light skews from the normal direction, the spectral shift of the transmittance spectrum is connected to the retardation-shift.

3. Result

We measured the transmittance spectra of the birefringent filter at several different incident angles, and we further calculated the retardation-shift of the inner helical waveplate with the measured transmittance spectra. Firstly, we measured the transmittance spectrum at the normal direction. Then, we measured the transmittance spectra at 45° polar angle, while the azimuth angle varied from 0° to 315° with 45° intervals. In the measured transmittance spectra, we intercepted the wavelength range from 470 nm to 550 nm and normalized the transmittance, as shown in Fig. 3(a), and we calculated the retardation-shift by calculating the spectral shift. In the intercepted wavelength range, there are only one peak wavelength and one valley wavelength in each spectrum, so the influence of absorption and reflection on transmittance can be eliminated in the normalization processing, and the normalized transmittance is only dependent on retardation. In the calculation, we calculated the retardation-shift of the inner helical waveplate while it was used as a half-waveplate, which is corresponding to the valley wavelength in the transmittance spectrum. In order to reduce the error caused by measuring accuracy, we took the average value of the wavelengths whose transmittance is less than 0.01 as the valley wavelength. The valley wavelengths in the normalized transmittance spectra were shown in Fig. 3(b), the valley wavelength was 487.455 nm at the normal direction, and the valley wavelength shifted slightly while the incident direction skewed to 45° polar angle. The valley wavelengths distributed in the range from 485.9 nm to 488.4 nm. We measured the birefringence of the liquid crystal polymer, and calculated the dispersion of birefringence, as shown in Fig. 3(c) [27]. The difference of birefringence at wavelengths of 485 nm and 489 nm was only 0.0004. Thus, we ignored the dispersion of birefringence and regarded that the ratio of spectral shift was equal to the retardation-shift. The retardation-shift can be calculated by

$$\frac{{\Gamma - {\Gamma _0}}}{{{\Gamma _0}}}\textrm{ = }\frac{{\lambda - {\lambda _0}}}{{{\lambda _0}}},$$
where $\Gamma = ({k + {1 / 2}} )\lambda $ is the retardation corresponding to the valley wavelength $\lambda $ at an oblique direction, ${\Gamma _0} = ({k + {1 / 2}} ){\lambda _0}$ is the retardation corresponding to the valley wavelength ${\lambda _0}$ at the normal direction. Figure 3(d) shows the comparison of the experimental retardation-shift, the calculated retardation-shift of the inner helical waveplate, and the retardation-shift of the conventional birefringent waveplate. In the experimental result, the maximum increment of retardation is 0.194%, and the maximum reduction of retardation is -0.311%. The experimental result well agrees with the calculated result. As a comparison, the maximum retardation-shift of the conventional waveplate is larger than 10%, and the retardation-shift of the inner helical waveplate is reduced by 2 orders of magnitude at 45° polar angle.

 figure: Fig. 3.

Fig. 3. Measured and calculated results. (a) Normalized measured transmittance spectra at different incident angles. The black line is the normalized transmittance spectrum at the normal direction, other lines are the normalized transmittance spectra at 45° polar angle. (b) Valley wavelengths in the normalized transmittance spectra. (c) Birefringence of the liquid crystal polymer. The inset figure shows the change of birefringence from 485 nm to 489 nm. (d) Comparison of retardation-shift of the inner helical waveplate and the conventional birefringent waveplate, the blue line is the retardation-shift of the conventional birefringent waveplate, the red line is the calculated retardation-shift of the inner helical waveplate, the red-rhomb points are the experimental retardation-shift of the inner helical waveplate.

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4. Discussion

4.1 Self-compensation effect

The angle-insensitive retardation of the inner helical waveplate is based on the self-compensation effect in the twisted nematic liquid crystal. The inner helical waveplate can be viewed as a multilayer optical system, in which each monolayer liquid crystal is a birefringent waveplate. The angle-sensitivity of the monolayer liquid crystal is the same as that of the conventional birefringent waveplate, and the retardation-shift at different incident angles shows a special symmetry. The retardation of monolayer liquid crystal at different incident angles can be calculated by formula [28]:

$$\Gamma \textrm{ = }\frac{{2\pi \textrm{d}}}{\lambda }\left( {{\textrm{n}_e}\sqrt {1 - \frac{{{{\sin }^2}\theta {{\sin }^2}({\phi_k} - \phi )}}{{n_e^2}} - \frac{{{{\sin }^2}\theta {{\cos }^2}({\phi_k} - \phi )}}{{n_o^2}}} - {n_o}\sqrt {1 - \frac{{{{\sin }^2}\theta }}{{n_o^2}}} } \right),$$
where ${\phi _\textrm{k}}$ is the direction of slow axis. Figure 4(a) shows the retardation-shift of the monolayer liquid crystal. At two orthogonal azimuth angles, the retardation-shift with variation of polar angle is opposite, and the maximum retardation-shift is above 20%. Under ideal conditions, all liquid crystals are parallel to the substrate’s plane, and there is no tilt angle. Here, we analyze the self-compensation effect of the inner helical waveplate under ideal conditions. In the proposed double-deck inner helical waveplate, the director of liquid crystals in the bottom and top deck with the same depth are orthogonal completely, so the retardation-shift of monolayer liquid crystal in the top deck can be compensated by other monolayer liquid crystal in the bottom deck. The compensation of the two 90° twisted liquid crystal layers exits at all incident angles. As result, the retardation of the inner helical waveplate is angle-insensitive. We have calculated the retardation-shift of the inner helical waveplate under ideal conditions, and we plot the retardation-shift at different incident angles, as shown in Fig. 4(b). In the polar angle range from 0° to 60°, the maximum increment and reduction of retardation-shift are 0.5% and -0.2%, respectively. The self-compensation effect relies on the 180° twisted helix structure, so the angle-insensitivity is affected by the change of twist angle. While the twist angle is not 180°, a few monolayers liquid crystal can’t be compensated by other orthogonal monolayers liquid crystal, and the retardation of the inner helical waveplate becomes more sensitive to the viewing angle. We have calculated the impact of twist angle on the maximum retardation-shift, and the result is shown in Fig. 4(c). Even the retardation-shift of the inner helical waveplate is far less than that of the conventional birefringent waveplate, the retardation-shift of the inner helical waveplate is still dependent on the refractive index of the material. We have calculated the maximum retardation-shift varied with the different ordinary refractive index while the birefringence is fixed at 0.23, and the result is shown in Fig. 4(d). With the increasing of ordinary refractive index, the maximum retardation-shift becomes smaller. The maximum retardation-shift is only 0.2% at 60° polar angle when the ordinary refractive index is increased to 1.7.

 figure: Fig. 4.

Fig. 4. Self-compensation effect and angle-sensitivity of the inner helical waveplate. (a) Retardation-shift of monolayer liquid crystal. (b) Retardation-shift of the inner helical waveplate. (c) The maximum retardation-shift varied with the twist angle. (d) The maximum retardation-shift varied with the ordinary refractive index.

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4.2 Influence of tilt angle

We have analyzed the self-compensation effect in the inner helical waveplate under ideal conditions and plotted the retardation-shift of the inner helical waveplate, but the result is slightly different from the experimental result because the tilt angle has been ignored. The tilt angle is inevitable in fabrication progress, and it affects the angle-sensitivity of the inner helical waveplate. The liquid crystal cells have been used as the molds, and the orientation of liquid crystals on the substrates’ surfaces is obtained by rubbing method. Except for the orientation, the rubbing process also leads to the tilt of liquid crystal molecules. To calculate the retardation-shift of the inner helical waveplate more accurately, we further consider the influence of the tilt angle on angle-sensitivity of the inner helical waveplate. There are three possible arrangements of liquid crystal molecules in the inner helical waveplate, as shown in Fig. 5(a). In the proposed double-deck inner helical waveplate, the liquid crystal molecules twist 90° in each deck, and the tilt angles of liquid crystal molecules distribute from 1° to -1° in both decks. The director of liquid crystals in the bottom and top decks with the same depth are orthogonal completely, and the influence of the tilt angle on angle-sensitivity is minimized. Considering the tilt angle, the retardation-shift of the double-deck inner helical waveplate is in the range from -0.4% to 0.8% in the polar angle range from 0° to 60°, as shown in Fig. 5(b). This result well agrees with the experimental result. In comparison, we also calculated the retardation-shift of the inner helical waveplates fabricated in a single anti-parallel/parallel aligned liquid crystal cell. In the inner helical waveplate fabricated in a single anti-parallel aligned liquid crystal cell, the tilt angles of liquid crystal molecules distribute from 1° to -1°. The orthogonal monolayers liquid crystal have different tilt angles, and the self-compensation effect is not complete. We have calculated the retardation-shift of the anti-parallel aligned inner helical waveplate, and the retardation-shift is in the range from -1.1% to 1.8%, as shown in Fig. 5(c). In the inner helical waveplate fabricated in a parallel aligned liquid crystal cell, the liquid crystal molecules at the top and bottom substrates are arranged parallelly, and all the liquid crystal molecules tilt 1°. We have calculated the retardation-shift of the parallel aligned inner helical waveplate, and the retardation-shift is in the range from -0.8% to 1.3%, as shown in Fig. 5(d). Compared with other arrangements, the proposed double-deck structure has weaker angle-sensitivity. Three structures represent three arrangement types of liquid crystal molecules in the inner helical waveplate: the tilt angles of liquid crystal molecules in the top and bottom decks are symmetrical in the double-deck inner helical waveplate; the liquid crystal molecules are splay in the anti-parallel aligned inner helical waveplate; the liquid crystal molecules are tilted in the parallel aligned inner helical waveplate. There are several possible arrangements of the inner helical waveplate, and any possible arrangement corresponds to one of the arrangement types. We number the arrangement types of double-deck inner helical waveplate, anti-parallel aligned inner helical waveplate and parallel aligned inner helical waveplate as type I, type II and type III, respectively. The other possible arrangements of the inner helical waveplate and the corresponding types are shown in Table 1.

 figure: Fig. 5.

Fig. 5. Influence of tilt angle on angle-sensitivity. (a) Liquid crystals arrangements in different inner helical waveplates. (b) Retardation-shift of the double-deck inner helical waveplate. (c) Retardation-shift of the anti-parallel aligned inner helical waveplate. (d) Retardation-shift of the parallel aligned inner helical waveplate.

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Tables Icon

Table 1. Other arrangements of the inner helical waveplate and corresponding types

View Table

4.3 Application in wide color gamut display

The retardation of the inner helical waveplate is angle-insensitive, so the inner helical waveplate has more applications than the conventional waveplate. For example, the birefringent filter consisting of an inner helical waveplate and two polarizers, as shown in Fig. 2(a), is a wide-view angle filter (WVAF), and the WVAF can be used to enlarge the color gamut of LCD. Like the conventional birefringent filter, the transmittance spectrum of the WVAF is also connected to the retardation of the inner helical waveplate, so the transmittance spectrum of WVAF is continuously adjustable by adjusting the retardation. Figure 6(a) shows the variation of the transmittance spectra of the WVAF while the retardation of the inner helical waveplate changes, the transmittance spectrum is redshifted with the increasing of retardation. While the retardation of the inner helical waveplate is 7.6π at 550 nm, the three transmittance peaks in the transmittance spectrum of the WVAF correspond to blue, green, and red peaks in the spectrum of LCD. We fabricated a WVAF and combined it with a LCD which has quantum dots (CsPbBr3/CdSe) backlight. Figure 6(b) shows the improvement of WVAF on the spectrum, the WVAF narrows the full width of half maximum of the peaks and eliminates the crosstalks between the peaks. After going through the color filter in the LCD, the primary colors are obtained. Figure 6(c) shows spectra of the primary colors of the original LCD and enhanced LCD. The narrower peaks and less crosstalk lead to an improvement of color gamut [29], and the color gamut is enhanced from 86%Rec.2020 to 94%Rec.2020, as shown in Fig. 6(d). The WVAF has a huge improvement for wide color gamut display and breaks the limit of LCD’s color gamut [30]. The excellent result also shows potential in other optical fields.

 figure: Fig. 6.

Fig. 6. Application of the inner helical waveplate in wide color gamut display. (a) Spectral shift of the WVAF. The retardations are for λ=550 nm. (b) Spectral improvement by WVAF. The red line is the transmittance spectrum of WVAF, the blue lines are the spectra intensity of quantum dots LED without/with WVAF. The peak wavelengths change from 453 nm, 524 nm and 636 nm to 453 nm 524 nm and 638 nm. The full width at half maximum reduces from 21 nm, 22 nm and 26 nm to 16 nm, 20 nm and 24 nm, and the crosstalk between adjacent peaks is eliminated while WVAF is used. (c) Spectra of the primary colors of the original LCD and enhanced LCD. (d) Color gamut in CIE 1931-xy coordinates. The color gamut is enhanced from 86%Rec.2020 to 94%Rec.2020.

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5. Conclusion

In summary, we have proposed an inner helical waveplate whose retardation is almost completely insensitive to the incident angle, and it breaks the limit of angle-sensitivity on the application of waveplate. We fabricated the inner helical waveplate by using liquid crystal polymer and measured the retardation-shift of the inner helical waveplate in a birefringent filter. In the measured result, the biggest retardation-shift was only -0.311% at 45° polar angle. By analyzing the self-compensation effect, we explained the principle of angle-insensitivity of the inner helical waveplate, and the theoretical retardation-shift was calculated. Under ideal conditions, the retardation-shift was less than 0.5% in the polar angle range from 0° to 60°. Moreover, we investigated the influence of tilt angle on the angle-sensitivity of the inner helical waveplate, and the optimal structure was given to guide the fabrication. Both experimental results and theoretical calculation confirmed the angle-insensitivity of the inner helical waveplate. The inner helical waveplate has more applications than the conventional birefringent waveplate. We applied the inner helical waveplate in a LCD and further enhanced the color gamut on the existing basics. As a waveplate that breaks the limit of angle-sensitivity, the inner helical waveplate will bring a great improvement in many optical fields.

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 (6)
Fig. 1.
Fig. 1. Fabrication of the inner helical waveplate. (a) Structural formulas of monomers. (b) Schematic diagram of fabricating progress. (c) Schematic diagram of the double-deck structure of the inner helical waveplate.

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Fig. 2.
Fig. 2. Measurement of the inner helical waveplate. (a) Schematic diagram of measuring light path. (b) Schematic diagram of incident angle. The orange line is the incident direction, the blue dash line is the slow axis of the inner helical waveplate, θ is the polar angle, ϕ is the azimuth angle.

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Fig. 3.
Fig. 3. Measured and calculated results. (a) Normalized measured transmittance spectra at different incident angles. The black line is the normalized transmittance spectrum at the normal direction, other lines are the normalized transmittance spectra at 45° polar angle. (b) Valley wavelengths in the normalized transmittance spectra. (c) Birefringence of the liquid crystal polymer. The inset figure shows the change of birefringence from 485 nm to 489 nm. (d) Comparison of retardation-shift of the inner helical waveplate and the conventional birefringent waveplate, the blue line is the retardation-shift of the conventional birefringent waveplate, the red line is the calculated retardation-shift of the inner helical waveplate, the red-rhomb points are the experimental retardation-shift of the inner helical waveplate.

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Fig. 4.
Fig. 4. Self-compensation effect and angle-sensitivity of the inner helical waveplate. (a) Retardation-shift of monolayer liquid crystal. (b) Retardation-shift of the inner helical waveplate. (c) The maximum retardation-shift varied with the twist angle. (d) The maximum retardation-shift varied with the ordinary refractive index.

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Fig. 5.
Fig. 5. Influence of tilt angle on angle-sensitivity. (a) Liquid crystals arrangements in different inner helical waveplates. (b) Retardation-shift of the double-deck inner helical waveplate. (c) Retardation-shift of the anti-parallel aligned inner helical waveplate. (d) Retardation-shift of the parallel aligned inner helical waveplate.

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Fig. 6.
Fig. 6. Application of the inner helical waveplate in wide color gamut display. (a) Spectral shift of the WVAF. The retardations are for λ=550 nm. (b) Spectral improvement by WVAF. The red line is the transmittance spectrum of WVAF, the blue lines are the spectra intensity of quantum dots LED without/with WVAF. The peak wavelengths change from 453 nm, 524 nm and 636 nm to 453 nm 524 nm and 638 nm. The full width at half maximum reduces from 21 nm, 22 nm and 26 nm to 16 nm, 20 nm and 24 nm, and the crosstalk between adjacent peaks is eliminated while WVAF is used. (c) Spectra of the primary colors of the original LCD and enhanced LCD. (d) Color gamut in CIE 1931-xy coordinates. The color gamut is enhanced from 86%Rec.2020 to 94%Rec.2020.

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Tables (1)

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Table 1. Other arrangements of the inner helical waveplate and corresponding types

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Equations (4)

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T =  cos 2 ( Γ / Γ 2 2 ) ,
Γ  =  ( 2 π Δ nd / 2 π Δ nd λ λ ) 2 + 4 π 2 .
Γ − Γ 0 Γ 0  =  λ − λ 0 λ 0 ,
Γ  =  2 π d λ ( n e 1 − sin 2 θ sin 2 ( ϕ k − ϕ ) n e 2 − sin 2 θ cos 2 ( ϕ k − ϕ ) n o 2 − n o 1 − sin 2 θ n o 2 ) ,
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