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We propose an optical compensation scheme that uses uniaxial films for perfect elimination of light leakage over the entire viewing cone in a homogeneously-aligned liquid crystal cell. Uniaxial films with different dispersion characteristics are used so that they can compensate one another to achieve achromatic optical compensation. Owing to the rotational symmetry of the polarization change on the S2–S3 plane of the Poincaré sphere, we can eliminate the light leakage at all azimuth angles. The contrast ratio of the proposed configuration for white light is higher than 3000:1 at a polar angle of ± 85°, irrespective of the azimuth angle.
© 2014 Optical Society of America
1. Introduction
Among various liquid-crystal display (LCD) modes, the in-plane switching mode exhibits the widest viewing angle because the liquid crystals (LCs) are homogeneously aligned initially and rotate within a plane parallel to the substrates when an in-plane field is applied [1–3]. However, further improvement is needed for viewing high-quality dark images from the bisector direction of the crossed polarizers. Several compensation schemes have been proposed to eliminate the off-axis light leakage [4–10]. Although a 100:1 iso-contrast contour at an optimized wavelength of 550 nm can cover the entire viewing cone, light leakage at other wavelengths, e.g., red and blue, remains very severe.
The polarization state of light that passes through retardation films depends on the wavelength because phase retardation is inversely proportional to the wavelength of the incident light. Therefore, a significant reduction in the contrast ratio, gray level inversion, and color shift can be observed in LCD panels. Several approaches have been proposed to reduce the off-axis light leakage, but developing an efficient method is difficult because suitable retardation films are expensive or difficult to manufacture. A trade-off exists between the performance of the compensation films and the cost of the films in choosing the compensation schemes. Moreover, dispersion in uniaxial films worsens the light leakage caused by the compensation films at off-axis viewing angles. To overcome this problem, retardation films with negative or zero dispersion are being developed, but they are not widely used yet because of high manufacturing cost [11].
In our previous paper, we proposed a compensation method in which we can reduce the light leakage to lower than 1/70 of the light leakage generated at an azimuth angle of 45° in a biaxial configuration [12]. However, light leakage at other azimuth angles still exists. The angle at which the contrast ratio is higher than 50% of the maximum value is less than ± 60°, which may be insufficient for application in high-performance TVs. Furthermore, the positive C film with zero dispersion used in this work may not be easy to fabricate. Thus, an urgent need to develop a practical compensation method is required to widen the viewing angle of LCDs.
In this paper, we propose an achromatic compensation configuration for a perfect dark state over the entire viewing cone in a homogeneously-aligned LC cell. We used uniaxial films with different dispersion characteristics so that they can compensate one another to achieve achromatic optical compensation. Because of the rotational symmetry of the polarization change on the S2–S3 plane of the Poincaré sphere, we can eliminate the light leakage at all azimuth angles. The retardation values can be optimized with the aid of the Poincaré sphere [13–16]. To verify the performance of the proposed optical configuration, we calculated its optical characteristics using a simulation program named “TechWiz LCD” (Sanayi System, Korea). We found that the off-axis light leakage can be eliminated perfectly at all azimuth and polar angles using the proposed configurations.
2. Off-axis light leakage in a homogeneously-aligned LC cell
The major cause of light leakage in an LCD is the change in the effective angle between the absorption axes of two crossed polarizers when viewed from oblique directions, especially from the bisector of the crossed polarizers. The absorption axes of the two crossed polarizers make an angle of 2tan−1(cosθ), depending on the polar angle θ. As θ increases, the angle between the two crossed polarizers deviates further from 90°. As a result, the light leakage increases as the polar angle increases.
Several compensation schemes using uniaxial films, such as + A/+C/+A [5], + A/–A [8], and + A/+C [9] have been proposed to eliminate the light leakage associated with crossed polarizers. These uniaxial configurations are used to move the polarization state from the transmission axis of the polarizer to the absorption axis of the analyzer to eliminate the off-axis light leakage, although the rotation routes of the polarization state on the Poincaré sphere are not the same. The light leakage in an LC cell, which exists even after the compensation, is mainly caused by the fact that the retardation value of a uniaxial film is a function of wavelength λ of the incident light. As an example, the calculated polarization changes at θ = 70° and an azimuth angle of ϕ = 45° on the Poincaré sphere in the + A/+C/+A configuration is shown in Fig. 1.The optic axis of the first [second] positive A plate is parallel to the absorption axis of the second [first] polarizer. The retardation values of the positive A plates and the positive C plate are 92 nm and 152 nm, respectively. Although the green light is moved from the transmission axis of the polarizer to the absorption axis of the analyzer, the red and blue lights deviate from the absorption axis of the analyzer because of the 1/λ dependence of the phase retardation. Because the light leakage caused by the wavelength dependence of the phase retardation cannot be removed using additional uniaxial films or by changing the film configuration, it remains as a major cause of light leakage in LCDs.
Fig. 1 Polarization change in each color on the Poincaré sphere in the + A/+C/+A configuration. θ = 70°, ϕ = 45°.
If we use films with negative dispersion whose refractive index is proportional to the wavelength, the light leakage for the blue or red light may become as small as that at the design wavelength of 550 nm [11]. However, the cost associated with a film with zero or negative dispersion can be much higher than that of a film with normal dispersion because fabrication of the former films is difficult. The performance of the compensation method that uses a single or two biaxial films is much better than that of the method that uses uniaxial films because the deviation at each wavelength is reduced by the small radius of rotation of the polarization state or the symmetrical rotation of the polarization state on the Poincaré sphere. However, the compensation using biaxial films can be expensive for practical display applications. Among the different compensation schemes, a trade-off exists between the performance and cost of the compensation films.
Figure 2(a) shows the polarization change at ϕ = 45° and θ = 70° on the Poincaré sphere when a homogeneously aligned LC cell is compensated in the + A/+A/+C configuration using two orthogonal positive A plates and a positive C plate [12]. The optic axis of the first [second] positive A plate is parallel to the absorption axis of the second [first] polarizer. The retardation values of the first positive A plate, the second positive plate, and the positive C plate are 185, 38, and 125 nm, respectively. The dispersion can be effectively removed by setting the degree of dispersion of the plates so that the first A plate (which has a high retardation value) has a weak dispersion, and the second A plate (which has a small retardation value) has a strong dispersion. The positive C plate is used to convert the polarization states of the light that has passed through the two A plates into a light that is polarized linearly along the absorption axis of the analyzer (point 4). Finally, the polarization states at all visible wavelengths are effectively accumulated at the absorption axis of the analyzer.
Fig. 2 Polarization change in each color on the Poincaré sphere in the + A/+A/+C configuration. (a) θ = 70°, ϕ = 45°. (b) θ = 70°, ϕ = 30°
Although the compensation films are optimized to suppress the light leakage at ϕ = 45°, the polarization states are not accumulated at the absorption axis of the analyzer, and light leakage remains at the other azimuth angles, as shown in Fig. 2(b). The polar angle θ in which the contrast ratio is higher than 50% of the maximum value is less than ± 60°. This result might be insufficient for application in the next-generation high-performance TVs. Furthermore, we need a positive C plate with zero wavelength dispersion because it cannot completely cancel out the deviation in the ellipticity angle when it has a normal dispersion. However, a zero-dispersion film entails a high cost because it is not easy to fabricate.
3. Optical compensation scheme
In this paper, we propose an + A/+A/+C/+A/+A optical compensation scheme using two sets of orthogonal positive A plates and a positive C plate for perfect elimination of the dark-state light leakage over the entire viewing cone in a homogeneously-aligned LC cell. Normal dispersion of a uniaxial film commonly increases the dark-state light leakage. However, in our proposed structure, the strong dispersion of the uniaxial films makes the polarization states accumulate at the absorption axis of the analyzer; therefore, we use it in an opposite manner to remove the light leakage at off-axis viewing angles. Because the deviation in the inclination angle cannot be controlled by the C plate, we dissociate the deviation in the retardation value from the wavelength in terms of the inclination angle ϕ (the azimuth angle on the Poincaré sphere) and the ellipticity angle θ (the polar angle on the Poincaré sphere) in the polarization ellipse [14]. Then, we individually eliminate the deviations in the inclination and ellipticity angles using normal dispersion of films. The first orthogonal positive A plates is used to move the polarization states at all visible wavelengths to the S1 axis. A positive C plate was used to move the polarization state of the light to the symmetry point with respect to the S1 axis. The second orthogonal positive A plates to move the polarization states at all visible wavelengths to the absorption axis of the analyzer. The polarization states for all visible wavelengths can be accumulated at the absorption axis of the analyzer by sequential reduction of the deviation in terms of the inclination and ellipticity angles. Furthermore, because the proposed configuration has rotational symmetry on the Poincaré sphere [17], the polarization states at all visible wavelengths stay at the absorption axis of the analyzer for any polar and azimuth angles.
Figure 3(a) shows the proposed + A/+A/+C/+A/+A configuration using two sets of orthogonal positive A plates and a positive C plate. The use of two orthogonal positive A plates allows for symmetrical rotation of the polarization state on the Poincaré sphere. When unpolarized light from a backlight unit traverses through the polarizer, it becomes linearly polarized, as shown in Fig. 3(b). The polarization state is located at point 1, which deviates from the absorption axis of the analyzer at point 6. The two positive A plates, whose slow axes are orthogonal to each other, convert the polarization state of the light that passes through them into another elliptical polarization state at point 3(0, θ0), whose azimuth angle is the same as that in the S1 axis. Because the slow axes of the two A plates are orthogonal to each other, the rotations of the polarization state caused by each A plate (on the Poincaré sphere) are in a direction opposite to each other; thus, the wavelength dispersion is cancelled by the two orthogonal A plates. The dispersion can be effectively removed by setting the degree of dispersion of the plates so that the first A plate (which has a high retardation value) has a weak dispersion, and the second A plate (which has a low retardation value) has a strong dispersion. The positive C plate with normal dispersion converts the polarization state at point 3 into point 4(0, -θ0), which is the symmetry point of point 3 with respect to the S1 axis. If the retardation values and the degree of dispersion of the two A plates above the C plate are the same as those of the two A plates below the C plate, the polarization state move exactly symmetrically to the absorption axis of the analyzer. Finally, the polarization states at all visible wavelengths are effectively accumulated at the absorption axis of the analyzer at point 6. Because the rotation of the polarization states has a rotational symmetry on the S2–S3 plane of the Poincaré sphere, we can effectively eliminate the light leakage at any polar and azimuth angles. The path difference on the northern hemisphere can be canceled out by the path difference on the southern hemisphere. Moreover, zero or negative dispersion films are not used, which are incidentally difficult to fabricate and very expensive for practical display applications.
Fig. 3 (a) Compensation scheme of the + A/+A/+C/+A/+A configuration. (b) Polarization change in each color on the Poincaré sphere in the + A/+A/+C/+A/+A configuration. θ = 70°, ϕ = 45°.
We set the parameters of the films by computer simulation to confirm the performance of the proposed compensation scheme, as listed in Table 1. The first positive A plate has a weak wavelength dispersion, whereas the second positive A plate has a strong wavelength dispersion. The retardation values and the degree of dispersion of the two A plates above the C plate are the same as those of the two A plates below the C plate. The C plate has a weak wavelength dispersion. Conventional compensation schemes have poor characteristics when films with normal dispersion are used. In the proposed configuration, however, uniaxial films with normal dispersion are used to remove the deviation in the polarization states over the entire visible wavelengths. The retardation values and the degree of dispersion of the films can be freely changed and optimized under the above-mentioned condition.
Table 1. Parameters of the three uniaxial films used in the + A/+A/+C/+A/+A configuration.
The wavelength dependence of the polarization change at θ = 70° on the Poincaré sphere in the + A/+A/+C/+A/+A configuration is shown in Fig. 4.The polarization states at all visible wavelengths are accumulated at the absorption axis of the analyzer, irrespective of ϕ, because of the rotational symmetry in the polarization rotation route. The path difference on the northern hemisphere can be perfectly canceled out by the path difference on the southern hemisphere.
Fig. 4 Wavelength dependence of the polarization change in each color on the S2–S3 plane of the Poincaré sphere in the + A/+A/+C/+A/+A configuration. (a) θ = 70°, ϕ = 45°. (b) θ = 70°, ϕ = 30°.
4. Numerical results and discussion
The dark-state light leakage was calculated using a simulation program named “TechWiz LCD 1D.” In this numerical calculation, we assumed that the pretilt angle of the LC layer is 0°. We also assumed an ideal polarizer. A cold cathode fluorescence lamp, which is a broadband light source with continuous spectrum, was used as the light source. The bright state of a homogeneously aligned LC cell can be obtained by applying an in-plane electric field between the patterned electrodes formed on the bottom substrate. The applied electric field twists the LC directors from 0° to 45°, which generates light transmission. The LC parameters are listed as follows: birefringence Δn = 0.0987 at λ = 550 nm and dielectric anisotropy Δε = 8.2. The cell gap is 4 μm. The width of the patterned electrodes and the gap between them are 4 and 6 μm, respectively.
To demonstrate the compensation performance, we calculated the light leakage over the entire range of polar angles at ϕ = 45°, as shown in Fig. 5(a).The red line represents the dark-state light leakage in the + A/+C/+A configuration. A strong off-axis light leakage can be observed at any polar angle. The green and blue lines represent the light leakages in the + A/+A/+C and + A/+A/+C/+A/+A configurations, respectively, which show little light leakage over the entire visible spectra. We also calculated the light leakage as functions of ϕ at θ = 70°, as shown in Fig. 5(b). The red line represents the dark-state light leakage in the + A/+C/+A configuration. A maximum off-axis light leakage of 0.2110% can be observed at azimuth angles of 45°, 135°, 225°, and 315°. The green line represents the light leakage in the + A/+A/+C configuration, which shows a maximum dark-state light leakage of 0.0476% at azimuth angles of 22.5°, 67.5°, 112.5°, 157.5°, 202.5°, 247.5°, 292.5°, and 337.5°. Although the light leakage at ϕ = 45° is eliminated, light leakage still exists at other azimuth angles. The blue line represents the light leakage in the + A/+A/+C/+A/+A configuration, which shows a maximum dark-state light leakage of 0.0011% at an azimuth angle of 115°. It is approximately 45 times lower than that in the + A/+A/+C configuration. This difference is attributed to the symmetrical rotation of the polarization state on the Poincaré sphere, as shown in Fig. 4(b), which results in a high contrast ratio over the entire viewing cone for the white light, which also helps reduce the color shift in low gray-level images [18].
Fig. 5 Dependence of the light leakage (a) on θ at ϕ = 45° and (b) on ϕ at θ = 70°. The values of the light leakage shown here were obtained by averaging the light leakage at each wavelength ranging from 450 to 650 nm with the spacing of 25 nm.
The wavelength dependence of the maximum light leakage is shown in Fig. 6, where the red, green, and blue curves represent the maximum light leakage in the + A/+C/+A, + A/+A/+C, and + A/+A/+C/+A/+A configurations, respectively. The maximum light leakage at 550 nm in the + A/+C/+A configuration can be reduced to zero because it has a symmetrical rotation on the Poincaré sphere, as shown in Fig. 4(a). Because the red and blue lights deviate from the absorption axis of the analyzer owing to the 1/λ dependence of the phase retardation, the maximum light leakages at 450 and 650 nm are quite severe. The light leakage over the entire visible spectra is greatly suppressed in the + A/+A/+C configuration compared with that in the + A/+C/+A configuration. Although the light leakage in the + A/+A/+C configuration is reduced, it is not completely removed owing to the light leakage at any arbitrary azimuth angle. The + A/+A/+C/+A/+A configuration can effectively eliminate the light leakage over the entire light wavelength because uniaxial films with different dispersion characteristics can compensate one another, and the configuration provides symmetrical rotation of the polarization state on the Poincaré sphere. With better dark state, the contrast ratio and viewing angle of a full-color LCD will be further improved.
Fig. 6 Wavelength dependence of the maximum light leakage over the entire azimuth angles at θ = 70°.
We calculated the iso-luminance contour of the dark state using a simulation program named “TechWiz LCD 2D,” assuming that the LCs have a zero pretilt angle, as shown in Fig. 7. Light leakage higher than 0.002% is observed at a polar angle of ± 20° in the + A/+C/+A configuration, but light leakage in the + A/+A/+C configuration is still less than 0.002% at a polar angle of ± 40°. Light leakage is smaller than 0.002% over the entire viewing cone in the + A/+A/+C/+A/+A configuration. These results indicate that the dark-state light leakage for the white incident light can be eliminated over the entire viewing cone using normal dispersion of the films and symmetric configuration. The contrast ratio is also calculated assuming a zero pretilt angle of the LC layer. The viewing angle with a contrast ratio of 3000:1 in the + A/+C/+A configuration is ± 35°, as shown in Fig. 8(a).The + A/+A/+C configuration shows a wider viewing angle of ± 50°, as shown in Fig. 8(b). The viewing angle of the + A/+A/+C/+A/+A configuration is much wider than that of the + A/+A/+C configuration because of the lower off-axis dark-state light leakage, as shown in Fig. 7(c). The viewing angle of the + A/+A/+C/+A/+A configuration with a contrast ratio of 3000:1 is over ± 85° irrespective of the azimuthal angle, as shown in Fig. 8(c).
Fig. 7 Iso-luminance contours of the dark states: (a) + A/+C/+A, (b) + A/+A/+C, and (c) + A/+A/+C/+A/+A configurations.
Fig. 8 Iso-contrast contours obtained assuming zero pretilt angle of LC: (a) + A/+C/+A, (b) + A/+A/+C, and (c) + A/+A/+C/+A/+A configurations.
Although the proposed compensation method shows an excellent viewing angle characteristics when the pretilt angle of the LC layer is 0°, achieving a zero pretilt angle may not be easy. To study the effect of the pretilt angle on the viewing angle characteristics, the light leakage for a pretilt angle of 2° is shown in Fig. 9. In all cases, the effect of the pretilt angle results in an increase in the light leakage. However, the proposed method still shows an improvement over the previous technologies although the remaining light leakage is not negligible. These results indicate that lowering the pretilt angle is essential for complete elimination of the off-axis light leakage. Because obtaining a zero pretilt angle using the rubbing technique is difficult, employing non-contact alignment techniques might be preferable, such as the photo alignment and ion-beam alignment [19–22], to realize a wide-viewing-angle LCD.
5. Conclusions
We have proposed achromatic compensation configurations using normal dispersion films to eliminate the dark-state light leakage over the entire polar and azimuth angles. Using the symmetrical rotation of the polarization state on the Poincaré sphere, the dark-state light leakage over the entire viewing cone for the white light can be effectively eliminated. The light leakage in the proposed + A/+A/+C/+A/+A configuration was 45 times lower than that in the + A/+A/+C configuration. The contrast ratio of the + A/+A/+C/+A/+A configuration for white light is higher than 3000:1 at a polar angle of ± 85° irrespective of the azimuthal angle. All the films we used have normal wavelength dispersion, which can be easily fabricated at a relatively low manufacturing cost.
Acknowledgments
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2011-0029198).
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