Poincare Sphere Analysis of the Pretilt Angle Effect on the Viewing Angle of a SingleDomain FFS LiquidCrystal Mode
 Author: Lee DongJin, Oh SeongWoo, Shim GyuYeop, Choi JunChan, Lee JounHo, Kim Byeong Koo, Kim HakRin
 Publish: Journal of the Optical Society of Korea Volume 20, Issue1, p156~164, 25 Feb 2016

ABSTRACT
We demonstrated the pretilt angle effect on the viewing angle properties of a singledomain fringefield switching (FFS) liquid crystal (LC) mode. By performing the Póincare sphere analysis, we investigated, in detail, the origin of the viewing angle asymmetry that exists in the singledomain FFS LC mode both in the fieldon and fieldoff states. Using this analysis, we confirmed that the pretilt angle reduces the viewing angle symmetry in the singledomain FFS LC mode. Finally, we examined the effect of a zero pretilt angle on the viewing angle symmetry by evaluating real singledomain FFS LC cells.

KEYWORD
Viewing angle property , Poincare sphere , Fringefield switching , Liquid crystal , Pretilt angle

I. INTRODUCTION
During the last decade, the fringefield switching (FFS) liquid crystal (LC) mode has been widely used for mobile phones, tablets, and highend notebook displays, owing to its high transmittance and low power consumption required for ultrahigh resolution devices [1]. In particular, a singledomain FFS LC mode has good transmittance efficiency as compared with a multidomain FFS LC mode that exhibits inevitable reduction in the transmittance efficiency owing to the LC disclination lines caused by discontinuous LC distributions in the boundary of domains [24]. Thus, the singledomain FFS LC mode has been widely used for highresolution displays, particularly in the small pixels for the mobile displays that require ultrahigh resolution and low power consumption. However, a pretilt angle in the polar direction is unavoidable during the rubbing process for aligning the LC molecules. The presence of the pretilt angle in planar LC modes causes the asymmetry in viewing angle in terms of the light leakage and grayscale inversion. This asymmetry negatively affects the viewing angle properties such as the light leakage, color shift, and grayscale inversion in the specific viewing angle direction [5, 6]. To enhance the viewing angle properties of the singledomain planar mode, many optical compensation techniques have been proposed [715]. These optical compensation methods can reduce the light leakage and remove the grayscale inversion. However, these techniques do not eliminate the viewing angle asymmetry that persists owing to a nonzero pretilt angle in the singledomain FFS LC mode. Despite some clear advantages such as high transmittance, high aperture ratio, and low power consumption, the asymmetric performance of the singledomain FFS LC mode has been an obstacle to its adoption for use in mobile displays.
In previous work, Ohe reported the viewing angle dependence on the pretilt angle in the inplane switching (IPS) LC mode [5]. In the FFS mode, because LC directors on the surface are affected by the vertical component of the fringefield, the viewing angle dependence on the pretilt angle does not exactly match the previous result reported for the IPS mode [6]. For the FFS mode, we employed the parallel rubbing method to reduce the tilt distribution of the bulk LC layer [16]. Although the asymmetric luminance in the fieldoff state and in the low grayscale level could be effectively reduced, we could not achieve a perfect solution owing to the presence of a pretilt angle on the surface. In our recent work, to improve the viewing angle properties of the singledomain FFS LC mode, we proposed a promising method to realize the zero pretilt angle by employing a reactive mesogen (RM)stabilized polystyrene (PS) layer [6]. The photo alignment technology has been mature for manufacture and can be applied to realize the zero pretilt angle as well [17]. For the clear understanding of the viewing angle results in the singledomain FFS LC mode, we need a comprehensive study of the evolving polarization state of the light passing through an LC layer with a pretilt angle.
In this study, we simulated the viewing angle properties of the light leakage and grayscale inversion depending on the pretilt angle in the singledomain FFS LC mode. To understand the tendency of the light leakage and grayscale inversion depending on the viewing direction, we performed the Póincare sphere analysis and investigated the origin of the asymmetric viewing angle problems. Finally, we fabricated a singledomain FFS cell with the zero pretilt angle and confirmed the simulation results.
II. EXPERIMENTS
To understand the pretilt angle effect on the offaxis transmittance in the singledomain FFS LC mode, we performed numerical calculations using commercial software (Techwiz LCD 3D, Sanayi System Co., Ltd.). Figure 1 shows the schematic structure and optic axes of the single domain
FFS LC mode for the simulation in detail (
θ_{k} : polar angle of the viewing direction,ϕ_{k} : azimuthal angle of the viewing direction, andα : surface pretilt angle). The physical properties of the employed LC material are as follows: dielectric anisotropy ofΔε = 7.9; elastic constants ofK_{11} = 10.2 pN,K_{22} = 6.9 pN, andK_{33} = 13.6 pN; and refractive indices ofn_{e} = 1.5885 andn_{o} = 1.4859. We conducted the simulation for 0°, 2°, and 4° pretilt angles while keeping the other parameters unchanged. We simulated the viewing angle properties for the azimuthal angleϕ ranging from 0° to 355° in steps of 5°, and for the polar angleθ ranging from 0° to 80° in steps of 10°. The induced voltage ranged from 0 V to 10 V, sufficient for obtaining maximum transmittance in all simulation conditions. From the simulation results, we could determine the severest viewing angle direction asθ_{k} = 70° andϕ_{k} = 40°, regardless of the pretilt angle. This is the same result as a reported one [14]. The offaxis light leakage and the grayscale inversion were analyzed at this severest viewing angle direction and voltage conditions. In addition, to explain the simulation results in detail, we analyzed the polarization state of the light passing through the LC layer by extracting the corresponding Stokes parameters and its trace depending on the voltage on the Póincare sphere. Finally, we fabricated singledomain FFS LC cells and evaluated their viewing angle performance for different pretilt angles, and compared these results to the simulation results.III. RESULTS: VIEWING ANGLE SIMULATION
In the crossed polarizer condition, light leakage is an inevitable phenomenon in oblique view due to the effective absorption angle change. The angle between the absorption axes of the two polarizers is changed into the effective angle,
φ , as follows [14]:where
ϕ_{p} andϕ_{a} are the azimuthal absorption angles of the polarizer and the analyzer, which are 173° and 83°, respectively, in our simulation structure, as shown in Fig. 1(b), andϕ_{a} −ϕ_{p} is π/2 in the crossed polarizer condition. Eq. (1) also implies thatφ cannot be 90° ifθ_{k} is not zero. This means that the offaxis light leakage in the fieldoff state occurs in the oblique viewing condition, and it is related to the origin of the grayscale inversion.The extent of the light leakage in the oblique viewing angle varies depending on the surface pretilt angle and the positional asymmetry of the light leakage becomes more severe as the pretilt angle increases, as we reported in our previous paper [6]. We reported the viewing angle properties of the singledomain FFS LC mode in terms of voltagedependent transmittance and contrast ratio depending on the pretilt angle of the alignment layer [6]. In that study, as the pretilt angle increased, the voltage (
V_{inv} ) that causes the maximum grayscale inversion in a viewing angle ofθ_{k} = 70° andϕ_{k} = 40° increased as well, and the viewing angle asymmetry became more pronounced. Figure 2(a) shows the simulated transmittance variation as a function of applied voltage atθ_{k} = 70°,ϕ_{k} = 40° and 130° in this study. The horizontal dashed lines correspond to the initial transmittance levels in the fieldoff state (T_{0V} ) for each pretilt angle condition. Forϕ_{k} = 40°, the bounce in the transmittance variation becomes more severe andV_{inv} increases with increasing the pretilt angle, as shown in Fig. 2(a) (open symbols connected by solid lines). Forϕ_{k} = 130°, the bounce in the transmittance variation is not observed, and the light leakage increases with increasing the pretilt angle, as shown in Fig. 2(a) (closed symbols connected by dashed lines). The values ofT_{0V} and transmittance atV_{inv} (T_{inv} ) for the different pretilt angle conditions are summarized in Table 1.Figures 3(a) to 3(c) show the transmittance variations in the fieldoff (closed circles) and
V_{inv} (open inverted triangles) in the different pretilt angle conditions, as a function of the azimuthal viewing angle direction. In all plots, shaded areas indicate the azimuthal viewing angle range in which the grayscale inversion occurs. As shown in Fig. 3, the transmittance asymmetry in the fieldoff state and atV_{inv} , and the grayscale inversion asymmetry atV_{inv} become more severe with increasing the pretilt angle. The results in Fig. 2(a) and Figs. 3(a) to 3(c) are in an excellent agreement with our previous results [6].Figure 2(b) and Figs. 3(d) to 3(f) show the results applying the optical compensation method. We used a biaxial film (
n_{x} : 1.521,n_{y} : 1.519,n_{z} : 1.520; thickness: 138 μm) stacked on a negative C plate as a compensation film [12]. As the negative C plate, we used a triacetyl cellulose (TAC) film (n_{x} : 1.4793,n_{y} : 1.47962,n_{z} : 1.47890; thickness: 40 µm). As shown by the horizontal dashed lines in Fig. 2(b) and by the closed circles in Figs. 3(d) to 3(f), the optical compensation method helps to reduce the offaxis light leakage and transmittance bounce irrespective of the pretilt angle. However, theT_{inv} asymmetry in the azimuthal viewing angle direction in the nonzero pretilt angle condition is not eliminated, as shown by the open triangles in Figs. 3(e) and 3(f). This asymmetry cannot be eliminated even by using the optical compensation technique owing to the presence of the surface pretilt angle. To validate the pretilt angle effect on the viewing angle properties of the singledomain FFS LC mode, we need to analyze in detail using the Póincare sphere the polarization state passing through an LC layer with a nonzero pretilt angle.IV. RESULTS: OPTICAL ANALYSIS BY USING POINCARE SPHERE
4.1. Oblique Viewing Conditions at
？_{k} = 40° and 220°4.1.1. Pretilt Angle = 0°
Figure 4 shows the Póincare spheres for the optical analysis of the viewing angle properties depending on the pretilt angle, the viewing angle direction, and the applied voltage.
P ,A , andT indicate the transmission axes of the polarizer, the analyzer, and the polarization state of the incident light positioned before the analyzer in the normal viewing condition, respectively. In the fieldoff state, there is no light leakage in the normal viewing condition becauseT andA are always located on opposite sides of each other. However, in the oblique viewing directions ofϕ_{k} = 40° and 220°, which are indistinguishable between the head and tail of the LC director in the zero pretilt angle condition, the effective transmission axes of bothP andA move toward the horizontal direction. Therefore,P andA move to the new transmission axes ofP_{t} andA_{t} , respectively, and the angle between the absorption axes of the two polarizers is changed into the effective angle,φ , as shown in Eq. (1). For the oblique viewing directions ofϕ_{k} = 40° and 220°,P_{t} does not coincide with the analyzer absorption axisA_{a} , and from Eq. (1), the effective polarizer angleφ is calculated as 105° atθ_{k} = 70°, which produces the light leakage in the fieldoff state, as shown in Fig. 4(a).Moreover, when the light propagates into a uniaxial medium such as an LC layer in oblique incidence, the phase retardation is induced by the azimuthal angle mismatch between
P_{t} and the LC optic axis. In general, when the optic axis of a uniaxial medium is oriented at the tilting angleα and the azimuthal angleϕ_{n} , the phase retardation of the uniaxial medium in oblique incidence of light, can be expressed as [18]:where
ε _{xz} =(n_{e} ^{2}n_{o} ^{2})sinα cosα cos(ϕ_{n} −ϕ_{k} ) andε_{xz} =n_{o} ^{2}+(n_{e} ^{2}−n_{o} ^{2})sin^{2}α . As shown in Eq. (2), the phase retardation depends on the orientation of the optic axesα andϕ_{n} . When the pretilt angle is zero in the LC layer, i.e., when the optic axisα becomes 0° in the initial state, the slow axesΨ_{ϕ=40°} andΨ_{ϕ=220°} of the oblique viewing directions ofθ_{k} = 70° atϕ_{k} = 40° and 220° are 90.5°, which coincides withA_{a} , and the phase retardations are 1.27π in both cases, when calculated by using Eq. (2). The consequent Stokes parameters (S_{1} ,S_{2} ,S_{3} ) are (−0.8437, −0.3757, −0.3834) for the polarization state ofT_{ϕ=40°, ϕ=220°} in Fig. 4(b). As a result, after passing the LC layer, the extent of light leakage is the same for the oblique viewing directions ofϕ_{k} = 40° andϕ_{k} = 220° because the deviation of polarization stateT fromP_{t} is also the same forϕ_{k} = 40° andϕ_{k} = 220°, as shown in Fig. 4(b).4.1.2. Pretilt Angle ≠ 0°
In the fieldoff state, the pretilt angle affects the phase retardation of the incident light, as shown in Eq. (2), as well as the incident light angle, owing to the viewing direction dependency on the birefringence of the LC director. Therefore, the slow axes and the phase retardation of the incident light are formed a little differently between the oblique viewing directions of
ϕ_{k} = 40°, which is observed from the head position of the LC director, andϕ_{k} = 220°, which is observed from the tail position of the LC director. The slow axesΨ_{ϕ=40°} andΨ _{ϕ=220°} of the oblique viewing directions ofθ_{k} = 70° atϕ_{k} = 40° andϕ_{k} = 220° are formed in the counterclockwise position based onP_{t} in the Póincare sphere, and are calculated asΨ_{ϕ=40°} = 91.6° (which is larger than that of the zero pretilt angle owing to the headup viewing effect of the LC director) andΨ _{ϕ=220°} = 89.3° (which is smaller than that of the zero pretilt angle owing to the taildown viewing effect of the LC director) when the pretilt angle is 2°. Based on Eq. (2), the phase retardations for each case are calculated as 1.23π and 1.32π, and these values are different from that of the zero pretilt angle condition owing to the dependence of the viewing angle direction on the birefringence of the LC director. Hence, incident light passing through the LC layer exhibits different polarization states betweenT_{ϕ=40°} andT_{ϕ=220°} , as shown in Fig. 4(c), with the Stokes parameters (−0.8005, −0.4821, −0.3560) for the polarization state ofT_{ϕ=40°} and (−0.8772, −0.2704, −0.3967) for the polarization state ofT_{ϕ=220°} in Fig. 4(c), respectively. The extent of the light leakage is determined by the variation in the distance ofT_{ϕ=40°} orT_{ϕ=220°} fromA_{a} , respectively. Therefore, the light leakage in the viewing direction ofϕ_{k} = 40° is larger than that in the viewing direction ofϕ_{k} = 220° becauseT_{ϕ=40°} is farther fromA_{a} thanT_{ϕ=220°} in the nonzero pretilt angle. This result is in a good agreement with the simulation result in Fig. 3(b), which shows larger light leakage at the head position of the LC director.Based on
P_{t} , both the slow axesΨ_{ϕ=40°} andΨ_{ϕ=220°} are formed in the opposite direction to the rotating direction of the LC easy axis, which is driven by the applied voltage and is shown by thick blue arrows in Figs. 4(b) and 4(c). Therefore, when the applied voltage increases, both the slow axesΨ_{ϕ=40°} andΨ_{ϕ=220°} rotate in the clockwise direction. Consequently,T_{ϕ=40°} andT_{ϕ=220°} become closer to and then passA_{a} at a voltage larger thanV_{inv} . This means that the grayscale inversion occurs in both directions as the applied voltage increases. Besides, the grayscale inversion andV_{inv} in the viewing direction ofϕ_{k} = 40° are larger than those in the viewing direction ofϕ_{k} = 220° becauseT_{ϕ=40°} has to rotate farther fromA_{a} thanT_{ϕ=220°} owing to the difference between the positions ofΨ_{ϕ=40°} andΨ_{ϕ=220°} , as shown in Fig. 4(c). These are in a good agreement with the simulation result in Fig. 2(a) and Figs. 3(a) to 3(c), which show a more severe grayscale inversion asymmetry and higherV_{inv} with increasing the pretilt angle.As a result, the asymmetric light leakage and the transmittance distribution are caused by the presence of the LC pretilt angle in the viewing directions of
ϕ_{k} = 40° and 220°, and the grayscale inversion is particularly more severe in the viewing direction ofϕ_{k} = 40°.4.2. Oblique Viewing Conditions at
？_{k} = 130° and 310°4.2.1. Pretilt Angle = 0°
In the oblique viewing directions of
ϕ_{k} = 130° and 310°,P_{t} is also not coincident withA_{a} , as shown in Fig. 4(d), but is located in the opposite direction with respect toA_{a} compared to the orientation in Fig. 4(a), which corresponds to the viewing directions ofϕ_{k} = 40° and 220°. This follows because the effective polarizer angleφ is calculated as 75° atθ_{k} = 70°, based on the condition in Eq. (1). Therefore, this mismatch betweenP_{t} andA_{a} also induces the light leakage in the fieldoff state, as in the case ofϕ_{k} = 40° and 220°.In addition, when the pretilt angle is zero in the LC layer, i.e., the optic axis
α becomes 0° in the initial state, the slow axesΨ_{ϕ=130°} andΨ_{ϕ=310°} of the oblique viewing directions ofθ_{k} = 70° atϕ_{k} = 130° and 310° are 75.5°, which is coincident withA_{a} , and the phase retardations are 1.32π in both cases, as calculated from Eq. (2). The consequent Stokes parameters are (−0.6004, 0.6771, 0.4255) for the polarization state ofT_{ϕ=130°, ϕ=310°} in Fig. 4(e). As a result, after passing through the LC layer, the extent of light leakage is almost the same for theθ_{k} = 70° oblique viewing directions ofϕ_{k} = 130° andϕ_{k} = 310°, which is similar to the cases involving the oblique viewing directions ofϕ_{k} = 40° andϕ_{k} = 220°, as shown in Fig. 4(b).4.2.2. Pretilt Angle ≠ 0°
The analysis for the nonzero pretilt angle in the viewing directions of
ϕ_{k} = 130° and 310° in the fieldoff state is similar to the case in Fig. 4(c), which corresponds to the viewing directions ofϕ_{k} = 40° and 220° in terms of inducing variations in the slow axes. However, the slow axesΨ_{ϕ=130°} andΨ_{ϕ=310°} of the oblique viewing directions ofθ_{k} = 70° atϕ_{k} = 130° andϕ_{k} = 310° are formed in the clockwise position based onP_{t} in the Póincare sphere, and are calculated asΨ_{ϕ=130°} = 73.8° (which is smaller than that of the zero pretilt angle, owing to the headup viewing effect of the LC director) andΨ_{ϕ=310°} = 76.3° (which is larger than that of the zero pretilt angle, owing to the taildown viewing effect of the LC director) when the pretilt angle is 2°. The phase retardations of each case are calculated as 1.28π and 1.36π from Eq. (2), and these values are different from that of the zero pretilt angle condition, owing to the viewing direction dependency on the birefringence of the LC director. Hence, for each case, the incident light passing through the LC layer exhibits different polarization states T_{ϕ=130°} andT_{ϕ=310°} , as shown in Fig. 4(f), and the consequent Stokes parameters are (−0.5128, 0.7531, 0.4121) for the polarization state ofT_{ϕ=130°} and (−0.6777, 0.5995, 0.4258) for the polarization state ofT_{ϕ=310°} in Fig. 4(f). In addition, the light leakage in the viewing direction ofϕ_{k } = 130° is larger than that in the viewing direction ofϕ_{k} = 310°, because the deviation ofT_{ϕ=130°} fromA_{a} is farther than that ofT_{ϕ=310°} . This is in a good agreement with the simulation result in Fig. 3(b), which shows larger light leakage at the head position of the LC director.Furthermore, the grayscale inversion does not occur because, based on
P_{t} , the induced slow axesΨ_{ϕ=130°} andΨ_{ϕ=310°} are formed in the same direction as the rotating direction of the LC easy axis, which is driven by the applied voltage and is shown by thick blue arrows in Figs. 4(e) and 4(f). Therefore,T_{ϕ=130°} andT_{ϕ=310°} followed byΨ_{ϕ=130°} andΨ_{ϕ=310°} are already formed in the clockwise direction ofA_{a} in the Póincare sphere, and do not passA_{a} when the applied voltage increases, unlikeT_{ϕ=40°} andT_{ϕ=220°} in Figs. 4(b) and 4(c). As a result, the only difference between the viewing directions betweenϕ_{k} = 130° andϕ_{k} = 310° is the extent of light leakage and the grayscale inversion does not occur at both the viewing directions.4.3. Oblique Viewing Angle Properties after Applying a Compensation Film
Figure 5 shows the Póincare sphere analysis of the singledomain FFS LC mode using a biaxial optical compensation film. The polarization state of the light passing through the biaxial compensation film, marked by the open circle in Fig. 5, is close to the analyzer absorption axis
A_{a} and the LC slow axisΨ [6]. Therefore, the polarization state passing through the LC layer, denoted byT , does not strongly deviate fromA_{a} [6, 12]. As a result, because the extent of light leakage is determined by the distance ofT fromA_{a} , the light leakage can be dramatically reduced in the oblique viewing direction, as shown by the horizontal dashed lines in Fig. 2(b) and closed circles in Figs. 3(d) to 3(f). In addition, because the polarization state in the fieldoff state is close toA_{a} , the transmittance bounce, which occurs at the low grayscale level, is also reduced, as shown by open symbols in Fig. 2(b). However, in the nonzero pretilt angle condition, because the slow axes and the phase retardations of the incident light are slightly different between the oblique viewing directions ofϕ_{k} = 40° in Fig. 5(b) (or 130° in Fig. 5(d)), which is observed from the head position of the LC director, andϕ_{k} = 220° in Fig. 5(b) (or 310° in Fig. 5(d)), which is observed from the tail position of the LC director, the incident light passing through the LC layer also exhibits different polarization states as shown in Figs. 5(b) and 5(d). As the applied voltage increases, the slow axes rotate as shown by the thick blue arrows in Figs. 5(b) and 5(d), and the difference between two polarization states becomes obvious. This leads to the transmission difference in the grayscale level and to the asymmetric viewing angle properties when comparing betweenϕ_{k} = 40° and 220°,ϕ_{k} = 130° and 310°. Although the light leakage and grayscale inversion can be improved by using the compensation method, the viewing angle asymmetry in the grayscale level in the nonzero pretilt angle condition cannot be eliminated by using only the optical compensation method.From the Póincare sphere analysis, we confirmed the surface pretilt anglerelated difference between the viewing angle properties in the singledomain FFS LC mode. In addition, even though a compensation method is applied, we verified that the surface LC pretilt angle has to be zero for characterizing the symmetrical transmittance in the fieldoff state and at the low grayscale level as well as for minimizing the grayscale inversion.
V. RESULTS: VIEWING ANGLE MEASUREMENT
To verify the simulation result related to the pretilt angle effect, we fabricated singledomain FFS cells for two types of pretilt angle conditions and evaluated the viewing angle performance of the fabricated cells. For the nonzero pretilt angle condition, we used a conventional polyimide layer with the pretilt angle of 2°. To obtain the zero pretilt angle condition, we employed a polystyrene layer stabilized with UV curable reactive mesogen (RM). These two types of singledomain FFS cells were fabricated as described previously [6].
To demonstrate obviously the dependence on the oblique viewing angle direction in the measured result, we crosssectioned the viewing planes along the diagonal direction of
ϕ_{k} = 40° through 220° (A_{1}−A_{2}) andϕ_{k} = 130° through 310° (B_{1}−B_{2}). In Fig. 6(a), for the A_{1}−A_{2} direction, the light leakage increased atT_{0V} and the grayscale inversion became severe atT_{inv} for the oblique viewing angle direction, irrespective of the alignment layers. In particular, for the singledomain FFS LC cell with the PI layer, the asymmetric transmittance distribution and more serious grayscale inversion in the direction ofϕ_{k} = 40° appeared as in nonzero pretilt angle simulations that were described in the previous section. Moreover, as shown in Fig. 6(b), for the B_{1}−B_{2} direction, the asymmetric transmittance distribution of the singledomain FFS LC cell with the PI layer was maintained atV_{inv} owing to the initial asymmetry of light leakage at 0 V; however, there was no grayscale inversion, irrespective of the alignment layers. These results on the crosssectioned viewing planes of A_{1}−A_{2} and B_{1}−B_{2} were in a good agreement with our simulation results.Figure 6(c) shows the contrast ratio obtained by dividing
T_{inv} byT_{0V} as a function of the polar viewing angle on the crosssectioned viewing planes of A_{1}−A_{2} and B_{1}−B_{2}. The value of CR (ϕ = 310°)/CR (ϕ = 130°) was maintained at around 1, irrespective of the polar viewing angle and the pretilt angle (that is, the alignment layers). However, the value of CR(ϕ = 220°)/CR(ϕ = 40°) for the singledomain FFS LC cell with the PI layer increased with increasing the polar viewing angle, while that of the singledomain FFS LC cell with the RMstabilized PS layer was maintained at around 1. This implies that the asymmetric transmittance in the oblique viewing direction is seriously affected by the pretilt angle, especially for the azimuthal viewing directions ofϕ = 40° andϕ = 220° in the single domain FFS LC mode.VI. CONCLUSION
In the singledomain FFS LC mode, the phase retardation and the effective angle influenced by the pretilt angle affect the light leakage and the grayscale inversion in the oblique view. In this paper, we used the Póincare sphere for conducting a detailed analysis of the asymmetric viewing angle properties of the light leakage and the grayscale inversion in relation to the pretilt angle in the singledomain FFS LC mode. The light leakage and the grayscale inversion in relation to the applied voltage could be estimated with the positions of the analyzer absorption axis (
A_{a} ) and the polarization state of the light passing through the LC layer (T ) on the Póincare sphere, and their positional comparison.Although the light leakage was dramatically reduced by using the optical compensation method irrespective of the pretilt angle, the asymmetry in grayscale level of the nonzero pretilt angle condition could not be eliminated even by using the optical compensation method. To enhance the asymmetric viewing angle properties in the singledomain FFS LC mode, the zero pretilt angle condition is essential, and we validated this conclusion by measuring the viewing angle properties of a fabricated singledomain FFS cell with zero pretilt angle
The analysis using the Póincare sphere employed in this study is very helpful for understanding the influence of the pretilt angle on the polarization state of the light passing through LC layers, and is likely to become an important tool for estimating the optical performance of LC devices.

[FIG. 1.] (a) Schematic structure and (b) optic axes of the singledomain FFS LC mode for the simulation and definition of the viewing direction.

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[FIG. 2.] Simulation results for the viewing angle properties of the singledomain FFS LC mode, in terms of transmittance, as a function of the applied voltage at the viewing conditions of θk = 70°, ？k = 40° and 130° (a) without an optical compensation film and (b) with a biaxial optical compensation film.

[TABLE 1.] T0V and Tinv in the oblique viewing directions of θk = 70° at ？k = 40° of the singledomain FFS LC mode without and with a biaxial compensation film (nx: 1.521, ny: 1.519, nz: 1.520; thickness: 138 μm)

[FIG. 3.] Asymmetric transmittance in the azimuthal viewing direction, for different pretilt angle conditions in the singledomain FFS LC mode at θk = 70°. (a), (b), and (c) Pretilt angles of 0°, 2°, and 4°, respectively, without an optical compensation film. (d), (e), and (f) Pretilt angles of 0°, 2°, and 4°, respectively, with a biaxial optical compensation film.

[FIG. 4.] Poincare sphere analysis for different pretilt angles, viewing angle directions, and applied voltages. (a) and (d) Variation of effective transmission axes in the oblique polar viewing direction. (b) and (c) Analysis for the oblique polar viewing direction, with azimuthal directions of ？k = 40° and 220°, without and with an LC pretilt angle, respectively. (e) and (f) Analysis for the oblique polar viewing direction, with azimuthal directions of ？k = 130° and 310°, without and with an LC pretilt angle, respectively. (P, A, and T: transmission axes of the polarizer, the analyzer, and the polarization state of the incident light positioned before the analyzer in the normal viewing condition, respectively. Pt and At: effective transmission axes of the polarizer and the analyzer for the oblique viewing directions. Aa: effective absorption axis of the analyzer for the oblique viewing directions. T？=i and Ψ？=i: polarization state and slow axis, for different oblique viewing angles i, respectively. i denotes 40°, 130°, 220°, and 310°.)

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[FIG. 5.] Poincare sphere analysis for the fieldoff state in the singledomain FFS LC mode, applying a biaxial optical compensation film. (a) and (b) Analysis for the oblique polar viewing direction, with azimuthal directions of ？k = 40° and 220°, without and with an LC pretilt angle, respectively. (c) and (d) Analysis for the oblique polar viewing direction, with azimuthal directions of ？k = 130° and 310°, without and with an LC pretilt angle, respectively. (Pt and At: effective transmission axes of the polarizer and the analyzer for the oblique viewing directions. Aa: effective absorption axis of the analyzer for the oblique viewing directions. T？=i and Ψ？=i: polarization state and slow axis, for different oblique viewing angles i, respectively. i denotes 40°, 130°, 220°, and 310°.)

[FIG. 6.] Experimental results for the transmittance and contrast ratio of a crosssectioned plane, A1？A2 and B1？B2, in the fieldoff state (V0V) and in the low grayscale level (Vinv). (a) Comparison of transmittance along the A1？A2 viewing direction. (b) Comparison of transmittance along the B1？B2 viewing direction. (c) Comparison of contrast ratio along the A1？A2 and B1？B2 viewing directions.