Generation of Geometric Extra Phase and Accompanying Temporal Effects in Asymmetric Optically Compensated IPS-LCDs and FFS-LCDs

This paper reports the generation of an extra phase and the accompanying temporal effects in an asymmetric optically compensated in-pane-switching (IPS) liquid crystal (LC) system and a fringe-field-switching (FFS) liquid crystal display (LCD) exhibiting a twofold faster response speed in the switching-off process compared with that in single and symmetric IPS-LCDs and FFS LCDs for the first time. To explain the experimental results, we derived an approximate analytical formula for the optical output intensity that includes an extra phase advancement and conducted simulations to achieve normally black operation using a dynamic optical retarder.

Our approach reported in the present paper represents an alternative to the abovementioned approaches. In a preliminary previous work, we reported the electro-optical performances of asymmetric optically compensated tunable birefringent (TB) mode LCD exhibiting two-fold fast response speed in the switching off process [7]. For this reason, this present work was conducted aiming at the extension of the previous work to this proposed asymmetric optically compensated IPS and FFS LCDs (Asymmetric OC-IPS and FFS-LCD). The present work is related to the geometry phase, originally described by Pancharatnum [12] and Berry [13] in their historically representative papers. The present paper also updates previous work by introducing a dynamic optical retarder [7] for realizing electro-optical characteristics with by introducing a dynamic retarder, we realized normally black state normally black operation, accompanying with a simulation utilizing a simulator, SHINTECH LCD MASTER. In conjunction with a simulation using a SHINTECH LCD MASTER simulator, we introduce a dynamic retarder, to realize normally black operation.

Optical Configuration of our Asymmetric IPS-LC System
In Figure 1, angle ϕ 1 is the switching azimuthal angle of LC molecules and ϕ 2 is the setting azimuthal angle of a compensator (+A Plate) whose angle is set to ϕ 2 = 3π/4 − α, which can be controlled using a dynamic retarder, when we use an IPS cell for the compensator.

Optical Configuration of our Asymmetric IPS-LC System
In Figure 1, angle ϕ1 is the switching azimuthal angle of LC molecules and ϕ2 is the setting azimuthal angle of a compensator (+A Plate) whose angle is set to ϕ2 = 3π/4 − α, which can be controlled using a dynamic retarder, when we use an IPS cell for the compensator. The whole system is sandwiched between crossed polarizers, where the incident light field into the LCD system is polarized in the x-direction and the transmitted wave is polarized in the y-direction. Labels e1 and o1 in Figure 1 indicate that the axes of the extraordinary wave and the ordinary wave, respectively, and labels e2 and o2 indicate those of the compensator, respectively.
When ϕ2 = 3π/4 and ϕ1 = π/4, the system is symmetric and generates a black state; under these conditions, the extra phase is not generated and the high response speed is not achieved.

Analytical Derivation of Normalized Optical Transmission of a Single IPS-Cell
Using the system shown in Figure 1, we here carry out a 2 × 2 Jones matrix calculation [14] for I1 of a single cell.
The input electrical field is 1 0 We then have a projected field in the x-y coordinate: where c1 and s1 are cos(ϕ1) and sin(ϕ1), respectively, here G11 = exp(−i Γ11) and G12 = exp(−i Γ12); in addition, δ1 = Γ11 − Γ12, where each of which is the phase delay in the e1 and o1, from the incident wave, respectively. We have the x-y components such that: Then, = 2E0 sin(2ϕ1)exp(−iδ1). The whole system is sandwiched between crossed polarizers, where the incident light field into the LCD system is polarized in the x-direction and the transmitted wave is polarized in the y-direction. Labels e 1 and o 1 in Figure 1 indicate that the axes of the extra-ordinary wave and the ordinary wave, respectively, and labels e 2 and o 2 indicate those of the compensator, respectively.
When ϕ 2 = 3π/4 and ϕ 1 = π/4, the system is symmetric and generates a black state; under these conditions, the extra phase is not generated and the high response speed is not achieved.

Analytical Derivation of Normalized Optical Transmission of a Single IPS-Cell
Using the system shown in Figure 1, we here carry out a 2 × 2 Jones matrix calculation [14] for I 1 of a single cell.
Thus, we have the optical output intensities and the normalized optical transmission for the single cell: The normalized transmission is then A δ 1 = 1.3π for n-IPS and n, p-FFS and 1.04π for p-IPS were determined based on the properties of the LC materials and the LCD cell fabrication details (Section 3.3).

Derivation of Normalized Optical Transmission Intensity of OC-IPS with 2 × 2 Jones Matrix Calculations
We here derive the equation for the proposed asymmetric OC-IPS and FFS shown in Figure 1. This derivation is carried out by replacing the c 1 and s 1 terms in Equation (1) with c 2 and s 2 and Γ 21 − Γ 22 . In addition, by inserting E 1 (x) and E 1 (y), we obtain We derive E 2 (y) as follows: where δ 2 is again the difference in phase delay between the e 2 and o 2 axes: We then have: And δ 2 = δ 1 = 1.3π for n-IPS and n, p-FFS and 1.04π for p-IPS as evaluated based on the physical properties and the LCD cell fabrication conditions described in Section 3.3. Then, with sin 2 (ωt) = 1/2 and without exp(−iδ 2 ) to normalize the optical intensity and transmission. I 2 = I 0 sin 2 (2ϕ 2 − 2ϕ 1 ) sin 2 (δ 1 /2)sin 2 (δ 2 /2) (10) If we substitute ϕ 2 = π/4 − α into Equation (11), we obtain an equation with a phase-advancement shift, of 2α: In our system, the symmetry breaking introduces a phase shift, which leads to a fast response in the switching-off process. This effect is shown later in Figure 3. When LC-cell and the A-plate are crossed, ϕ 1 = ϕ 2 = π/4 and δ 1 = δ 2 = 1.3π, the symmetric system then produces the black (dark) state and no ultrafast switching process occurs.   We next explain the switching process in our OC-LCDs, along with the contents of Figure 2. Figure 3 shows simulation results for the normalized transmission and compares T1 (I1) with T2 (I2) against the switching angles calculated using Equations (7) and (12). The top and central parts in this figure show the behaviors in the switching-off process, and the bottom and right parts show the behaviors in the switching-on process. Thus, the ϕ1 for T2 (I2) starts from a degree of −α, and the ϕ1 for the T1 (I1) starts from −45°.

Results and Discussion
The results in Figure 3 are interpreted as follows (1) The T2 (I2) has a phase advancement of α over the I1(T1), (2) According to the top area, the T2 (I2) starts the decay process with a finite inclination, whereas the T1 (I1) starts the decay process with no inclination. This decay in the absence of inclination is attributed to the fast response in the decay process, which was experimentally demonstrated in the present research. This phenomenon is a purely optical effect, where the decay process occurs as the common molecular relaxation for both the symmetric and asymmetric systems. (3) The I2 (T2) has a finite value at the right bottom because of energy conservation, which means that the operation is not normally black. The realization of a normally black operation will be described in Section 3.4. We next explain the switching process in our OC-LCDs, along with the contents of Figure 2. Figure 3 shows simulation results for the normalized transmission and compares T 1 (I 1 ) with T 2 (I 2 ) against the switching angles calculated using Equations (7) and (12). The top and central parts in this figure show the behaviors in the switching-off process, and the bottom and right parts show the behaviors in the switching-on process. Thus, the ϕ 1 for T 2 (I 2 ) starts from a degree of −α, and the ϕ 1 for the T 1 (I 1 ) starts from −45 • .
The results in Figure 3 are interpreted as follows (1) The T 2 (I 2 ) has a phase advancement of α over the I 1 (T 1 ), (2) According to the top area, the T 2 (I 2 ) starts the decay process with a finite inclination, whereas the T 1 (I 1 ) starts the decay process with no inclination. This decay in the absence of inclination is attributed to the fast response in the decay process, which was experimentally demonstrated in the present research. This phenomenon is a purely optical effect, where the decay process occurs as the common molecular relaxation for both the symmetric and asymmetric systems. (3) The I 2 (T 2 ) has a finite value at the right bottom because of energy conservation, which means that the operation is not normally black. The realization of a normally black operation will be described in Section 3.4.  Figure 4 shows the experimentally obtained transmittance-voltage (V-T)-curves of IPS LCDs, as recorded at 25 °C using a DMS-703 (Autronic Melchers, GMb) instrument. Interestingly, in the symmetric compensation system, the introduction of optical compensation introduces a wide operating voltage range, as shown in Figure 4. Regarding the V-T curve, refer to [14], where the Freedericksz transition is described.  Figure 5 shows the V-T curves of the p-OC-IPS device without optical compensation (α = 0) and the p-OC-IPS device with optical compensation, (α = −6.8°). The proposed asymmetric OC-IP produces T = 0 at 4 V; which means a non-normally black operation. In general, an LCD is operated normally black or normally white; thus, a dynamic optical compensator, which has been updated from the device described in our previous work [7], was used (see Section 3.5).  Figure 4 shows the experimentally obtained transmittance-voltage (V-T)-curves of IPS LCDs, as recorded at 25 • C using a DMS-703 (Autronic Melchers, GMb) instrument. Interestingly, in the symmetric compensation system, the introduction of optical compensation introduces a wide operating voltage range, as shown in Figure 4. Regarding the V-T curve, refer to [14], where the Freedericksz transition is described.  Figure 4 shows the experimentally obtained transmittance-voltage (V-T)-curves of IPS LCDs, as recorded at 25 °C using a DMS-703 (Autronic Melchers, GMb) instrument. Interestingly, in the symmetric compensation system, the introduction of optical compensation introduces a wide operating voltage range, as shown in Figure 4. Regarding the V-T curve, refer to [14], where the Freedericksz transition is described.  Figure 5 shows the V-T curves of the p-OC-IPS device without optical compensation (α = 0) and the p-OC-IPS device with optical compensation, (α = −6.8°). The proposed asymmetric OC-IP produces T = 0 at 4 V; which means a non-normally black operation. In general, an LCD is operated normally black or normally white; thus, a dynamic optical compensator, which has been updated from the device described in our previous work [7], was used (see Section 3.5).  Figure 5 shows the V-T curves of the p-OC-IPS device without optical compensation (α = 0) and the p-OC-IPS device with optical compensation, (α = −6.8 • ). The proposed asymmetric OC-IP produces T = 0 at 4 V; which means a non-normally black operation. In general, an LCD is operated normally black or normally white; thus, a dynamic optical compensator, which has been updated from the device described in our previous work [7], was used (see Section 3.5). Using these quantities, The experimental results in Tables 1 and 2, indicate that the response time of the proposed asymmetric OC-IPS and OC-FFS devices are reduced by 42-56% compared with those of single cells and symmetric OC-IPS and OC-FFS devices. Approximately the same results were obtained for the OC-FFS device, and we will report the corresponding data elsewhere. These results indicate that the response time in the switching-on process will be greatly reduced by adopting the overdriving technique [12].

Experimental Results of Response Time
The physical properties of the LC materials and the specifications of the LCD ce in the present work are described as follows: The cell gap of the sample cells was 3. Using these quantities, The experimental results in Tables 1 and 2, indicate that the response time of t posed asymmetric OC-IPS and OC-FFS devices are reduced by 42-56% compare those of single cells and symmetric OC-IPS and OC-FFS devices. Approximately th results were obtained for the OC-FFS device, and we will report the correspondin elsewhere. These results indicate that the response time in the switching-on proce be greatly reduced by adopting the overdriving technique [12].

Temporal Derivatives of I 1 and I 2 and Their Comparison
We here derive temporal derivatives of I 1 and I 2 For an OC-IPS: Thus, we obtain a formula, the F-function, by taking the ratio between Equations (13) and (14) as follows, where the two minus signs cancel each other: The F-function ( ∂I 2 ∂t / ∂I 1 ∂t ) is shown in Figure 6.

= cos(4 ) − sin(4 )cot(4 )
The F-function ( ) is shown in Figure 6.  Figure 6 shows that the temporal derivative of I2 is much larger than that of I1 during the switching-off process, consistent with the experimental results obtained in the present work. However, it also shows that this effect terminates at a switching angle of 15° and that the relation is thereafter inverted. However, if necessary, a dynamic compensator can be used to eliminate the phase-advancement after the decay process for the switching-on process, the removal of the applied voltage causes an overvoltage, resolving this problem [11].
This practice is demonstrated in Figure 7.   Figure 6 shows that the temporal derivative of I 2 is much larger than that of I 1 during the switching-off process, consistent with the experimental results obtained in the present work. However, it also shows that this effect terminates at a switching angle of 15 • and that the relation is thereafter inverted. However, if necessary, a dynamic compensator can be used to eliminate the phase-advancement after the decay process for the switching-on process, the removal of the applied voltage causes an overvoltage, resolving this problem [11].
This practice is demonstrated in Figure 7.
Symmetry 2021, 13, 1143 7 of 9 = −2 sin(4 ) cos(4 ) − sin(4 )cot (4 ) Thus, we obtain a formula, the F-function, by taking the ratio between Equations (13) and (14) as follows, where the two minus signs cancel each other: = cos(4 ) − sin(4 )cot (4 ) The F-function ( ) is shown in Figure 6.  Figure 6 shows that the temporal derivative of I2 is much larger than that of I1 during the switching-off process, consistent with the experimental results obtained in the present work. However, it also shows that this effect terminates at a switching angle of 15° and that the relation is thereafter inverted. However, if necessary, a dynamic compensator can be used to eliminate the phase-advancement after the decay process for the switching-on process, the removal of the applied voltage causes an overvoltage, resolving this problem [11].
This practice is demonstrated in Figure 7.