In Figure 5.16 the evolution of the average twistφd is plotted versus time for a range of applied voltages from 1 to 10 V. The average twistφd
is the mean value of the director twist angle at all nodes of the irregular mesh. The initial director orientation is chosen parallel to they-axis (a twist of 90◦) and the succeeding driving configurationsC1−C2−C3−C1− C2−C3−C1were applied, each for a duration of 250 ms. The first period with C1 applied is not strictly necessary since the director is already aligned along they-direction. It is added to illustrate that the azimuthal angle of the average director in this configuration remains along they- direction. The minimum voltage required to rotate the director over an angle of 360◦is 4 V. Near the rotation threshold the total switching time is larger than 250 ms, but with increasing voltage the switching time
decreases.
Figure 5.16: Variation of the average twistφdversus time for different voltages when applying the following sequence of driving configura- tions:C1−C2−C3−C1−C2−C3−C1. Each driving configuration is applied for 250 ms, starting with the director aligned along they-direction.
The evolution of the average twist φd from one driving configura- tion to the next follows approximately an exponential decay. Table 5.1 gives the time constant of the exponential decay, which is a measure of the device speed. In the top row of the first column, the time constant is given for the device with an applied voltage of 5 V. The reported time constant is quite large. However, a reduction of the time constant can be achieved by several means, as illustrated in the table. Increasing the driving voltage, as shown in the bottom row of the table, is an obvi- ous means to lower the time constant. The stronger electric field results in a faster response of the liquid crystal. The dielectric layer lowers the electric field strength in the liquid crystal layer. Therefore reduc- ing the thickness of the dielectric layer brings the liquid crystal closer to the electrodes and increases the field strength inside the liquid crys- tal layer, as illustrated in the second column. In the third column, the thickness of the dielectric layerdis kept the same as in the default case, but its dielectric constant εis increased. In section 5.3.2.a was shown that this increases the strength of the electric field in the liquid crystal layer and thus leads to a faster response of the director.
5.3 Director simulations 105
Table 5.1: Time constant of the exponential decay of the average twist φd with 5 and 10 V applied. Column 1 gives the time constant for the proposed device (default): thickness of the liquid crystal layer d=2.1àm, thicknessdo=1.3àm and dielectric constantεd=3.5 of the dielectric layer, dimensions and spacing of the hexagonsa=3àm and b =5àm. Column 2 shows the effect of reducing the thickness of the dielectric layer and column 3 of increasing its dielectric constant. Col- umn 4 shows the effect of a change in the dimensions of the hexagonal electrodes and their spacing.
a=5àm default d=1.0àm εd=8.5 b=3àm
5 V 117 ms 94 ms 49 ms 62 ms
10 V 36 ms 33 ms 24 ms 22 ms
With the default device configuration of Table 5.1, the tilt angle of the director is lower than 30◦ in the whole liquid crystal layer. For higher voltages, a higher dielectric constant or a thinner dielectric layer the tilt increases up to angles of 60◦ in certain regions. This has a pro- found effect on the homogeneity of the liquid crystal layer and thus on the applicability of the device as a reconfigurable wave plate. An al- ternative approach is to change the size and spacing of the hexagonal electrodes. In this case the time constant can be reduced without a sig- nificant increase in the average tilt angle as shown in the fourth column of Table 5.1. The polar anchoring parameterWppractically does not in- fluence the switching time, but it limits the tilt angle near the surface.
Table 5.2: Time constant of the exponential decay of the average twist φdfor different thicknesses of the liquid crystal layer and applied volt- ages of 5 and 10 V. (All other parameters as in the default case of Ta- ble 5.1).
1.0àm 2.1àm 3.0àm 5 V 80 ms 117 ms 166 ms 10 V 33 ms 36 ms 56 ms
Changing the liquid crystal layer thickness also affects the switch- ing speed. The electric field is the strongest at the bottom of the liquid crystal. For a thicker liquid crystal layer the time constant is expected to increase due to the weaker driving fields at the top. This agrees with the time constant behavior of other liquid crystal devices driven by hor- izontal electric fields [35]. Table 5.2 details the influence of the liquid
crystal layer thickness on the speed of the device. For operation as a wave plate, a certain optical phase retardation is required and chang- ing the thickness of the liquid crystal layer is then not an option.
Finally it is interesting to note that the liquid crystal parameters are not critical to the device operation. In Table 5.3 the switching time con- stant is compared for a number of different liquid crystal materials.
The parameters of these liquid crystals differ over a broad range [10, 11, 32], but the time constants remain similar. The dominant influence on the time constant is the rotational viscosityγ1. For the liquid crys- tals 6CHBT and 5CB,γ1 is significantly lower, leading to smaller time constants.
Table 5.3: Time constant of the exponential decay of the average twist φd for different liquid crystals and applied voltages of 5 and 10 V. (All other parameters as in the default case of Table 5.1).
E7 ZLI-4792 5PCH 6CHBT 5CB
5 V 117 ms 115 ms 112 ms 88 ms 82 ms
10 V 36 ms 45 ms 37 ms 33 ms 30 ms