Optical polarization states of a liquid-crystal blue phase II

The advantages and uniqueness of blue-phase-based electro-optical devices are predicted. In this paper, we present relevant electro-optics behaviors of the transmitted and reflected lights of BPII and try to explain those phenomena through studying the polarization states of the lights. There are two stages of electro-optical behaviors seen in an in-plan-switching BPII cell. Because of the Kerr effect, the birefringence of the linear polarized light is induced and saturated 0.021 at 150 V, and the Kerr constant is ≈ 3 × 10−10 mV−2. As the applied voltage is stronger (>200 V), the influence of the deformation of the lattice structure dominates the transmitted/reflected intensity at different wavelengths, which causes a discontinuous change in the transmitted light intensity and a huge variation in the azimuth angle (80◦) of the polarization state of the transmitted light. As a result the deformation of the lattice structure of the BPII not only induces a linear birefringence but also induces a change in optical rotatory power and then affects the polarization state of the light. These experimental results show that the electro-optical nature of the BPII cell is more complicated than the well-known BPI phase. They also show that BPII can be used not only in transflective devices, but also in field-tunable optical devices. © 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement


Introduction
Blue phase liquid crystals (BPLCs) are one of the chiral liquid-crystal phases, appearing in a narrow temperature range between the isotropic and cholesteric phases.In BPLCs, the molecules spontaneously form structures consisting of double-twisted cylinders (DTCs) and a network of disclinaiton lines.According to arrangements of the DTCs and the disclination lines, three structurally distinct types of blue phase are identified: BP III, BP II, and BP I, appearing in order of decreasing temperature from the isotropic phase.BPIII exhibits a disordered structure [1,2]; BPI and BPII display high-ordered lattice structures, giving rise to unusual physical properties, including a fast electro-optical response [3,4] and Bragg reflection of visible light [5].These characteristics make BPI and BPII very promising materials for prospective applications in novel displays and photonic technology [6][7][8][9][10].In the recent 10 years, we see many publications mentioning the advantages and unique features of BP-based electro-optical devices; but we also find that there are open questions and challenges [11] waiting to be solved by exploring the physical properties of the BPs [12][13][14].
The electro-optic properties of BPI or BPII have been explained by the Kerr effect [15], which is dominated by the magnitude of the Kerr constant K.The theoretical Kerr constant and response time of the cubic BPs should be proportional to the square of the chiral pitch, which controls the lattice parameters of the cubic BPs [16].Because the lattice structures of BPI and BPII are different, the Kerr constant of BPII was found to be proportional to the cube of the chiral pitch [4].It predicts that BPII's electro-optic performance may be better than that of BPI [4,17].Owing to the intrinsic DTC being local anisotropy for the linear polarized light and exhibiting optical activity, based on macroscopic observation, BPs consisting of the DTCs can change the polarization state of transmitting light from linearly polarized light into elliptical light [18,19].In BPII, the optical rotatory power depends on the saturated birefringence and the Bragg reflection wavelength [18].This means that the deformation of the lattice structure can induce a change in optical rotatory power and affect the polarization state of the transmitted light.In this paper, we propose using polarimetry and measurement of the intensity detection to explore the transmitted and reflected optical responses of an in-plane-switching BPII cell.The experimental results present that BPII can be used in transflective devices, as we saw with BPI [20].Both the field-dependent linear birefringence and optical activity should be considered when we look at the electro-optic properties of BPII.These related experimental results given here were not provided or discussed in other previous papers and they will help us to understand the properties of BPII and to develop BPII photonic devices.

Material preparation and measurement
20-wt% left-handed chiral dopant NC01 (from Daily Polymer and its helical twisting powers HTP ≈ 16.7 µm −1 )was mixed with nematic liquid crystal (dielectric anisotropy ∆ε = 5.94, and linear birefringence ∆n ≈ 0.09 at 530 nm) to obtain blue phases in this study.In order to prevent the blue phase from being induced by a supercooled process or an electric field, the phase transition of the LC mixture was checked under slow cooling/heating speeds (0.2 • C /min) in a null field via measurement of the reflection spectrum and the Kossel diagram, as shown in Fig. 1.The phase sequence of the LC mixture is Iso.35 • C BPII 28 • C BPI 21 • C and the temperature range of the BPII is 7 • C. In the following experiments, the BP material was kept in the BPII state (32 • C) by the precision hotstage.Before we started to investigate the electro-optical response of the BPII, we would like to know the change in the reflection peak with an applied voltage.We poured our BP material into a 7.5-µm empty cell consisting of two substrates with transparent conductive films.The reflection peak of BPII in our cell in the null field was at 406 nm.When the applied vertical electric field was larger than 2.13 V/µm, only the intensity of the reflection peak became stronger because of the realignment of the lattice plane induced by the director reorientation.An obvious red shift in the reflected peak happened after 2.66 V/µm and the wavelength shift (∆λ) depended on the square of the electric field, as shown in Fig. 2, due to the one-dimension lattice distortion of the BP lattice.The change in the reflection peak was reversible after turning off the electric field.To measure the the electro-optical response and polarization state of an in-plan-switching BPII (IPS-BPII) cell, we poured the BP material into a 7.5-µm empty cell consisting of interdigital comb-like electrodes, where the electrode width and gap are 8 and 12 µm, respectively.The experimental setup for measuring the electro-optical response was based on a transmission/reflection microscopic system with crossed polarizers, in which the transmission axes of the polarizers and analyzer were at 45 • and −45 • with respect to the direction of the in-plan electric field.The polarization state was measured by Polarimetry (PAX5710VIS-T, Thorslab), and the probe beam was supplied by a tunable multi-wavelength LED light source(SLC-SA02-US, Mightex).The experimental setup is shown in Fig. 3.A 1-kHz square-wave AC signal was applied to drive the IPS-BPII cell through the electrode pattern.Due to the limitation of our power supply, the highest AC voltage, we can apply, was 400 V.

Results and discussion
Intensities of the transmitted and reflected light of the IPS-BPII cell were measured by the crossed-polarizer microscope equipped with a tunable multi-wavelength LED light source.Notice that we did not put any reflector behind the cell, the reflected light of the IPS-BPII cell came from the periodic lattice structure inside the BPII, as we mentioned in our previous paper [20].Figure 4 exhibits the voltage-dependent transmission/reflection for different incident wavelengths.Basically, the transmission behaviors can be explained very well by the electro-optical Kerr effect [15], as shown in Eq. ( 1) in the low voltage regime.
where ∆n ind is the induced birefringence of the linear polarization light due to the electro-optic Kerr effect and can be described by the incident wavelength λ, Kerr constant K, and the electric field E, as shown in Eq. ( 2).In Eq. ( 1), the ϕ is the angle between the polarization direction of the incident light and the induced optical axis of the BPII, and d is the effective cell gap.Because the electric field in our sample was applied in the plane of the substrate with the interdigital comb-like electrodes, it was suggested that the field-induced optical axis axis was parallel to the direction of the in-plane electric field.Thus, the ideal value of ϕ is π/4 to obtain the maximum intensity.Under this condition, the transmittance only depends on the phase retardation (i.e. the second term in Eq. ( 1)).The induced birefringence of linear polarization light in our sample was obtained by a polarimeter, and its saturated value is 0.021 occurring at 150 V, and the Kerr constant ≈ 3 × 10 −10 mV −2 .This amount of the Kerr constant in BPII is consistent with the results in other papers [4,15].As the description of Eq. ( 1), one can understand that the phase retardation, as well as the transmitted intensity, decreases with shifting to the longer incident wavelength in Fig. 4. When we look at the voltage-dependent transmission in Fig. 4, we can divide the electro-optic behavior into three stages.Below the 150 V, it follows Eq. ( 1) as the ϕ is kept at π/4 .Between 150 V and 225 V, although the induced birefringence is saturated, the transmittance continuously increases.At 225 V, we see a discontinuous change in the transmitted intensity.
The phase retardation is dominated by not only the induced birefringence, but also the effective thickness d in Eq. (1).Ratio of the effective thicknesses between transmission and reflection cases is 1:2, because the in the reflection case the incident light passes the cell gap twice.We can expect that at the same applied voltage, the phase retardation of the reflected light will be twice of the transmitted light.When the phase retardation in Eq. ( 1) is over π/2, the light intensity starts to decline, as reflecting light in Fig. 4. The reflected intensity of the IPS-BPII cell achieves the highest level at 150 V when the total phase retardation of the reflected light in Eq. ( 1) is π/2.The effective optical light path, which can be calculated from Eq. (1) by using ∆n = 0.021 and λ = 450 nm, is 10.7µm.Similar to the behavior of the transmitted light, the reflected intensity cannot keep at a constant value when the phase retardation is already saturated.The change in the reflected intensity at a high voltage (> 150 V) depends on the incident wavelengths.From Fig. 2, we knew that a red shifting in the reflected wavelength can be detected when the applied voltage stretches the lattice.As the applied voltage is increased, the deformation of the lattice structure becomes serious and then affect the reflected wavelength.Thus, we can expect that voltage-dependent reflection of the BPII in the Fig. 4 is dominated by two possibilities: the phase retardation, because of the Kerr effect; and the Bragg reflection caused by the periodical lattice structure of BPI.
Comparing the electro-optical responses of transmitted/reflected light of the IPS-BPII cell in Fig. 4 to that of the electrical-controlled-birefringence (ECB) cell, such as a nematic cell, we can summarize the difference: When the birefringence for the linear polarized light is saturated, the transmission and reflection do not remain constant in the IPS-BPII cell.The transmission curve shows discontinuous behavior and the reflection curves with 530 nm and 450 nm continuously decrease after 150 V.The above experimental results imply that besides the Kerr effect, in the IPS-BPII cell, other mechanisms of the electro-optical responses should be considered.In order to further discussion on these unusual and complicate electro-optical behavior, we introduce the observation of the polarization states of transmitted and reflected lights of the IPS-BPII cell directly through the polarimeter.In the measurement on the polarization states of the transmitted/reflected lights, the polarization of the incident light was controlled by a linear polarizer, where the transmission axis was at 45 • with respect to the direction of the applied electric field in the IPS-BPII cell, as drawn in Fig. 3.The changes in the transmitted and reflected polarization states are exhibited in Fig. 5.The left and right in the Fig. 5 mean the left-handed (clockwise) and right-handed (anticlockwise) polarization.In Fig. 5, the transmitted light keeps on the left-handed elliptical polarization, but the reflected light changes from left-handed polarization to right-handed one at high applied voltage (V > 300 V).Comparing to the polarization state at the other wavelength (530 nm), we still can see the similar behaviors of the polarization states of the transmitted/reflected lights.But, the change in the polarization handiness of the reflected light occurs when the applied voltage is larger than 320 V at 530 nm.For longer wavelength (655-nm) light, the polarization state of the reflected light keeps on the left-handed polarization until 400 V.We also find that the transition of the polarization handiness of the reflected light is accompanied by a reduction of the elliptical angle.Because these phenomena depend on the incident wavelength, we think that they might present the deformation degree of the lattice structure in the high voltage.
According to the polarization ellipse equation, the amplitude ratio (E 0y /E 0x ) and phase difference of the two perpendicular directions can determine the azimuth angle of the polarization (Ψ), and the ellipticity angle ( χ) shown in Fig. 6.The voltage-dependent azimuth angle and ellipticity of the transmitted polarization state are summarized in Fig. 6.Because BPII exhibits optical isotropy for the linear polarized light and the optical rotatory power is small when the incident wavelength (450 nm) is away from the Bragg reflected peak (406 nm), the polarization state of the transmitted light is not changed at V = 0.As the electric field was applied to the BPII through the interdigital comb-like electrode, due to the electro-optic Kerr effec, BPII's optical anisotropy was induced at 45 • with respect to the polarization state of the incident light.The contribution of the induced birefringence changes the polarization state of the incident light from linear to elliptical when increasing the applied voltage.In Fig. 6, the maximum ellipticity angle is about 30 degrees, and at the higher applied voltage (>300 V), the ellipticity angle decreases.In our sample, because of the small induced birefringence, from Eqs. ( 3) and (4), we can expect that the influence of the phase difference on the azimuth angle is weaker than that on the ellipticity angle.Using Eq. ( 4) and the ellipticity angle in Fig. 6, we can calculate the amplitude ratio, the amplitude ratio decreases 36 % when increasing the applied voltage to 400 V.This also explains the voltage-dependent transmission at 450 nm in Fig. 4. The transmittance of the 450-nm light starts to reduced at 300 V, because the amplitude ratio decreases.It means that the polarization direction of the light exiting the IPS-BPII cell is changed and the ϕ in Eq. ( 1) is less than 45 • .Moreover, the change in the amplitude ratio is also the reasons for obvious variation in the azimuth angle after 300 V in Fig. 6.In the reflection part of Fig. 5, the polarization state is close to linear polarization at different applied voltages, but again the azimuth angle is changed obviously after 300 V.The obvious change in the azimuth angle (i.e.amplitude ratio) can be explained by consider the influence of the optical activity of the BPII.The optical activity rotates the polarization direction of the incident light, which depends on the incident wavelength.As we know, the anomalous optical activity can be induced at the wavelength close to the central reflected peak.Thus, when the central reflected peak is changed by tuning the electric field, the optical activity may change its value and affect the polarization states.From Figs. 4, 5, we can find that a periodic structure and chirality still exist in the IPS-BPII cell and it is why we can detect the reflected light.The contribution of the optical activity from the chirality of the BPII must be considered when we discuss the electro-optical response in the IPS-BPII cell.These experimental results show that the electro-optical phenomenon of the IPS-BPII cell is complicated when we look into the change in the polarization state.The related experimental results are not provided here as they were discussed in the previous studies.

Conclusion
In this paper, we present the interested electro-optics behaviors of the transmitted and reflected lights of BPII and discuss them by measuring polarization states of the light in the IPS-BPII cell.Through the direct measurement of the polarization state, it can help us to discuss the interesting and unusual electro-optic phenomena of BPII.There are two stages of the electro-optical behaviors being seen in an in-plan-switching BPII cell.In the low applied voltage (<200 V), the transition between the optical isotropy and isotropy of the BPII is induced by Kerr effect and the Kerr constant is ≈ 3 × 10 −10 mV −2 .When the applied voltage is larger than 200 V, the influence of the deformation of the lattice structure dominates the transmitted/reflected intensity at different wavelength.When we look at the electro-optic characteristics of the IPS-BPII cell, we should consider both the effect of the field-induced linear birefringence and field-dependent optical activity, which is related to the lattice deformation of BPII.The experimental results shows that the IPS-BPII cell shows the ability to be used in transflective device, because of the contribution of the Kerr effect, lattice structure and the optical activity.

Fig. 1 .
Fig. 1. (Left)Temperature-dependence reflected wavelengths during the cooling/heating processes.(Right) The Kossel diagrams at BPI and BPII.The wavelength of the probe beam is 405 nm.

Fig. 2 .
Fig. 2. Shift in the reflected wavelength in the BPII cell under an application of a vertical electric field.

Fig. 3 .
Fig. 3.The experimental setup of the measurement on the polarization state.