1. Introduction

Cholesteric liquid crystals (CLCs) are materials that have selective reflection properties by arranging themselves in a periodic helical structure. They can be made with two basic components, a nematic liquid crystal (NLC) and a chiral dopant. The distance over which the director rotates by one cycle is called the pitch. Since the director has no polarity, the period of the helical structure is optically equal to a half of the pitch. When light is incident parallel to the CLC helical axis, only a circularly polarized light with the same handedness as the cholesteric helix is strongly reflected. The center wavelength of the reflection band is called a Bragg wavelength, $\lambda =\overline{n}P=(n_e+n_o)/2$, where the n_e and n_o are extraordinary and ordinary refractive indices of the nematic liquid crystal respectively, and P is pitch of the CLC. Because of the birefringence in the liquid crystal, the reflection band is quite broad, which is given by $\Delta \lambda =\Delta nP=(n_e-n_o)P$ [1,2]. The reflection spectrum from a CLC can be changed by various external stimuli (e.g. electric field, heat, or light). Because of these features, CLCs have been studied in various active photonic applications. In particular, the electric field is mainly used to control the optical properties of CLCs.

There are two primary methods in which a planar CLC cell can be electrically driven. One is to apply an electric field parallel to the helical axis, and the other is to apply it perpendicular to the helical axis. Application of an electric field that is normal to a planar cholesteric layer has been actively studied in bi-stable cholesteric displays and smart windows. The electric field can cause the material to switch between reflective and non-reflective states and the transmittance can be controlled [3–8]. A homogeneously aligned CLC cell driven by an electric field perpendicular to the helical axis is called in-plane switching (IPS) of CLC. Since the CLC pitch can be changed according to the in-plane electric field intensity, the reflection band of the CLC cell also changes due to the applied electric field. The reflected wavelength band can be changed continuously or discontinuously depending on the cell thickness and anchoring condition. These features are used to develop various optical devices, such as CLC dye lasers and notch filters [9–16]. However, in IPS applications for CLC cells, there is a disadvantage that the pitch variation is difficult to uniformly arrange between the electrodes [17], and the pitch transition occurs very slowly, non-simultaneously, and irreversibly. Some studies have investigated using a polymer stabilization process to improve these effects [18–21]. Recently, Y. Inoue group have reported the fast pitch variation in CLC with high response speed using a flash lamp. They observed spectral broadening of the reflection band at the CLC in ms response around the visible wavelength band [22]. However, research on pitch transition dynamics in a cholesteric layer is not sufficient. Most of the previous researches on the CLC pitch transition typically assume that the director configuration inside the cell remains quasi-static during the pitch transition. The dynamics of thin cholesteric layers can be more important from an application point of view because they can potentially be used to construct multi-stable displays and switches [17]. In the conventional quasi-static state, the pitch transition occurs very slowly and allows for a quasi-static approximation that assumes the homogeneous helical structure is not distorted and changes slowly over time. Therefore, it is impossible to observe pitch transition dynamics in the quasi-static state.

In order to observe the pitch transition dynamics in the CLC cell, a wavelength-swept laser (WSL) can be used as an optical broadband source. The WSL has wide 3 dB bandwidth and high-speed scanning. The main advantage of using a WSL is that signals in the wavelength domain have a one-to-one correspondence with signals in the time domain [23–29]. It is very difficult to measure the dynamic wavelength variation of the Bragg reflection due to the dynamic pitch transition in the wavelength domain when the electric field is applied to the CLC cell. This is because wavelength measurements in the spectral domain using an instrument like an optical spectrum analyzer are typically slow due to the slow response of mechanical operation. However, thanks to the main advantage of WSL, dynamically changing the wavelength band can be observed easily in the time domain [30–32].

In this paper, we successfully observe the dynamic pitch jump in a CLC cell with strong anchoring conditions using a WSL as an optical broadband source. We confirm that the previous quasi-static state does not induce a dynamic pitch jump because it does not allow distortion of the helical structure. Through in situ observation of the CLC cell texture, it can be seen that the quasi-static pitch variation occurs slowly and discontinuously by dislocation line motion. In order to investigate the pitch jump, we apply a normal driving method and an over driving method. The over driving method for dynamic pitch jump is performed by applying an electric field sufficient to expel the π wall from the equilibrium helical structure. The over driving field acts not only unwind the helix in a cell, but also shortens the response time of a pitch jump. By measuring the transmission spectrum of the CLC cell dynamically, we observed the entire pitch jump process according to the applied electric field. Application of the over driving field to the in-plane electrode CLC cell shows a dynamic pitch jump in the CLC cell with response time reduced to less than 800 ms.

2. Background

There are two methods used to observe pitch jumps in a CLC cell driven with an electric field. In the over driving method, a high voltage is applied momentarily to a liquid crystal display device, which shortens the reaction time [33,34]. Since the response time of the director decreases as the applied voltage increases, the response time can be reduced by using the over driving method. The rise time in the IPS mode is given by

where $\gamma$ is the rotational viscosity, $\Delta \epsilon$ is dielectric anisotropy, $K_2$is twist elastic constant, $l$is the distance between electrodes, and $d$ is the cell thickness [33]. Figure 1 shows a schematic diagram for normal driving and over driving. In the normal driving method, a voltage is applied in order to obtain a target transmittance, and the response time required to obtain the target transmittance is very long. However, the over driving method shown in Fig. 1(b) can shorten the response time by applying a higher voltage than the normal driving for obtaining the target transmittance. Therefore, it is possible to considerably reduce the time required to reach the target transmittance τ_R using the over driving method rather than the normal driving method.

 

Fig. 1 Liquid crystal driving methods. (a) Normal driving method and (b) over driving method.

Download Full Size | PDF

The CLC cell can be composed of nematic liquid crystal and chiral dopant. By controlling the concentration of the chiral dopant, the natural pitch of the CLC P = 1/(C x HTP) can be determined, where C is the concentration and HTP is the helical twist power of the chiral dopant. The pitch varies when the CLC is confined in a thin film of the substrates with strong anchoring because the directors are fixed on the substrate and the half pitch number of CLC should be quantized by the boundary condition. In a thin film where the anchoring force strongly affects the CLC layer, the pitch value is determined by:

where d is the CLC cell thickness, and N is the half pitch number [10]. When no electric field is applied, the pitch with N half pitches is designated as P₀, and that with N-1 half pitches is designated as P₁. For a finite thickness, the pitch changes discontinuously by expelling one π wall at a time to avoid elastic energy divergence. The π wall where the angle between the directors and the field direction range from 0 to π tends not to align along the electric field direction in order to maintain the helical structure. As the electric field intensity increases, other regions favoring alignment along the electric field direction are expanded and the π walls contract. This phenomenon increases the deformation energy of the CLC. The total energy per unit surface of the CLC is given by

where $K_{22}$is the twist elastic constant, $q_0=2\pi /P_0$, $\Delta \epsilon$ is dielectric anisotropy, and ${\varphi }_n$is the twist angle in the N half pitch state. When the deformation energy of the N-1 half pitch state is lower than that for the N half pitch state, the π wall is expelled from the helical axis and the CLC cell has N-1 half pitch [35]. Therefore, when sufficient electric field intensity is applied to the CLC cell, the pitch is changed by relaxation to a lower energy density configuration that containing the number of N-1 half-turns in a layer.

3. Experiments

The fabricated CLC structure is homogeneously composed of aligned horizontal electrode substrates with infinite surface anchoring strength. The electrode layer is coated on one substrate so that an electric field could be applied perpendicular to the helical axis. The alignment layer is formed by polyimide (AL3046) on both substrates. The width between electrodes is 210 μm, which is about 8 times larger than the diameter of the laser source, and the cell thickness is about 13 μm. The CLC is inserted into the cell as an isotropic phase, and the rim was filled with epoxy to prevent contact with air.

The CLC was prepared by mixing a nematic liquid crystal (ML-9704) and a chiral dopant (S811) in order to locate the Bragg wavelength of 1304.2 nm. Figure 2(a) shows the normalized transmitted spectrum when no electric field is applied to the cell. The center wavelength is 1304.2 nm, and the 3-dB reflection bandwidth is 84.8 nm. Figure 2(b) shows a photograph of a microscope image of the cell in the planar state when no electric field is applied. The dark areas of the photograph are the electrodes, and a horizontal electric field is applied in the central bright area. The white dot in the central bright area is a laser beam with ~25 μm diameter. The red lines above the electrode region are oily streaks, which usually appear when the directors are bent in CLC layers [34,36,37].

 

Fig. 2 (a) Normalized transmittance spectrum and (b) microphotograph of the planar CLC state when the applied electric field is zero.

Download Full Size | PDF

Figure 3(a) shows the schematic diagram of the WSL, which is used as a broadband optical source. The WSL consists of two semiconductor optical amplifiers (SOAs), an optical isolator, a 10% output coupler, an optical circulator, three polarization controllers, a diffraction grating with 600 grooves/mm, two achromatic doublet lenses, and a polygonal scanning mirror [23]. Two SOAs are used to achieve high output power. The wavelength scanning filter contains a diffraction grating, a telescope, and a polygonal scanning mirror. It allows scanning over a wide range of wavelengths. The telescope is made from two achromatic doublet lenses in an infinite-conjugate configuration with the grating at the front focal plane of the first lens and the polygonal scanning axis at the back focal plane of the second lens. The parallel beam from the collimator is diffracted by the diffraction grating and the first order beam is aligned along the optical axis of the telescope. The respective wavelength components have different convergence angle at the polygonal scanning mirror. Therefore, the polygonal scanning mirror reflects back only the spectral components within a narrow resolution band normal to the front facet of the polygonal scanning mirror. As the polygonal scanning mirror rotates, the laser wavelength is continuously swept within the gain band over time. The center wavelength, 3 dB scanning range, repetition rate, wavelength scanning speed, and average output power are 1310 nm, 133 nm, 3.6 kHz, 0.73 nm/μs, and 80 mW, respectively. Figures 3(b) and 3(c) show the optical spectrum and the temporal output of the WSL, respectively. As mentioned above, the optical spectrum and the temporal output show a one-to-one correspondence with each other.

 

Fig. 3 (a) Experimental setup for wavelength-swept laser, (b) optical spectrum in wavelength domain, and (c) pulse profile in temporal domain.

Download Full Size | PDF

Figure 4 shows a schematic diagram of the experimental setup for measuring the dynamic pitch jump in the CLC cell. The WSL output is divided by a 3-dB optical fiber coupler and then is incident on the measurement setup and a fiber Bragg grating (FBG) through an optical circulator. The beam incident on the measurement setup is set to left-handed circularly polarized light using a polarization beam splitter (PBS) and a quarter wave plate (QWP), and is then incident vertically on the CLC cell. The beam transmitted through the CLC cell is separated into two beams through a beam splitter (BS), which are incident on a CCD camera (Tucsen) and an optical fiber collimator, respectively. The FBG is used as a reference signal, and its reflection wavelength and line width are 1284.5 nm and 0.02 nm, respectively. At the second 3 dB fiber coupler, the beam from the BS and the reflected beam from the FBG are combined. Finally, the combined beam is converted to an electrical signal by a high-speed photodiode, sampled with a DAQ (data acquisition) module, and stored and processed using the LabView program.

 

Fig. 4 CLC dynamic pitch measurement setup scheme. (WSL: wavelength-swept laser, PBS: polarization beam splitter, QWP: quarter wave plate, BS: beam splitter, CCD: charge-coupled device, FBG: fiber Bragg grating)

Download Full Size | PDF

Figure 5(a) shows the temporal profile of the combined beam, which is measured with the LabView program. The peak signal represents the reflected wavelength from the FBG. Since the output of the WSL in the time domain corresponds to the wavelength in the spectral domain, the temporal profile can be converted into a wavelength profile based on the FBG signal. Figure 5(b) shows a graph obtained by converting the time axis in Fig. 5(a) into wavelength. The sampling rate is set to 2 Msamples/s, and the spectrum can be resolved at approximately 0.35 nm intervals. 5 kHz sinusoidal AC voltage is applied to the CLC cell using a function generator (Agilent) and an amplifier (Trek). The RMS voltage ranges from 20 V_rms to 860 V_rms. The corresponded electric filed ranges from 0.08 V/μm to 4.11 V/μm. All measurements are designed to be precisely controlled by the LabView program.

 

Fig. 5 Transmission signal from a CLC cell (a) in the time domain and (b) the same spectrum with the axis transformed to wavelength when the applied electric field is zero.

Download Full Size | PDF

4. Results and discussions

The applied electric field is adjusted to increase by 0.1 V/μm in order to observe the quasi-static pitch variation in the CLC cell. Figure 6 shows the photomicrographs and the normalized transmission spectra according to the electric field. In Fig. 6(a), 6(b), and 6(c), the bright white dot at the center shows the incident light source. The inset graphs in Fig. 6(a), 6(b), and 6(c) correspond to the normalized transmission spectra for each electric field shown in the photograph. Figure 6(a) shows the CLC cell texture when the applied electric field is 0.08 V/μm, which is close to zero. This is designated as the P₀ state. The pitch maintains the P₀ state continuously while increasing the electric field up to about 1.40 V/μm as shown in Fig. 6(d). Figure 6(b) shows that the pitch changes from the P₀ to the P₁ state by moving of dislocation line after applying an electric field of 1.42 V/μm. The dashed line represents the dislocation line, and the inner and outer regions of the dashed line have states P₀ and P₁, respectively. The domain of the P₁ state is presented as a dark region (outside the dashed line) and gradually expands as the dislocation line moves. The transmission spectrum changes discontinuously as the measurement area changes from the domain in the P₀ state to the domain in the P₁ state. As the reflection band moves towards longer wavelengths, the intensity of the transmission beam increases. Therefore, the white dot of the WSL beam in the P₁ state is brighter than that in the P₀ state. The pitch is maintained in the P₁ state continuously while the electric field increased to about 2.80 V/μm. Figure 6(c) shows the CLC cell texture after the pitch is changed from the P₁ to P₂ state as the applied electric field increases up to 2.85 V/μm. This variation is also occurred by moving of the dislocation line [10,38]. This is expected due to the non-uniform potential barrier of the electrode [39,40]. If the potential barrier is relatively low in a certain region, then the pitch transition occurs locally, and the region gradually expands. These results seem to show quasi-static variation in that the homogeneous helical structure remains undistorted and only the pitch is slowly changes with time. Therefore, pitch transition does not occur simultaneously over the entire region during quasi-static variation [10,17,38]. Figure 6(d) shows the transmission spectra measured at an electric field intensity ranging from 0.08 V/μm to 3.77 V/μm in 0.1 V/μm increments. The critical electric fields causing transitions from P₀ to P₁ and from P₁ to P₂ are 1.42 and 2.85 V/μm, respectively. The left edge wavelength of the reflection band shifted to longer wavelengths of 42.8 nm and 45.2 nm for the two transitions, respectively.

 

Fig. 6 Microphotographs of the CLC cell when the applied electric field strength is (a) 0.08 V/μm, (b) 1.42V/μm, (c) 2.85 V/μm, and (d) the normalized transmission spectra as the electric field strength increases from 0.08 V/μm to 3.77 V/μm in 0.1 V/μm increments.

Download Full Size | PDF

Two driving methods were applied to observe the dynamic pitch jump in the CLC cell. As a normal driving method, the intensity of driving electric field is set to observe the dynamic pitch jump from the P₀ to the P₁ state. Figure 7 shows the transmission spectra over time after applying a normal driving electric field of 2.93 V/μm. The values in the figure legend indicate the elapsed time in milliseconds. The electric field of 2.93 V/μm is sufficient to maintain stable pitch in the P₁ state. However, it shows that the pitch still remains in the P₀ state if the electric field is applied for less than 1 second. Figure 7(a) shows the transmission spectra from 100 ms to 140 ms of elapsed time after applying normal driving. The spectra appear to compress by about 30 nm over the first 40 ms. The spectra recover their shapes for 220 ms after compression, thus maintaining the P₀ state as shown in Fig. 7(b). These phenomena can explain why the electric field intensity is not sufficient to expel the π wall. There was no change in the transmission spectrum for a few seconds thereafter. However, after about 16 s elapsed, it was observed that the pitch completely changed from the P₀ to the P₁ state. Figure 7(c) shows the transmission spectra from 3.6 s to 16 s of elapsed time when the applied electric field intensity changes from 0.08 V/μm to 2.93 V/μm. This is because the domain of the P₀ state disappears as the domain of the P₁ state expands. Therefore, transmittance around 1290 nm, which is the left edge of the reflection band of the P₁ state, gradually increases. Conversely, the transmittance around 1360 nm, which is the right edge of the reflection band of the P₀ state, gradually decreases. The pitch transition does not occur over the entire region simultaneously under normal driving. However, as the P₀ state begins to change in some area, the area gradually expands, and later the entire area is converted to the P₁ state. Figure 7(d) shows the entire transmission spectra variation for the moving domain when the electric field is applied to the CLC cell for during 16 s. The Visualization 1 plays a movie of the in situ observation of dynamic variation of the transmission spectra for normal driving method. The same process progresses rapidly when the electric field applied to the CLC cell increases further. However, in this experiment, the next pitch jump could not be observed due to the bandwidth limitation of the WSL.

 

Fig. 7 Microphotographs of the CLC cell over (a) 0 s, (b) 0.38 s, and (c) 13 s of elapsed time after an electric field of 2.93 V/μm was applied. (d) The transmittance spectra as the pitch discontinuously changes with time from the P₀ to the P₁ state (see Visualization 1).

Download Full Size | PDF

Next, we applied the over driving method to the CLC cell. It is predicted that applying an over driving electric field to the CLC cell will reduce the response time required to the change the pitch and expel the π wall from the helical axis [33–35]. Figure 8 shows the transmission spectra over time after applying an over driving electric field of 4.11 V/μm for 352 ms and then reducing the electric field to 2.68 V/μm. From the results shown in Fig. 8, the pitch variation in the CLC cell can be divided into three sections based on the elapsed time. The first section shows compression of the reflection band in the CLC cell, as shown in Fig. 8(a). Figure 8(a) shows transmission spectra corresponding to 73 ms to 160 ms of elapsed time after driving. The change in the transmission spectra starts from 73 ms after the over driving method is applied. Thereafter, the width of the reflection band gradually increased until reaching about 160 ms, while the magnitude of the reflectance tended to decrease [22,41]. Finally, it became difficult to distinguish the reflection band, and the reflectance was reduced to almost 50% for all wavelength bands. This compression phenomenon was also observed during normal driving, as shown in Fig. 7(a), but the decreasing reflection band width was relatively smaller than that of Fig. 8(a).

 

Fig. 8 CLC cell transmittance spectra for different elapsed times. (a) Reflection band compression, (b) inhomogeneous helical structure, (c) relaxation of helical structure with blueshift, and (d) three-dimensional transmittance spectra when 4.11 V/μm electric field is applied for 352 ms, followed by application of a 2.68 V/μm driving field (see Visualization 2).

Download Full Size | PDF

In addition, it gradually decreased and then recovered to the original reflection band. This can be seen to affect the helical structure in the cholesteric layer by changing the polar angle of the directors between the electrodes, which is a similar to birefringence control [16]. The second section illustrates a phenomenon that occurs between 160 ms and 430 ms of elapsed time, as shown in the transmission spectra in Fig. 8(b). One can see that the reflection band gradually recovers over time. The transmission spectrum around 352 ms, which is the point at which the applied electric field is reduced from 4.11 V/μm to 2.68 V/μm, is mixed with the reflection band for the pitch in the P₀ and P₁ states. Immediately after reducing the electric field, the two pitch components were mixed at a similar rate, but over time the P₁ structure dominated. The third section shows the process of reaching equilibrium with pitch in the P₁ state. Figure 8(c) shows the process where the P₁ state reaches equilibrium for a short time, and the left edge of the reflection band simultaneously shifts to shorter wavelengths. This process can be seen as relaxation of the helical structure. Figure 8(d) shows three-dimensional transmission spectra showing the overall pitch jump process. It is divided into three sections, as shown in Fig. 8(d). The CLC pitch jump was completed within 800 ms after the over driving electric field is applied. The Visualization 2 was recorded an in situ dynamic variation of the transmission spectra for over driving method. Due to the fast response of the transmission spectra, the movie was slowly played.

5. Summary

We have successfully observed the dynamic pitch jump in cholesteric liquid crystal (CLC) layers having infinite strength surface anchoring conditions by using a high-speed and wide bandwidth wavelength-swept laser. In the case of quasi-static pitch variation, it is very difficult to observe the pitch jump dynamics because the helix distortion does not occur throughout the entire cell simultaneously. In order to measure the dynamics of the pitch jump, we applied two driving methods termed normal driving and over driving. In the case of normal driving, it has been confirmed that the reflection band in the measurement region is discontinuously shifted by movement of the defect wall, and the reflection band was compressed and recovered before the band shifted. However, dynamic pitch jump of the helix was not observed. In the case of over driving, it is possible to observe the entire dynamic pitch jump process in the helical structure of the CLC cell. Pitch variations in the CLC cell can be divided into three sections based on elapsed time. In the first section, the reflection band of the CLC cell was compressed from 73 ms to 160 ms after applying the over driving method. In the second section, a phenomenon occurs between 160 ms and 430 ms of elapsed time. It was found that the reflection band gradually recovered over time, and the reflection bands for the two pitch states were mixed. In the third section, pitch approaches equilibrium over 430 ms to about 800 ms of elapsed time after the pitch jump. This can be seen as a relaxation process in the helical structure. Therefore, the entire reaction time of the over driving method was about 800 ms, which is 10 times faster than the normal driving method. We hope that this study contributes to the development of fast in-plane switching research and the development of new CLC devices.