1. Introduction

In recent years, there has been a huge effort in finding suitable technologies for developing reflective optical devices whose selective spectral band could be dynamically controlled [1,2]. Tuning the reflection band by shifting the wavelength and/or switching it on and off is essential in applications such as color filter arrays, optical communications, ophthalmic lenses, smart windows, transparent/reflective displays, or multi-color lasers.

Cholesteric liquid crystals (CLC) are good candidates for these purposes. When these materials are placed in thin (a few µm) glass cells conditioned to induce a homogeneous –i.e., parallel to the glass plates– alignment of the molecules, CLCs self-organize in a helical structure twisting around an axis. This configuration is formally equivalent to a Bragg mirror, selectively reflecting one circular component of light, within a spectral band centered on a wavelength proportional to the helical pitch.

However, in conventional CLCs, electrically-driven color shifting is limited and practically difficult to obtain. One of the simplest ways to unwind the helix should be by in-plane-switching (IPS) i.e., by applying an electric field normal to the CLC helical axis in positive dielectric anisotropy $(\Delta \epsilon ={\epsilon }_{II}-{\epsilon }_{\perp }>0)$CLCs [3]. This would induce a color change towards longer wavelengths. However, a number of difficulties hinder this approach. Inter-digitized electrodes are required to create the in-plane electric field, the field within the cell is inhomogeneous, so the applied electric torque is spatially non-uniform [4]; consequently, the required applied voltage for IPS is very high. Moreover, the reflectance amplitude also decreases when increasing voltage as the number of periods inside the material decreases due to pitch elongation.

An alternative solution for color shifting exploits the pitch reduction occurring in positive ∆ε CLCs by electrically induced switch between planar state and focal conic state (Helfrich instability), when the electric field is applied between the two outer substrates, i.e., parallel to the CLC helical axis [5]. In that case, the strong anchoring energy of the CLC on the glass substrates forces the helix to squeeze near the interfaces inducing a shorter effective pitch and consequently a blue shift of the reflection peak. Nevertheless, this helix squeezing only exists in a very small tuning range of applied voltages thus requiring alternative solutions for their use in practical applications.

A first approach employed a polymer network to create liquid crystal gels where the reflected wavelength shows a blue-shift when a high voltage is applied [6]. A flexible CLC polymer film retaining the color induced by a voltage has been also proposed [7]. However, the electrically induced color is not tunable after the polymerization of the polymer network. Recently another research group introduced a stabilized Helfrich deformation in a positive ∆ε CLC cell polymerized with spatial pattern distribution that exhibits blue-shift with the applied voltage [1]. Contrary to previous technologies, the spectral shift range is 150 nm while preserving a reflectance value above 30%. Nevertheless, some haze can be expected from the stabilized Helfrich deformation structure. If this is not an issue for reflective displays, it can be a major limitation for optical devices working in transmission.

Negative ∆ε CLCs were also used for color shifting by applying an electric field perpendicular to the glass cells but there is no consensus on the underlying mechanism. The electrohydrodynamic effect was invoked to obtain a 10nm tuning range CLC laser using a 10V/μm DC voltage [8]. However, some other group used DC field patterned electrodes to induce distortion of the glass substrates. They suggested the CLC pitch modulation could be attributed to an electro-mechanical effect [9]. Here again, the tuning range was limited to 50 nm in the visible range for an applied voltage higher than 150V.

As a result, chiral liquid crystals phases other than standard CLCs have been explored for color shifting. A newly discovered LC phase known as heliconical cholesterics was shown to have selective reflection [10] and to exhibit a blue shift with the applied voltage. However, it requires a very specific positive dielectric anisotropy CLC that satisfies a particular relationship between its elastic constants for twisting K₂₂ and bending K₃₃: K₂₂> K₃₃.

Dual Frequency cholesteric liquid crystals (DFCLCs), obtained by mixing a Dual Frequency LC (DFLC) with a chiral dopant, have also demonstrated to produce Bragg reflection [11]. These materials are able to maintain the frequency-dependent properties of DFLCs while being organized in the periodical helical planar structure of cholesterics. DFCLC advantages over standard CLC arise from their peculiar behavior with frequency. Indeed, driving the device above and below their crossover frequency offers DFCLCs the possibility of achieving a reflection-transmission switch while avoiding focal conic state. Their possibility for color shifting in their reflective state has also been confirmed; however they require special electrode geometry, like in conventional CLCs [12]. These electrodes are known to be more complex and more expensive to produce than standard electrodes and make the homogeneity of the fields inside the cell more difficult to guarantee; using a standard electrode configuration is advantageous and simplifies the devices design considerably. Thus, being able to control the reflection peak position, while taking advantage of the DFLC properties with standard electrodes, would be very advantageous for practical applications.

In this work, we demonstrate that employing a specific configuration of a DFCLC (dual frequency nematic LC + chiral dopant) with standard electrodes, the reflection peak can be dynamically shifted on a wide spectral range when varying the applied frequency. This allows for a wide pitch modulation giving the possibility of obtaining a fully tunable reflection band shifting and switching in one device.

2. Experimental

Several dual frequency liquid crystals were evaluated for the study. A first constraint is that the birefringence Δn should be kept as low as possible, since the lower the birefringence, the narrower the reflection peak. The crossover frequency, fc, should be as low as possible as well, since driving the devices at high frequency produces dielectric heating of the system [13]. Crossover frequencies should ideally remain below fc = 5kHz. However, although this frequency is reasonable for high birefringence compounds, it is harder to reach for low birefringence DFLC mixtures, than for those with high birefringence compounds. These parameters are thoroughly explained in [14]. Finally we selected a DFLC mixture, W-1978C, purchased from Military University of Technology (MUT, Warsaw, Poland). The mixture exhibits a good trade-off of these characteristics with Δn = 0.123, fc = 1.54kHz and an approximately constant negative Δε above 10kHz, and at 1kHz, Δε = 1.85 and at 1MHz Δε = 2.55 [14].

A chiral dopant was selected for preparing cholesteric mixtures from the DFLC. Chiral dopants (CD) with high helical twisting power (HTP) are desirable so the amount of chiral dopant needed to achieve a certain cholesteric pitch is smaller,, . The difficulty relies in achieving high HTP. In general, highest HTP chiral dopants are achieved with compounds that possess axial chirality, unfortunately, the available number of such CDs is limited. The selected CD was R-5011 (HCCH, China), with an HTP = 96-106μm⁻¹.

Three dual frequency cholesteric liquid crystal mixtures were prepared with different chiral dopant concentrations. These were calculated for the DFCLC mixture to have a reflection peak in the blue (440nm), green (530nm) and red (620nm) wavelengths with 3.31%, 2.75% and 2.34% of chiral dopant respectively. Additional mixtures were prepared for the cell thickness variation study with reflection peaks in: 480nm, 500nm, 600nm and 660nm and chiral dopant concentrations of: 3.02%, 2.90%, 2.42% and 2.20% respectively.

The desired pitch (in µm) can be calculated with Eq. (1):

Cells with ITO coated glass substrates were obtained from E.H.C. co. Ltd. (Japan). The cells are conditioned for homogeneous alignment with rubbed polyimide, their thicknesses are 3 and 7µm, their active area 1cm², and ITO resistivity 10Ω/sq. Cells were filled up by capillarity in a hot stage at 110°C with any of the three DFCLC mixtures in isotropic state. Then the samples were cooled down for 20 minutes and wired. DFCLCs get aligned with the helix axes perpendicular to the substrates. The DFCLC layers were observed with a polarizing optical microscope Nikon Eclipse LV100POL in reflection mode. The devices were addressed using waveform function generator Agilent 33521A, and high voltage linear amplifier FLC electronics A400. Spectra were taken with an Ocean Optics USB4000 spectrophotometer. All measurements were carried out at room temperature. The cells did not suffer from dielectric heating upon applying voltage and the cells temperature was constant.

3. Results

3.1 Reflectance peak switch

The prepared DFCLCs mixtures got organized in the cholesteric helical planar structure of cholesterics that produces a Bragg reflection, while maintaining the frequency dependent properties of dual frequency LCs as well. The crossover frequency (fc) value did not shift significantly from the dual frequency nematic LC value. Crossover frequency is known to increase with added chiral dopants; the effect is well explained in [15].

Using the standard electrical driving of DFLC devices, i.e., switching the applied frequency below and above fc, like in standard DFLCs, the reflection peak can be switched on and off (transmission/reflection switching).

Figure 1 shows the electrooptical switching behavior of the three kinds of DFCLC devices, blue (440nm), green (530nm) and red (620nm), as seen by POM when changing the applied frequency.

 

Fig. 1 Dual Frequency Cholesteric LC switching behavior at different applied frequencies (100Hz (left), 15kHz (right)). For each kind of DFCLC devices (blue 440nm, green 530nm and red 620nm), the cell gap was 3µm.

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The texture images are taken at the edge of the ITO layer to show the pixel switching in reflection mode. The sketches on the bottom show the actual orientation of the liquid crystal molecules. In the off-state (middle images), the LC is organized in helical planar structure (reflective). Upon applying voltage at low frequencies (100Hz), the LC texture changes to focal conic above the threshold voltage (Vth), and, at higher voltages, it eventually changes to homeotropic state. We will refer to this second applied voltage as the working voltage (Vw); its value being the actual voltage required for achieving a transmissive state (Fig. 1, left).

If the applied voltage is switched off in this moment, the relaxation from homeotropic cannot return to the initial helical structure; rather the focal conic structure shows up, producing scattering and depolarization. Instead, the low frequency is switched to high frequency (15kHz) at the same applied voltage, the LC molecules reorient back from homeotropic to the helical structure (Fig. 1, right). As no relaxation of LC molecules is involved, the switching times of DFLCs with varying frequency are significantly short.

The working voltage increases with the amount of chiral dopant, the threshold to achieve homeotropic state increases with increasing helical twist. The voltage range of blue (440nm), green (530nm) and red (620nm) DFCLC devices are in the range of 60-90V. Applied frequencies of 100kHz and 15kHz were chosen as low and high frequency regimes based on the DFCLC Δε variation with frequency: Δε becomes constant below and above these frequencies respectively.

3.2 Reflectance peak shift and pitch modulation

The manufactured DFCLC cells were characterized at different applied frequencies (always above the working voltage). As explained above, when applying very low or very high frequencies, the DFCLC gets reoriented homeotropically or planar respectively. However, at intermediate applied frequencies –frequencies slightly above the crossover frequency (f≥fc)– the cholesteric pitch can be modified. The reflection peak position of a DFCLC with varying frequency in a 3µm thick cell is shown in Fig. 2. This effect can also be observed in Visualization 1. The original reflection peak is located at 530nm. At high applied frequencies, f>10kHz, and applied voltage above working voltage, V>Vw, the LC is in the helical planar configuration with the same pitch as in the off-state. When the frequency is lowered, from 10kHz to 3kHz, and the voltage is above working voltage, the helices starts to untwist, the pitch increases and the reflection peak is shifted to longer wavelengths, from 530nm to 635nm. The actual reflectance color of the cell is shown in the insets for each pitch change.

 

Fig. 2 Position of the DFCLC reflection peak vs. applied frequency and the corresponding LC textures shown in the micrographs (see Visualization 1).

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The alignment layer used in these devices is rubbed polyimide, which induces a preferential direction of the LC molecules on the surfaces. The LC molecules next to the surfaces are anchored to these surfaces, so the cholesteric helices are fixed at the top and bottom substrates and the number of turns that fit inside the cell bulk is a whole number of half-periods. When the helices untwist, the LC molecules anchored to the surfaces cannot rotate, thus the helix “jumps” to the next fixed position (rotated 180°), which corresponds to untwisting half a turn of a twist. This effect is shown in Fig. 2; the reflectance peak variation with frequency is not a smooth variation but in steps that corresponds to half a pitch loss on each jump: the pitch length producing a reflection in 530nm is 344nm, thus, there are a total of 8.5 pitches in a 3µm (measured 2.90 ± 0.05µm) thick cell, where the effective refractive index of the cholesteric structure in planar configuration is n_eff = 1.54. The next observed reflection occurs at 565nm, corresponding to 8.0 pitches inside the cell, and, accordingly, a reflection around 600nm implies a number of 7.5 of pitches.

Applying a voltage (V>Vw) at different frequencies, the pitch length can be tuned and the peak shifts to longer wavelengths. However, this shift also produces a decrease in the reflectance efficiency. Figure 3 shows the spectra measured for the DFCLC of a green device (reflection peak in off-state 530nm and 3µm thick cell) with unpolarized light –one of the two components of circular polarized light, the other component is transmitted. Theoretically, the cholesteric structure reflects 50% of the incident unpolarized light. In our case, the maximum reflectance is approximately 45% and small losses can be attributed to substrate and internal reflections. Then, in the frequency range of Δf = 3-15kHz the peak efficiency decreases down to 15% reflection of the total unpolarized light at frequencies closer to crossover frequency (4kHz).

 

Fig. 3 Reflectance efficiency variation and peak shift at different applied frequencies for a DFCLC device with an original reflection in 530nm and 3µm cell gap. The inset shows the reflectance efficiency variation with frequency for 3 and 7µm cell gaps.

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The reflectance efficiency is expected to decrease due to the overall fewer number of pitches in the LC bulk. In order to generate efficient Bragg reflection, a minimum cholesteric layer thickness is needed. Consequently, when the helix is untwisted, the number of layers would decrease and the efficiency would decrease as well.

This hypothesis was tested by measuring the reflectance efficiency variation with frequency in cells with different thicknesses (3 and 7µm). Remarkably, the reflectance losses showed the same trend and same efficiency values ( ± 3%) at frequencies close to crossover frequency (Fig. 3, inset). It is inferred that the helix untwist alone does not explain why the efficiency decreases with frequency. This effect, which is related to the helical structure and switching behavior of cholesteric liquid crystals, is discussed in the next section.

The reflection peak can be tuned over a wide range of wavelengths by modulating the pitch length. In general, upon applying a voltage at intermediate frequencies, the helices untwist and the peaks shift to longer wavelengths. However, another effect shows up when the LC molecules start tilting and the helices start unwinding. The surface alignment prevents the LC to acquire any different position, so the LC molecules next to the surface are anchored in fixed positions and the number of half-pitches is an integer. As the LC molecules start tilting, the helices also get squeezed, hence the pitch decreases slightly, but at some point, as the helices are unwinding, there is a 180° turn to the next fixed position with a loss of half pitch. This effect can be seen in Fig. 4: the reflectance peak was measured at different applied frequencies for 3 and 7µm cells (left and right)) for different starting pitch lengths (440, 480, 530 and 620nm for 3µm cells and 500, 590 and 660nm for 7µm cells). In general, the pitch squeezing effect is more pronounced for larger pitches (red), because there is more room for the helices to readjust, decreasing the pitch before jumping to the next fixed position. Moreover, the dynamic range, (the wavelength range where the peak shift is possible), decreases with longer pitches. For 7µm cell gap the dynamic range is narrower: the shift tunability decreases, from 80 to 100nm to 40-60nm. This is explained by the larger number of pitch turns, as the effect of every jump is proportionally lower than in thin cells.: the pitch length for a reflection peak occurring in 530nm is 344nm. In a 3µm cell (measured 2.90µm), there is a total of 8.5 pitches and in a 7µm cell (measured 6.90µm) there is a total of 20.0 pitches. An overall loss of half a turn implies that in the 3µm, now, having 8.0 pitches in total, the pitch length increased to 362nm, while in the 7µm cell (with 19.5 pitches), the pitch length increased to 353nm. The pitch length variation in 3µm cells is 9nm larger than for 7µm cells for the first pitch jump. This effect is increased as the total amount of turns decreases with successive jumps.

 

Fig. 4 Reflection peak shift at different applied frequencies and different pitch starting points for 3µm cell gap (left) and 7µm cell gap (right).

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4. Discussion

In the previous section, a special intermediate frequency regime was identified where the DFCLC dielectric anisotropy ∆ε, varies while staying in the negative dielectric anisotropy range. Upon decreasing the applied frequency, the reflection peak seems to slightly shift towards shorter wavelengths and then jump to longer wavelengths as if there were a small squeeze of the cholesteric helices followed by an elongation of the pitch.

The understanding of this jump phenomenon requires coming back to the behavior of CLC under applied voltage. Indeed, in this particular regime, the DFCLC mixture behaves as a CLC with a negative dielectric anisotropy ∆ε for an electric field applied parallel to the helical axis. In that case, the only mechanism for director destabilization is the electrohydrodynamic (EHD) distortion of the cholesteric planar texture [16]. It happens for negative CLCs with sufficient electrical conductivity anisotropy (Δσ≠0) under low frequency AC field (Carr-Helfrich mechanism). Because of the conductivity anisotropy, ions inside the medium move more easily in the direction of the electric field than perpendicular to it, creating a charge separation. This space charge will induce an electric field normal to the helical axis causing the liquid crystal to flow. As a result, two torques will enter in competition inside the DFCLC: the induced space charge torque Γ_EHD will tend to destabilize the initial orientation of the LC directors giving rise to a periodic bending of the cholesteric plane. On the contrary, the dielectric torque will tend to maintain the CLC helices perpendicular to the substrate plane. If ∆ε is large enough in absolute value, meaning the dielectric torque is large enough, the square grid perturbation resulting from the 2D periodic bending of the CLC can be followed by another planar texture. This LC planar texture will present a higher number of pitches inside the cell (increased by one or one half of turns), when the applied voltage is above a certain threshold V_{th_EHC} leading to a blue shift [17].

In the W-1978C material, the variation of the parallel component of the dielectric constant ε with the applied frequency was reported to be very steep between fc (around 1kHz) and 10kHz and to be almost constant above 10kHz [15]. During our experimental characterization, no significant change was noted for these values with the addition of chiral dopant. Moreover, the conductivity of our DFCLC was measured at the operative voltage (80V) parallel and perpendicular to the long molecular axis. A conductivity anisotropy Δσ of 1.84μS/m was found corresponding to a ratio ${\sigma }_{II}/{\sigma }_{\perp }=$8.75. This value is superior to the ${\sigma }_{II}/{\sigma }_{\perp }=$ 1.5 reported in [18] for a negative Δε CLC where EHD instabilities were already observed. Furthermore, Δσ and Δε have opposite signs unlike in [9]. As a result, our DFCLC should be a good candidate to exhibit the EHD effect in the intermediate frequency regime. For frequencies above 10kHz, Δε is almost constant and lower than −2.55, so the dielectric torque dominates over the EHD torque and the planar structure is maintained. When the excitation frequency f is decreased and f is small enough, threshold voltage in a standard negative ∆ε CLC decreases with the applied frequency [19]. In the case of DFCLC, Δε is also decreasing in absolute value, so the applied voltage threshold is increased by $1/\sqrt{\left|\Delta \epsilon \right|}$ [17]. As Δε varies from −2.55 to 0 when the excitation frequency varies from 10kHz to 1kHz, we can deduce that the threshold voltage is decreasing with the driving frequency. As a result, for a given applied frequency f and voltage V, such as V≥V_{th_EHC}: the space-induced torque contribution provokes a twist and bend of the liquid crystal molecules while the dielectric torque tends to stabilize the helical structure. Our hypothesis is that if the applied voltage is increased above the threshold V_{th_EHC}, the periodical bending of the helices coupled with the strong anchoring energy of the substrate surfaces leads to another planar texture with a number of pitches decreased by one half turn that provokes a jump towards longer wavelengths. It is the opposite of what was observed in [17] in a negative Δε CLC where the number of pitches in the cell was increased by one or by one half. We believe that this difference in the pitch behavior that can be attributed in both cases to the same EHD effect needs to be clarified in the future. A possible explanation could be linked to the difference in conductivity anisotropy existing between a conventional CLC as used in [17] and our material. As our DFCLC exhibits a ratio ${\sigma }_{II}/{\sigma }_{\perp }$ five times higher than a conventional CLC, the destabilization of the helix in this case is expected to be stronger and the angle between the normal to the substrate and the helix axis higher than in a traditional CLC leading to an easier untwisting of the helices. The process described above can be repeated several times when decreasing frequencies, inducing successive jumps. A reflectance loss is unavoidable due to the bending and twisting at the helices at each step.

Figure 5 shows a summary of the complete switching process of the DFCLC, (W-1978C + R-5011). The scheme of the LC molecule alignment is shown next to its corresponding texture, as seen between crossed polarizers. The LC switching behavior can be categorized in three segments: at low applied frequencies (below fc), the DFCLC behaves as a CLC with a positive dielectric anisotropy with an electric field applied parallel to its helical axis. When the applied voltage is increased, the planar structure is progressively transformed into a 2D grid and a fingerprint pattern (due to EHD) before going into focal conic state and finally homeotropic state. For frequencies above fc, the DFCLC behaves as a CLC with a negative dielectric anisotropy with an electric field applied parallel to its helical axis. For high frequencies (f>>fc), planar structure is maintained and at intermediate frequencies, several planar structures are formed successfully when frequency is decreased inducing an electrically driven discrete color shift.

 

Fig. 5 Complete switching process, textures and alignments of the DFCLC upon applying voltage at different frequency ranges

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5. Conclusions

In this work, we have demonstrated an electrically-driven reflective optical device whose Bragg reflection peak can be shifted towards longer wavelengths by modifying the driving frequency. It consists of a cell filled with a specific dual frequency cholesteric liquid crystal mixture with low crossover frequency and low birefringence. By exploiting the electrohydrodynamic effect in the intermediate frequency regime (where ∆ε is negative but varying), such cells can be driven using the standard electrode configuration rather than IPS. The device can also operate as a switch between transmission and reflection without encountering the focal conic state (haze) as it takes advantage of its dual frequency properties. This versatility in its working modes, as well as its moderate applied voltage, and acceptable reflectance amplitude (45% - 15%), make it suitable for many practical applications.