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Abstract
In this work, the optically anisotropic property of dual-frequency liquid crystals (DFLC) in terahertz (THz) regime has been experimentally investigated, which indicates that the refractive index and birefringence of DFLC can be continuously modulated by both the alternating frequency and intensity of the alternating electric field. This tunability originates from the rotation of DFLC molecules induced by alternating electric fields. The results show that by modulating the alternating frequency from 1 kHz to 100 kHz under 30 kV/m electric field, the 600 μm thickness DFLC cell can play as a tunable quarter-wave plate above 0.68 THz, or a half-wave plate above 1.33 THz. Besides, it can be viewed as a tunable THz phase shifter from 0 to π. Therefore, due to its novel tuning mechanism, DFLC will be of great significance in dynamic manipulating on THz phase and polarization.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Over past decades, terahertz (THz) technology and its applications have made tremendous progress in communications, imaging, security [1–3], benefiting from the rapid development of THz sources [4] and detectors [5]. Besides, key functional THz devices, such as filters [6], modulators [7], polarizers and wave plates [8], and isolators [9], have been studied extensively for wave manipulation. Among them, modulation of phase and polarization is always essential for the realization of various functionalities [10–13].
Liquid crystals (LC) are gaining increasing attention in active THz devices, due to the tunable refractive index and birefringence under external electric, magnetic, thermal, or optical fields in the broad THz band [14–17]. Optical properties and the tunability of traditional nematic LC have been widely investigated. Vieweg et al. measured the refractive index ne, no, and the absorption coefficient α of several nematic LC by using the THz-time domain spectroscopy (THz-TDS) [18]. Hsieh et al. reported a tunable THz phase shifter and quarter-wave plate based on a 570 μm-thick nematic LC cell of E7 driven by a 125 V biasing [19]. Wang et al. presented a reflective LC THz waveplate with sub-wavelength metallic grating and metallic ground electrodes [20]. Furthermore, the artificial microstructures filled with LC were proposed to enhance the tunability of THz active functional devices. For examples, Shrekenhamer et al. reported a THz LC tunable metamaterial absorber that can modify the absorption by 30% at 2.62 THz [21]. Wang et al. also demonstrated a graphene-assisted LC tunable THz absorber, and it supports a resonant frequency that can be tuned from 0.75 to 1 THz with an amplitude modulation of ~80% under the biased electric field [22]. Ji et al. demonstrated a dielectric metasurface-enhanced THz LC tunable phase shifter whose tunable phase shift reaches 0.33 π, 1.8 times higher than the ordinary LC cell without metasurface microstructure [23].
However, the thickness of the LC cells is a key problem in current THz LC devices. The wavelength of THz waves is much larger than that of the visible light. The thickness of the LC layer for THz phase devices is generally in the magnitude of tens or even hundreds of micrometers. Due to such large thickness, the LC molecular alignment is barely influenced by the anchor layer. Therefore, the molecular alignment rotates slowly and is hard to be set into the required initial state, especially when the external driving field is removed. In others’ work, the direction of the electric field is always parallel with the propagation direction of the terahertz wave. In this case, complicated transparency electrode structures with high terahertz transmission are needed. For instance, Wang et al. proposed porous graphene electrodes to drive a broadband tunable LC terahertz waveplate [24], and Yang et al. employed indium-tin-oxide nanowhiskers as transparent electrodes in a LC THz quarter-wave plate [25]. However, the intricate electrodes for traditional nematic LC relies on delicate fabrication techniques and the availability of new transparent electrode materials in the THz regime, which is becoming an obstacle in THz phase devices.
Therefore, the novel LC, such as chiral nematic LC [26], twisted nematic LC [27], and dual-frequency LC [28, 29], have been applied to solve this problem. Recently, the dual-frequency liquid crystals (DFLC), whose refractive index can be modulated by the alternating frequency of external alternating electric field, have been introduced into the THz regime [30, 31]. Chen et al. demonstrated an electrically controllable THz metamaterial combined with DFLC cell, in which the resonance frequency can be continuously moved by changing the alternating frequency of the external electric field [30]. Besides, Göbel et al. also realized a tunable THz filter based on the DFLC [31]. However, the optical anisotropic properties and the tuning rules of DFLC in the THz regime under the alternating frequency or different electric field intensity have not been explored systematically.
In this paper, we focus on the alternating-frequency-dependent anisotropic property of DFLC and its tuning rules in the THz regime. The refractive index and birefringence of three types of DFLC with different alternating-frequencies and intensities of the external alternating electric field are experimentally investigated via THz-TDS system. Moreover, the applications of the DFLC cell in the THz tunable waveplates and phase shifters are also explored. The large birefringence and its broad tuning range make DFLC a great candidate over traditional nematic LC in active THz phase devices.
2. Methods
Three DFLC, DP002-016, DP002-026 and DP022-122 (Jiangsu Hecheng Display Technology Co., Ltd), are investigated in this paper. They are all the nematic liquid crystal mixtures with large birefringence. The viscosity coefficient (γ), the phase change temperature from LC state to isotropic state (TN→I) and the response time to the varying electric field (t) are displayed in Table 1. These DFLC are all quickly responding to the electric field.
Table 1. Physical properties of the DFLC
As shown in Fig. 1(a), the DFLC cell is fabricated by five parallel copper wires sandwiched within two 500 μm-thick fused silica substrates. The five copper wires with diameters of 600 μm serve alternatively as positive and negative electrodes. The gap between adjacent copper wires is 3 mm to ensure that the electric field intensity is uniform and the electrodes do not affect transmission of THz waves. Then, the DFLC are injected into blank cells and the DFLC layers are all 600 μm as shown in Fig. 1(b). In the experiment, a square wave voltage (1 kHz~100 kHz, 0 V~90 V), whose alternating frequency and intensity are controlled by the signal generator and voltage amplifier, is applied to drive an alternating electric field between the neighboring electrodes, as displayed in Figs. 1(c) and 1(d).
Fig. 1 (a) Sample of the DFLC cell. (b) The cross-section and geometric parameters of DFLC cell. Schematic diagram when (c) the polarization direction is parallel to the electric field direction and (d) the polarization direction is orthogonal to the electric field direction.
A standard four parabolic-mirror THz-TDS system is utilized to measure the optical properties of the DFLC in the THz regime. THz pulses are generated by a photoconductive antenna excited by a Ti:sapphire femtosecond laser with 75 fs duration and 80MHz repletion rate at 800nm, and a (110) ZnTe crystal is used for detection. The experiments are performed at 25 °C. The refractive index n(ω), extinction coefficient κ(ω) and absorption coefficient α(ω) of the DFLC cell can be calculated by [7]:
where c is the speed of light in vacuum, ω is the angular frequency of THz waves, and d is the thickness of the DFLC layer. ∆δ(ω) = ∆δs−∆δr and t(ω) = Ts/Tr are the phase difference and the transmission amplitude between the sample and the reference, respectively. These parameters are obtained by using Fast Fourier Transform of the measured time-domain data.3. Results and discussions
3.1 Optical properties of randomly arranged DFLC in the THz regime
Frist, we measured the time-domain signals of the air, blank cell with copper wires, and three DFLC cells shown in Fig. 2(a), and obtained the transmission spectra of blank cell and three DFLC cells by using the air signal as the reference. The results are shown in Fig. 2(b). The transmission of the blank cell is about 80%, so its total insertion loss is 20%. The insertion loss of device includes two parts: one is the reflection loss which mainly comes from the interface mismatching in the device structure; the other is the absorption loss of the DFLC material. Considering Fresnel reflection of air-silica interface, the reflection of the silica-air-silica sandwich structure is just close to 20%, so the contribution of the copper wires on insertion loss is very small. The insertion loss of DFLC devices are higher than blank cell due to the absorption of DFLC, especially in the higher frequency range. For example, the insertion loss of LC-016 is 26% at 0.66 THz, which is 6% larger than that of the blank cell. But for the frequency below 0.55 THz, the transmission of LC-016 is slightly higher than blank cell because the Fresnel reflection on LC-silica interface becomes small.
Fig. 2 (a) Time-domain signals of air, blank cell, DP002-016, −026 and −122 without electric field. (b) Transmission spectra of blank cell and three DFLC cells. (c) The refractive index and (d) the absorption coefficient of three DFLC.
Then, we studied the optical properties of the DFLC without external electric field. According to Eqs. (1) and (2) with blank cell as the reference, the refractive index spectra and absorption coefficient curves of three DFLC without electric field biasing are drawn in Figs. 2(c) and 2(d). The DFLC molecules in the 600 μm-thick LC cell are randomly arranged, and the DFLC can be viewed as an isotropic state for THz waves when there is no electric basing or any other preprocessing. Comparison of the three samples shows that DP002-016 has the largest refractive index in the range from 0.2 THz to 1.6 THz. All of the three refractive index curves have negative dispersion with the increase of the frequency. The absorption coefficients of three samples are similar and smaller than 20 cm−1 below 1 THz, so the absorption loss of these three DFLC is small and tolerable in the THz applications.
3.2 Alternating frequency-dependent THz anisotropy of DFLC
Usually, molecules of nematic LC tend to assemble along the direction of electric field, making the LC a uniaxial crystal. However, different from the conventional nematic LC, the molecule alignment of DFLC is not only influenced by the electric field intensity but also by the alternating frequency (defined as fM). We measured the refractive index nx and ny when the polarization directions of linear polarized THz waves are along x-axis and y-axis, respectively, as shown in Figs. 1(c) and 1(d). The alternating electric field is always along y-axis. A THz polarizer is placed behind the DFLC cell. The polarization of which is parallel to the incident THz waves’ polarization direction in the measurement.
The alternating electric field of 30 kV/m with different alternating frequencies from 1 kHz to 100 kHz was applied to drive the three samples. Here, we mainly discuss the properties of DP002-016, the properties of DP002-026 and DP022-122 can be found in the last part of the paper. Figures 3(a) and 3(b) show that the time-domain signals of DFLC cell, which move forward for the x-polarized beam and backward for y-polarized one when the alternating frequency fM increases from 1 kHz to 100 kHz. Therefore, the corresponding refractive index of x- and y-polarization varies to the opposite directions with the increase of fM. They are calculated by Eq. (1) using the blank cell as reference, as shown in Figs. 3(c) and 3(d). The corresponding extinction coefficients shown as Figs. 3(e) and 3(f) are also calculated by Eq. (2). With the increasing fM, κx reduces but κy rises. Take 1 THz for example, κx changes from 0.088 to 0.057, while κy changes from 0.020 to 0.057. κy is smaller than κx, and both of them are always lower than 0.10 from 0.2 THz to 1.6 THz, which indicates the low absorption loss of DFLC in the THz regime no matter how the fM changes.
Fig. 3 Measured (a) x-polarized and (b) y-polarized time-domain signals of the DFLC (DP002-016) cells under the alternating electric field of different alternating frequencies and their corresponding refractive index (c) nx & (d) ny, and extinction coefficient (e) κx & (f) κy.
As shown in Figs. 3(c) and 3(d), there is refractive index dispersion in the THz regime. To simplify the discussion, we define a frequency-independent parameter “group refractive index” to describe the pulse delay induced by the DFLC cell, which is expressed by the pulse delay of the main peaks between the sample and reference as follows:
where Ts and Tr are the time of main pulse peak for the DFLC cells and the reference of the blank cell. Figure 4(a) shows the value of group refractive index when fM increases from 1 kHz to 100 kHz. It can be found that ngx starts to increase from 1.66 at 30 kHz to 1.80 at 80 kHz and it reaches the stable condition at 80 kHz, and the tunable range of ngx(100 kHz)−ngx(1 kHz) reaches 0.14. On the contrary, ngy reduces from 1.86 at 40 kHz to 1.66 at 90 kHz. The tunable range of the refractive index ngy(100 kHz)−ngy(1 kHz) reaches −0.2. The refractive indexes nx and ny experience opposite changing trends with different fM. It can be concluded that the DFLC exhibits an alternating frequency related optical anisotropy at THz regime. Therefore, the refractive index in x- and y-polarization can be continuously tuned by varying the alternating frequency fM of the external electric field with the constant amplitude of 30 kV/m.Fig. 4 (a) Group refractive index curves of with the increase of the fM. The black line is the curve of group refractive index for the y-polarized wave ngy and the red one is ngx. Schematic diagram of the alignment of DFLC molecules and refractive index ellipsoid of DP002-016 at 1 THz under the alternating electric field of (b) 1 kHz and (c) 100 kHz.
Figure 4(a) further indicates that the birefringence of two orthogonal polarizations, calculated by Δng = ngy−ngx, can be modulated by fM as well Δng, can be tuned from the maximum value of 0.2 at 1 kHz to 0 at 63 kHz, and then to the minimum value of 0.14 at 100 kHz. When fM is 63 kHz, the ngy becomes equal to ngx.
To explain this phenomenon, we discussed the tuning mechanism of the THz anisotropy of DFLC. The LC molecules tend to arrange uniformly along the same direction under the external electric field, showing the optical anisotropy. The long-axis direction of LC molecules (called as LC director) is just the optical axis of uniaxial crystal, and the refractive index of this direction is higher than that in the perpendicular plane of the long axis, which exhibits the nature of the positive uniaxial crystal (ne > no). The refractive index ellipsoid of DFLC is a rotational ellipsoid where the long-axis of LC molecules is regarded as the symmetry axis. At low alternating frequency (e.g. 1 kHz), the LC molecules are along the alternating electric field direction as shown in Fig. 4(b), which is similar to the traditional nematic LC. In this case, the optical axis of DFLC is along y-axis, ny>nx and Δn>0. When fM becomes large (e.g. 100 kHz) as shown in Fig. 4(c), the long axis of LC molecules rotates to be perpendicular to the alternating electric field, and the optical axis turns into the x-axis. In this case, nx>ny and Δn<0. To confirm this, we rotated the THz polarizer behind the DFLC cell to check whether the polarization state of THz waves changes or not. We define the rotation angle θ of THz polarizer as the angle between polarizer and polarization direction of incident THz waves. The results show that, when the alternating frequency is 1 kHz or 100 kHz, the transmission is largest at θ = 0° and near zero at θ = 90°. And when θ = ± 45°, the detected THz pulse signals are totally the same both with amplitude and phase. This proves that the output THz waves are still the original linear polarization state. When fM is 63kHz, ngy = ngx, and the optical axis of refractive index ellipsoid orients to an intermediate angle between x-axis and y-axis in the xy-plane. Therefore, the tunability of the anisotropy in DFLC originates from the rotation of LC molecules induced by switching the fM. Because of the tunable refractive index nx, ny and the birefringence Δn, the alternating frequency-controlled phase shifters and waveplates for THz waves can be realized by the DFLC cells.
3.3 Application for tunable THz wave-plate and phase shifter
We plotted the experimental THz birefringence and phase difference ∆δ of the 600 μm-thick DFLC cell under the electric field of 30 kV/m with dual fM of 1 kHz and 100 kHz in Figs. 5(a) and 5(b). The ∆δ(ω) of the DFLC cell can reach 0.5 π (fM = 100 kHz) at 1.01 THz and −0.5 π (fM = 1 kHz) at 0.68 THz, which means that the DFLC cell can play as a tunable quarter-wave plate when the THz waves is above 0.68 THz. The central operating frequency of this quarter-wave plate can be tuned from 0.68 THz to a higher frequency range by changing the alternating frequency fM. Moreover, when the frequency of the THz waves is above 1.01 THz, the THz waves can be converted from linear polarization to left or right circular polarization under the certain fM.
Fig. 5 (a) The birefringence and of the DFLC cell when the fM is 100 kHz and 1 kHz. (b) The phase difference between the two orthogonal states of polarization. (c) The refractive index difference and (d) the phase shift of the sample under the same polarization state when the alternating frequency is 100 kHz and 1 kHz.
As shown in Fig. 5(b), the ∆δ is up to π (fM = 100 kHz) at 1.57 THz and −π (fM = 1 kHz) at 1.33 THz, respectively, which adumbrates that a tunable THz half-wave plate can be realized, to convert THz wave from the linear polarization state to its orthogonal linear polarization state above 1.33 THz, and an arbitrary polarization state can be transformed above 1.57 THz by applying an appropriate fM from 30 kHz to 90 kHz and rotating angle.
In addition, the DFLC cell can also be used as the tunable THz phase shifter. Due to the anisotropy, the phase shifts for the two orthogonal polarizations are different as shown in Fig. 5(d). Consequently, the tunable ranges of refractive index (Δnd = n(100 kHz)−n(1 kHz)) of nx and ny are shown in Fig. 5(c). For example, the refractive index difference Δndy and Δndx at 1 THz is −0.20 and 0.15, respectively. As we discussed above, the tunable phase shift from 0 to π can be achieved at 1.33 THz for the y-polarized wave and 0~−π at 1.57 THz for the x-polarized wave through DP002-016 cell when the fM changes from intermediate frequency to 1 kHz or 100 kHz. The phase shift is nearly proportional to the frequency of THz waves. Moreover, to obtain a larger phase shift, the thickness of DFLC cell could be increased, but it would be at the expense of transmittance.
3.4 The response of THz anisotropy of DFLC to field intensity
The response of THz anisotropy of DFLC to field intensity is investigated. Comparing with the alternating frequency modulation, we need to preprocess the DFLC in this case. Firstly, the electric field of 30 kV/m with fM of 100 kHz is applied to make the sample in the initial anisotropic state, where LC molecules are perpendicular to the electric field as shown in Fig. 4(c). Then, the electric field is turned off. After these steps, we investigated the THz anisotropy of DFLC by increasing the voltage on the electrodes of the DFLC cells. At first, we applied 1 kHz electric field with its field intensity increasing from 0 to 30 kV/m. The experimental results are shown in Fig. 6. ngy increases with field intensity, while ngx reduces. ngy begins to increase at 13.3 kV/m, and ngx decreases from 10 kV/m, and they are both saturated above 20 kV/m. Therefore, we conclude that the molecule alignment of DFLC also responds to different electric field intensities. This tuning principle is similar to the traditional nematic LC.
Fig. 6 Group refractive index curves of DP002-016 with the electric field intensity increasing. The black line is the curve of group refractive index for the y-polarized wave ngy and the red one is ngx.
Therefore, the THz phase based on DFLC can also be controlled by the electric field intensity. However, compared with alternating frequency modulation, intensity modulation has some disadvantages. First, it requires the preprocess and a large electric field (>20 kV/m) to maintain the LC molecular alignment uniform. Second, this method is an irreversible one-directional modulation. The molecular alignment can rotate from 0° to 90° with the electric field intensity increasing from 0 to 30 kV/m, but it will maintain 90° state for a long time and it is hard to turn back to the original 0° state when the intensity of the external electric field decreases from 30 to 0 kV/m.
Obviously, the tuning method by changing alternating frequency fM on DFLC is superior to the traditional nematic LC in active THz applications, since the alignment of the DFLC molecules can be easily controlled and there is no requirement on the preprocess for the anchor layer. It is more flexible for such thick LC cells without the requirement of the electrode structure. More importantly, the phase manipulating is reversible, continuous and stable, while the response speed is much higher.
4. Results of other DFLC samples
Other two DFLC samples, DP002-026 and DP022-122, are all measured and analyzed. Depending on the different viscosity coefficients (γ) and response time (t) of three types of DFLC, the varying range of the refractive index and the response for the alternating frequency among those DFLC are different, but the general properties of them are similar, which indicates the tuning principle of the different DFLC is common and dependable.
The refractive index spectra in two orthogonal polarizations are displayed in Fig. 7. It is similar with the DP002-016 that the refractive index nx increases when fM increases from 1 kHz to 100 kHz and the ny decreases. However, the detailed refractive indexes and their tuning range are different from DP002-016. Figure 8 shows the group refractive index varying when the fM increases from 1 kHz to 100 kHz. It can be found that the ngx of all the DFLC cells rise up with the fM, while the ngy reduce, but the intermediate fM is different: 63 kHz for the DP002-016 and −122, and 26 kHz for DP002-026. The refractive index ellipsoid is also shown in the inset of Fig. 8. The detailed values of long and short axis in refractive index ellipsoid are different with that of DP002-016, and they further confirm that the tunability of these three DFLC all originate from the rotation of LC molecules induced by switching the fM. Figure 9 displays the response of THz anisotropy of the DP002-026 and DP022-122 on the intensity of alternating electric field. Both samples reach the saturated condition when the intensity is above 20 kV/m and the profiles of the group refractive index are similar to the DP002-016 cell, but the critical field intensity are different: 17kV/m for 026, 14kV/m for 016 and 12kV/m for 122.
Fig. 7 The refractive index nx and ny of (a) (b) DP002-026 and (c) (d) DP002-122 under the alternating electric field of different alternating frequencies.
Fig. 8 Group refractive index curves of (a) DP002-026 and (b) DP002-122 with the increase of the fM.
Fig. 9 Group refractive index curves of (a) DP002-026 and (b) DP002-122 with the electric field intensity increasing.
We can find that the DP002-016 has the largest birefringence and tuning range of refractive index among these three DFLC. Moreover, the different DFLC shows the different detailed parameters, such as the refractive index, tuning range, intermediated frequency, and critical field intensity. Therefore, these detailed data may help readers to choose a proper kind of DFLC in the certain application.
5. Conclusion
In conclusion, the THz optical anisotropy of the DFLC has been experimentally investigated under alternating electric fields. The refractive index and birefringence of DFLC can be tuned by both the fM and electric field intensity, but the former is outstanding because of the reversible tuning process and no requirement on the preprocessing. The tunability of DFLC originates from the rotation of LC molecules induced by different alternating electric fields. The optical axis of DFLC is along the electric field at the low fM (e.g.1 kHz) but perpendicular to the electric field at the high fM (e.g. 100 kHz). This property leads to a large tunable range of refractive index and birefringence, and can be applied as a tunable THz phase device. The experimental results confirm that the 600 μm-thickness DP002-016 DFLC cell can act as a tunable quarter-wave plate or a half-wave plate for the THz waves above 0.68 THz or 1.33 THz respectively. Besides, it can transform the THz waves above 1.57 THz to arbitrary polarization. Moreover, it also can be considered as a tunable phase shifter, which can make THz waves above 1.33 THz reach any phases from 0 to π. Therefore, the DFLC modulated by alternating bias frequency will be of great significance for potential active THz polarization and phase control devices.
Funding
National Natural Science Foundation of China (61505088, 61671491, 61378005); National Basic Research Program of China (2014CB339800); Natural Science Foundation of Tianjin (15JCQNJC02100); State’s Key Project of Research and Development Plan (Grant No. 2016YFC0101002); Open Fund of the Key Laboratory of Optical Information Science & Technology (Nankai University) (2017KFKT003); The Fundamental Research Funds for the Central Universities.
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