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The manipulation of terahertz (THz) signals, such as in phase control with modulation depths of 2π, is an important subject in THz photonics. In this work, an electrically controllable chiral liquid crystal (Ch-LC) cell with low chirality is used to develop a THz phase modulator with 2π tunability. The proposed Ch-LC device is insensitive to the polarization of electromagnetic waves in THz frequency range. The diluted chiral dopant enables the critical voltage of the Ch-LC cell to be effectively reduced to 0.24 V/μm from 3.65 for a typical Ch-LC cell with high chirality. The dependence of phase retardation on driving field and the polarization is examined. This THz 2π phase modulator has great potential for practical use.
© 2016 Optical Society of America
1. Introduction
In recent years, terahertz (THz) photonics have attracted much attention, especially on account of their importance to ultrafast dynamics in materials, environmental sensing and medical imaging [1–3]. The development of THz devices is therefore important. For example, quasi-optical components, such as phase shifters, are required for THz communication [4]. Although tunable phase shifters have several applications [5, 6], the depth of phase modulation for communication should be at least 2π since this value represents the time delay of one bit [7]. Numerous groups have developed tunable phase shifters in the THz frequency range [7, 8]. A 2π THz phase shifter that is based on a nematic liquid crystal (NLCs) has also been developed [9]. However, for such a device, strong polarization dependence is inevitable because its functions are based on birefringence within the NLC materials. So far, many methods to realize polarization-insensitivity in NLC optical devices have been proposed, including twisting the structure of the NLC film and using an axially symmetrical configuration [10–12]. Nevertheless, the perfect homogeneous alignment of NLC cells for THz devices is difficult to achieve using commonly used alignment films because the thickness of at least the sub-millimeter LC layer is large. Recently, a universal polarization terahertz phase controller that used randomly aligned NLCs was reported [13]. The scattering loss in the 0.1 mm-thick LC layer is reduced in the THz frequency range because the scattering textures have sizes of several tens of microns, which is much smaller than the wavelengths of THz waves (300 µm–1.5 mm). However, to achieve a 2π THz phase shift, the thickness of the NLC layer must be of the order of millimeters. The sizes of the scattering textures in a millimeter-thick LC cell are therefore larger, so scattering loss of the THz wave is inevitable.
Chiral nematic liquid crystals (Ch-LCs) are generally made of an NLC host and chiral agents. Ch-LCs have been utilized in several optical devices, including displays, filters, and distributed feedback lasers [14–16]. Typically, Ch-LCs have two stable states. One is the planar state with a periodic helical structure, whose axes are perpendicular to the cell surface; the other is the focal conic state with a multi-domain structure whose helical axes are oriented randomly throughout the cell. Each state has different optical properties that depend strongly on the pitch length and the operating wavelength. For example, the planar state exhibits Bragg reflection when the pitch is comparable with the optical wavelength. In contrast, the focal conic state weakly scatters light. The optical properties become totally different when the operating wavelength is much longer than the pitch length of the Ch-LCs, because light with a long wavelength cannot easily recognize a Ch-LCs’ helical structure. As a result, the optical rotation effects in a Ch-LCs medium are negligible and both planar and focal conic states exhibit isotropic properties. Several works have recently identified polarization-independent refractive indices of Ch-LCs [17, 18]. In general, the Ch-LC texture changes from the planar or focal conic states to the homeotropic state under the influence of an electric field. Birefringence is therefore induced with the optical axis in the direction of the electric field. Therefore, Ch-LCs can be used in polarization-insensitive devices that operate in the THz frequency range. Note that the gap of LC cell applied to THz frequency range is too thick to achieve perfect planar texture. Only focal conic texture of Ch-LCs was considered in the following experiment. Therefore, in this work, we proposes a polarization-independent 2π THz phase shifter using 5mm-thick Ch-LCs, whose textures switch from focal conic state to the homeotropic state in the presence of an applied electric field. The relationship between the driving electrical field and the pitch of the Ch-LCs is studied, along with the polarization independence of the devices.
2. Fabrication of sample
Liquid crystal materials were prepared by mixing a chiral material (high-HTP-1, Tsinghua University in China) with NLC BL006 (Merck) to form Ch-LCs. The mixture was in the isotropic phase and stirred for 4 h to ensure that a homogeneous solution was formed. The Ch-LCs were then injected into empty cells. The LC cell were constructed by sandwiching a layer of Ch-LCs between two fused silica windows with a thickness of 1.14 mm, coated with a 100 nm-thick indium-tin-oxide (ITO) layer, as the electrode. (Fig. 1(a)) The thicknesses of the Ch-LC layers were controlled using spacers with thicknesses of 328 μm, 4 mm, and 5 mm. The filled Ch-LCs contained 2.5–0.06% chiral dopant in the NLC host BL006 (Δn = 0.28 at 20°C in the visible range, Δε = 17.3, K11 = 17.9 pN, K22 = 33.5 pN, and K33 = 33.47 pN at 20°C in the low frequency). The HTP of the chiral material for the BL006 host is approximately 80 μm−1. Typically, the HTP value is used to evaluate the relationship between pitch (P) and the concentration of the dopant chiral material (C) [19]:
A P value in the range of 0.5–20 µm is thus obtained. In general, the pitch of Ch-LCs can be measured by Cano wedge cell [20]. However, the real value of the pitch of Ch-LCs didn’t be further confirmed because the planar texture cannot be formed in the cell with the few millimeter-thick cell gap. In this work, THz time-domain spectroscopy (THz-TDS) was applied to analyze the optical properties of the Ch-LC cells, the polarization-dependence, and the characteristics of the proposed THz phase shifter [21]. A reference cell was also prepared. Like the Ch-LC cells, the reference cell was prepared without filling Ch-LCs, as displayed in Fig. 1(b). A square-wave AC voltage with a modulation frequency of 60 Hz and tunable voltage of as high as 1400 V was applied to the electrode. In the small biasing field, the Ch-LCs exhibit a focal conic texture. Figure 1(c) presents the fabricated Ch-LC cell in the absence of an applied voltage. Clearly, the cell is opaque because the large scattering loss that is associated with a focal conic structure is in the visible frequency range.
Fig. 1 The scheme of the cell for the THz-TDS system: (a) Ch-LC cell and (b) reference cell; (c) the picture of Ch-LC cell device.
3. Experimental setup
Figure 2(a) shows the experimental setup for THz time domain spectroscopy. The laser system is a diode-pumped mode-locked Ti:Sapphire laser (Spectra Physics MaiTai). The central wavelength is 800 nm, and pulse width is about 100 fs with bandwidth (full-width-at-half maximum; FWHM) of around 10 nm. The output power is 800 mW with repetition rate of 80 MHz under 5 W pump power. First, the femtosecond laser output was then split into two beams for THz generation and detection. One of them is the pump beam for THz radiation generation and guided to an emitting photoconductive (PC) antenna. The other is the probe beam for THz radiation detection and guided to 600 um thickness ZnTe crystal for electro-optic sampling (EO-sampling) detection. The emitting antenna was mounted on a Si hemispherical lens to increase coupling efficiency of THz radiation. The PC dipole antenna was fabricated on the LT-GaAs sample with an antenna length of 30 µm, gap of 5 µm, an antenna width of 5 µm, and a transmission line width of 10 µm, respectively. The generated THz radiation was then collimated and focused using a pair of parabolic mirrors. Figure 2(b) and 2(c) show the temporal profile and its corresponding spectrum. Clearly, our system can operate from 0.1 to 1.5 THz.
Fig. 2 (a) Experimental setup for THz time domain spectroscopy; (b) the terahertz temporal profile and (c) the spectrum of THz.
4. Results and discussion
4.1 Electro-optical behavior of Ch-LCs in THz range
To investigate the electro-optical properties of the Ch-LCs in the THz range, two Ch-LC cells, cell 1 and 2, with different chiral pitches were used. The corresponding pitches in cells 1 and 2 are 1 μm and 0.5 μm, respectively, and the thickness of the two cells is 328 µm. Noted that the power of transmitted THz signal will be absorbed by ITO electrode. The THz signal after passing through LC cell whose substrates with 100 nm-thick ITO thin films is approximately half strength of THz-TDS. Nevertheless, the strength of transmitted THz signal is still sufficient for this work. Besides, the absorption of THz signal can be effectively improved by reducing the thickness of ITO thin film or using nanostructure of ITO as electrodes [22]. Figure 3(a) shows the temporal profile of the THz signal before and after it passes through the Ch-LC cells. Whereas Ch-LCs scatter visible light, the THz signals that had passed through the Ch-LC cells were detectable. The slight decreases in amplitude of the THz signal are attributable to the reflection between the window and the Ch-LC material that fills the cell. The absorbance, A, can be described as A = -log10T, where T is the transmittance. By considering the Fresnel equation, and extinction coefficients, the LC cell thickness, and the wavelength, A can be accordingly calculated as 0.35. The similar transmission behaviors of cell 1 and cell 2 indicate that transmission is almost independent of the pitch length of the Ch-LCs. Accordingly, the scattering in the THz frequency range can be neglected. Figure 3(b) presents the normalized THz temporal profile of the reference, and the focal conic texture and homeotropic texture of the Ch-LCs. In the absence of an applied voltage, the focal conic texture with randomly orientated domains is present in the Ch-LC cell. On the other hand, the second positive peak in the Fig. 3(b) comes from the multi-reflection between two electrodes with high refractive indices, ~30 at 0.75 THz [23]. From the calculation of delay time, 2nd/c, where n, d, and c are the refractive indices of Ch-LCs (~1.65), the thickness of the Ch-LC layers (328 μm), and the speed of light (3 × 108 m/s), the second peak should be after the main positive peak around ~3.6 ps. This value corresponds to the experimental delay time between two positive peaks.” Since the chiral pitch of the focal conic texture is much less than the THz wavelength, its refractive index can be regarded as a statistical average, and the effective refractive index (neff) of the focal conic texture can be expressed as [19]
where no and ne are the ordinary and extraordinary refractive indices of BL006. When an enough high voltage is applied to the Ch-LC cells, the focal conic texture becomes homeotropic, so THz wavelengths experience the ordinary refractive index. Therefore, the temporal shift between the reference and the homeotropic texture is shorter than that between the reference and the focal conic texture because no is smaller than neff. When the voltage is as high as 1200 V, providing a field of around 3.65 V/μm, a maximum peak shift of approximately 100 fs can be obtained, revealing that the signal has a phase shift of around 0.2 π at 1 THz. Besides, the value of no, ne, and κ (imaginary part of refractive index) in THz frequency range from 0.2 to 1.4 THz were derived here. As frequency increases, the value of no and ne all decrease, and their range are from 1.52 to 1.56 and from 1.78 to 1.82, respectively. The largest value of κ is only 0.034. Compared with the conventional LC widely applied in THz electrically tunable devices, such as E7, the values of κ are similar with each other. This shows the advantage of BL006 in the application of THz phase shifter.Fig. 3 (a) The temporal profile of the THz signal before and after THz signal passes through the Ch-LC cells, (b) Terahertz temporal profile of the reference, focal conic texture, and homeotropic texture.
4.2 Driving voltage for transition from focal conic texture to homeotropic texture
As mentioned above, a 328 μm-thick Ch-LC cell with a critical voltage of as high as 1200 V is needed to acquire a homeotropic texture. In this situation, a 2π Ch-LC THz phase shift, which is more than ten times the thickness of a Ch-LC layer, is difficult to realize. Notably, the high driving voltage that is used to change the Ch-LC from a focal conic texture to a homeotropic texture inevitably damages the material. Fortunately, the THz frequency corresponds to a radiation wavelength in the range 300 μm–1.5 mm. Relative to the pitch length of the Ch-LCs that are used herein (0.5-15 μm), the scattering loss caused by Ch-LCs in THz frequency regime is still negligible. Consequently, a critical electrical field that is required to make the texture homeotropic can efficiently be reduced by using Ch-LCs with a longer chiral pitch, as follows [19].
where P, K22, and Δε denote pitch, twist elastic constant, and dielectric anisotropy, respectively.Figure 4(a) presents the THz temporal profile before and after the signal passes through the cells that are filled with Ch-LCs with various pitch lengths. The thickness of all LC cells is fixed at 328 μm. The reference signal is the profile that is obtained after the signal passes through the reference cell. The temporal profiles of the Ch-LC cells with various pitches were investigated in the absence of an applied voltage. Clearly, the temporal profiles correspond to almost the same behavior as that of Ch-LC cells with various pitches. Second, the similarity of the relative time retardation of Ch-LC cells to the reference signal reveals that the average refractive indices in these cells should be close to each other. Following the establishment of the weak scattering in the Ch-LC cell with a long pitch, the critical voltage of Ch-LC cells is determined. The time retardation of the Ch-LC cells relative to the reference signal is decreased from the THz temporal profiles when the applied voltage is increased. The critical voltage is derived as the time retardation tends to saturate. Figure 4(b) displays the critical voltages for the transition from the focal conic texture to the homeotropic texture for Ch-LC cells with various pitch lengths. The critical voltage declines as the pitch increases. As the chiral pitch of the Ch-LCs increases to 15 μm, the critical voltage is greatly reduced to 80 V, corresponding to a field of approximately 0.24 V/μm. Experimental results agree closely with the theoretical prediction of the relationship between critical voltage and pitch.
Fig. 4 (a) The temporal profile of the THz signal before and after THz signal passes through the Ch-LCs cells filled with Ch-LCs with various pitch values; (b) driving voltage for different pitch lengths.
4.3 Electrically controlled 2π phase modulator
In principle, the thickness of an LC cell can be increased to increase the phase modulation depth. To achieve a phase retardation of greater than 2π, a thickness of more than 4mm should be required. Therefore, two Ch-LC cells with cell thicknesses of 4 mm and 5 mm were fabricated. These cells were filled with the same Ch-LCs with a pitch of about 15 µm. Notably, both 4 mm-thick and 5 mm-thick Ch-LC cells become transparent from opaque when the applied voltage exceeds 1000V, indicating that the texture of the Ch-LC cells has become homeotropic from focal conic. The time delay of the 4 mm-thick Ch-LC cell relative to the reference signal remains constant as applied voltage increases to 1400V. The same behavior is observed for a 5 mm-thick Ch-LC cell. Figures 5(a) and (b) show the THz temporal profiles of the reference cell, and the 4 mm and 5 mm-thick Ch-LC cells in the absence of an applied voltage. Initially, the Ch-LC cell exhibits the focal conic texture. When 1400 V is applied, the relative time delay between the reference cell and the 4 mm-thick Ch-LC cell decreases from 8.81 ps to 7.94 ps and the texture of the Ch-LC cell changes from focal conic to homeotropic, as displayed in Fig. 5(a). For the 5 mm-thick Ch-LC cell, the relative time delay between the reference cell and the 5 mm-thick Ch-LC cell decreases from 10.87 ps to 9.77 ps, as shown in Fig. 5(b). The corresponding increasing time delays for the 4 mm and 5 mm-thick cells are thus calculated as 0.87 ps and 1.1 ps, respectively. Since the period of 1 THz is 1ps, the relative time delay of 1.1 ps is 1.1 periods of 1 ps each. Hence, the phase retardation at 1 THz is larger than 2π for the 5mm-thick Ch-LC cell as the voltage is increased from 0 V to 1200 V. Figure 5(c) plots the applied voltage–dependent phase shift of the 5 mm-thick Ch-LC cell at various frequencies. The clear voltage-dependence of phase shift at various frequencies of THz radiation indicates that the phase shift or the relative time retardation can be controlled by altering the applied voltage. The response time of the 5 mm-thick Ch-LC cell was also measured using THz time domain spectroscopic system. Initially, the moving-stages was adjusted to find the peak position of terahertz temporal profile, and the intensity was defined as maximum transmission of THz temporal signal. Then, when the voltage was applied to Ch-LC cell, the intensity of THz temporal signal reduced, which was defined as minimum transmission, and the switching time was recorded by detector. The response time was defined as the switching time from 90 to 10% of the maximum transmission of THz temporal signal. The rising time and falling time of the proposed 5 mm-thick Ch-LC cell are about tens of seconds. Compared to the millimeter-thick NLC cell, whose falling time is in the range from minutes or hours [24], the proposed Ch-LC cell has a faster falling time. It may be associated to the helical texture of Ch-LC, which has fast switching time from hometropic to focal conic texture [25]. Further, the response time of the Ch-LC cell can be improved by applying the overshoot voltages, as shown in Fig. 5(d). The rising time and falling time can be reduced to few second and smaller than a second, respectively, when the applying voltage is larger than 2200 V.
Fig. 5 The THz temporal profiles after the reference cell (a) 4 mm Ch-LC cell and (b) 5 mm Ch-LC cell; (c) the applied voltage–dependent phase shift of the 5 mm Ch-LC cell for various frequencies; (d) the rising and falling time of the 5 mm Ch-LC cell for various overshoot voltages.
4.4 Polarization dependence of Ch-LC cell phase modulator
The polarization dependence of the Ch-LC cell in the THz frequency range is characterized. To investigate this polarization-dependence, the cell is rotated around the THz propagation direction using a rotation stage. The THz profile is then obtained as various voltages are applied to the cell. The peak times in the THz temporal profile are identified. Figure 6(a) shows the relative time delay (fs) (in the radial direction) of a THz wave between the reference signal and the signal after it has passed the 5 mm-thick Ch-LC cell in the absence of an applied voltage and at angles of the rotation stage of 0–360°.The polarization-dependency is also measured as the applied voltage changes to 700 V or 1400 V. The relative time delay increases with the applied voltage. The maximum value of approximately 1.1 ps is reached when voltage is as high as 1400 V. The curve is almost concentric, which clearly reveals the Ch-LC cell is polarization -independent. Notably, the temporal resolution of THz-TDS is around 7 fs, which is limited by the accuracy of the translation stage in the THz-TDS system. The standard deviation of relative time retardation is calculated to be about 33 fs when 1400 V is applied. Given the relative time retardation of 1.1 ps, the deviation corresponds to an accuracy of λ/50 (Fig. 6 (b)). For comparison, the polarization dependence of the NLC cell in the THz frequency range also was measured, as showed in Fig. 6(c). The thickness of NLC cell is 1.1 mm, and there isn’t any alignment treatment on the surfaces of the cell. Without an external voltage, the relative time retardation is random to the angles of the rotation stage of 0–360°. The largest deviation of 0.3 ps was observed, which strongly indicates NLCs cell for THz application is polarization-dependent. Besides, the possible reason to cause the large deviation in NLC cell is due to fluid alignment. LC molecules in millimeter-thick cell is fluid, and easily flow when the cell was rotated. However, the behavior that flow effect results in large deviation in Ch-LC cell didn’t be observed because the size of the scattering textures in Ch-LC cell is fixed by the helical texture with fixed pitch length.
Fig. 6 Polarization dependence of the THz phase shift of (a) 5 mm-thick Ch-LC cell at the 0, 700, and 1400 V, and (b) 1 mm-thick NLC cell at 0V.
To the best of our knowledge, this work demonstrates the first electrically controlled phase modulator that uses Ch-LCs and has a modulation depth of over 2π . Although such a 5mm-thick Ch-LC cell needs an extremely high applied voltage (above 1000 V), these issues includes high driving voltage and slow response time can be improved by adopted multi-stacking way [26]. This relevant work is in progress.
4. Conclusion
In this work, an electrically controlled 5 mm-thick Ch-LC cell was used to demonstrate a novel THz 2π phase shifter. This device initially exhibits the low chirality focal conic texture, which can be regarded as optically isotropic for THz frequencies and can be switched to the homeotropic texture by the application of an electric field. Therefore, the device has the advantage of being polarization-independent and having a polarization-dependent phase shift variation of less than two percent owing to the randomly orientated focal conic texture. The chiral dopant was diluted to increase the pitch length of the Ch-LCs from 0.5 to 15 μm, reducing the driving field from 3.65 to 0.24 V/μm. This polarization-independent THz 2π phase modulator has great potential for application in communication, imaging, and sensing.
Acknowledgments
The authors would like to thank the Ministry of Science and Technology of the Republic of China, Taiwan, for financially supporting this research under Contract No. MOST104-2112-M-110-012-MY2, MOST 104-2218-E-110 −008 -MY3 and MOST 103-2112-M-110 −012 -MY3. Ted Knoy is appreciated for his editorial assistance.
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