Tunable terahertz (THz) wave cells have been demonstrated by using magnetic-controlled birefringence in a randomly aligned liquid crystal (LC) cell embedded with three kinds of thermotropic LCs (5CB, E7 and BNHR). By using the THz time domain spectroscopy, these three LCs have been investigated under different low magnetic fields. Experimental results show that the randomly aligned LCs in 3mm thickness cells still have high birefringence controlled by a low magnetic field in the THz regime. The phase shift of π for BNHR cell is achieved over the entire testing range at 30mT, and the dynamic response process of BNHR under a weak magnetic field has also been investigated. When the initial magnetic field of 5mT is applied, unlike the continuous tunability of the cells filled with 5CB and E7, the BNHR cell has a great phase shift of 1.5π at 0.35THz before reaching the steady state. During that process the refractive index and absorption of BNHR vary with time due to its high viscosity, and a larger magnetic field can significantly shorten the response time. These indicate that the randomly aligned mm-thick LC layer of THz devices can be used as a tunable THz wave retarder with low a driving magnetic field and high phase modulation depth in a broad THz band. Therefore, a simple manufacturing technique and low magnetic control of these randomly aligned LC layers may explore some novel LC based THz devices for spatial light modulation, filtering and tuning tasks.
© 2016 Optical Society of America
Terahertz (THz) technology and its applications have made a dramatic growth in THz communication, imaging, material analysis, bio-medical technology, and security, etc [1–5]. Apart from the development of THz sources [6–8] and detectors [9, 10], THz applications require various functional THz devices [11–13]. For widespread adoption, tunable devices to manipulate THz waves, such as in phase control with modulation depths of π, is an important subject in THz photonics. Just like their well-developed counterparts in the visible and telecom bands, a number of THz devices employing liquid crystal (LC) have been investigated in recent years [14,15]. LC becomes an ideal candidate for researchers to explore novel active THz devices due to the large optical anisotropy, broad range of operating frequencies and high controllability with external fields [16–18]. The previous THz devices based on LC were mostly driven by electric field, and realized good tunability by switching the LC alignment with different electric fields. However, the lack of transparent electrodes in the THz range and high driving bias hinder the progress of this field [14, 19–21], though graphene has been investigated to be THz transparent electrodes for LC devices [22,23].
The LC device controlled by a weak magnetic field can overcome the limitations of electrodes and high driving bias, so THz magnetic-controlled LC devices attract extensive interest of researchers [15, 24]. Chen et al. employed a magnetic field to control the THz phase shifter with 5CB at 510mT , but it suffered from a strong magnetic field and low phase modulation. Then a stack-layered LC cell with E7 was utilized to obtain a greater phase shift , but this strategy led to additional loss. To obtain higher phase modulation up to π, the thickness of LC cell should be several millimeters due to the long wavelength of THz waves [27, 28]. However, the pre-alignment of LC molecules in the previous devices is difficult to be homogeneously and effectively controlled in such mm-thick LC cell. Only less than 1mm thickness LC layer can be induced into a uniform and homogeneous alignment by the commonly alignment layer. Randomly aligned LC layer could provide a simple and effective method for phase modulation. Recently, Sasaki et al. proposed a THz phase controller using a 0.1mm-thick randomly aligned 5CB layer . And then a polarization-independent THz phase retarder that used randomly aligned chiral nematic LC was reported . But so far, to achieve a high phase shift in terahertz regain, the birefringence and absorption of the mm-thick randomly aligned LC under weak magnetic field have not been sufficiently studied yet.
In this paper, we have fabricated a 3mm-thick LC cell, which is formed by two fused silica substrates without alignment layers, to investigate the tunable response of randomly aligned LCs under a weak magnetic field by the THz time domain spectroscopy (THz-TDS) system. Three different LCs 5CB, E7 and BNHR have been embedded in this cell as comparison. Experimental results demonstrate that the mm-thick randomly aligned LC layer can still show high birefringence under a weak magnetic field in the THz regime. The phase shift up to π is achieved over the entire testing range by magnetically controlling the BNHR cell and the corresponding magnetic field is only 30mT. The dynamic response process of BNHR at low magnetic field has also been investigated. When the initial magnetic field is applied, its refractive index and absorption vary with time before getting to the steady state due to its high viscosity. Unlike the continuous tunability of the cells filled with 5CB and E7, while the initial magnetic field is even as low as 5mT, the BNHR cell has a huge phase shift. The tunability, low driving magnetic field and high modulation depth in a broad THz band make the randomly aligned LCs available for spatial light modulation, filtering and tuning tasks.
2. Materials and experiment equipment
Three thermotropic LCs 5CB, E7 and BNHR (Bayi Space LCD, China) were used in our work for comparisons. The rod-like molecules have a dipole moment along the long molecular axis. Due to their simple synthesis process and large optical birefringence, these materials have been very well characterized in the visible. 5CB (4-Cyano-4′-pentylbiphenyl) is probably the most widely used LC monomer. E7 and BNHR are the mixed LCs, which can be used as polymer-dispersed liquid crystal for LC devices and display applications due to their large optical birefringence. All the three LCs are the positive dielectric anisotropy LC, that is no<ne, and they exhibit a large birefringence of Δn5CB = 0.16, ΔnE7 = 0.21 and ΔnBNHR = 0.25 in the visible light range at 20°C. The parameters of refractive indices and viscosity coefficient (γ) in the visible range are shown in Table 1. BNHR has the highest birefringence and viscosity among the three.
We used a standard four parabolic-mirror THz-time domain spectroscopy (THz-TDS) system in the experiments. As shown in Fig. 1(a), THz pulses are generated by a photoconductive antenna excited by a Ti:sapphire femtosecond laser with 75fs duration of 80MHz repetition rate at 800nm. A (110) ZnTe crystal is used for detection. The effective spectral range of our THz-TDS system is 0.05 to 2.5THz, with a 105 signal to noise ratio. The temporal resolution is 40fs, which is determined by the minimum step of precise stepping motor in the system. And the spectral resolution is 25GHz, which depends on the total delay time of measurement. The experiments were performed at 25°C with the humidity of less than 5% to avoid complications from water vapor.
For the LC measurement, two pieces of fused silica substrates of 1.25mm thickness without alignment layers were assembled together to form a 3mm-thick LC cell in which LC molecules were randomly aligned, as shown in Fig. 1(b). The cell was settled at the focal point of THz-TDS system. There was a pair of electromagnets to produce tunable static magnetic field, as shown in Fig. 1(a). The external magnetic field was arranged to be orthogonal to the propagation and polarization direction of THz waves.
3. Results and discussions
3.1 Optical properties of LCs in the THz regime
When there was no magnetic field applied, the randomly aligned LC in our LC cell was an isotropic medium. Here, the isotropic phases of LCs without magnetic field were measured firstly, and the empty cell was set as the reference. Figure 2(a) presents the time-domain signals of reference and three LC samples. For the time-domain signals, the delay time of the sample signal compared to the reference is proportional to the refractive index of LC, while the attenuation in the amplitude of the sample signals compared to the reference is proportional to the absorption of LC in the THz regime. The refractive index n(ω) and absorption coefficient spectra α(ω) were obtained as shown in Figs. 2(b) and 2(c) by using Fourier transform of the time-domain data, which can be calculated by 
In the absence of magnetic field, according to Eq. (1), the refractive indexes of 5CB, E7 and BNHR are 1.633, 1.675 and 1.694 at 0.2THz, respectively. And there is a low dispersion from 0.2 to 1THz. According to Eq. (2), the absorption coefficients of 5CB, E7 and BNHR are 1.1, 0.6 and 1.3cm−1 at 0.2THz, respectively, and increase with the frequency as shown in Fig. 2(c). Compared with the two traditional LCs 5CB and E7, the BNHR has a larger refractive index and a larger loss.
3.2. Magnetically induced birefringence of LCs in the THz regime
Then, the effect of external magnetic field on randomly aligned LC was investigated. As shown in Fig. 3(a), the linearly polarized THz wave is normally incident to the LC cell, and the direction of magnetic field is orthogonal to the propagation direction and polarization direction of THz waves. The refractive indexes nx for 5CB, E7, and BNHR under different magnetic fields were obtained in Figs. 3(b)-3(d), respectively. Without the external magnetic field, the LC molecules are randomly aligned in their isotropic phase, of which the refractive index is nx(0) = ny(0) = niso. When magnetic field is applied to the LC cell, the LC molecules tend to be reoriented along the external magnetic field and the LC layer becomes a uniaxial medium. When the electric field becomes higher, the LC molecules tend more closely to the direction of external magnetic field, and under a sufficiently high magnetic field, homogeneous alignment of LC molecules is induced parallel to the y axis. So the refractive index nx(30mT) reaches a minimum value that is the ordinary refractive index (no) and ny(30mT) corresponds to a value of extraordinary refractive index (ne). Figure 3(b) shows that the refractive index nx of 5CB sample gradually reduces from 1.623 to 1.565 at 1THz. In the spectrum of E7 sample in Fig. 3(c), it is found that the refractive index can be continuously decreased from 1.672 to 1.585 at 1THz. Interestingly, for the BNHR sample as shown in Fig. 3(d), we observe an obvious decrease of refractive index from 1.680 to 1.596 at 1THz when B = 5mT, and this is much higher than the changes of two others. When we continue to enhance the magnetic field up to 30mT, the refractive index of BNHR only drops to 1.581 at 1THz. This result indicates that the arrangement of randomly aligned BNHR molecules varies greatly under a very weak magnetic field. It can be also concluded that the domain textures and the defects of randomly aligned LC layer have no side effect because there is no sharp resonance of the refractive index spectra in the range of 0.2 to 1THz as shown in Figs. 3(b)-3(d) .
For the randomly aligned LC molecules, the refractive index niso is described as Table 2. Clearly, the LC parameters in the THz regime in Table 2 are slightly higher than those in the visible light in Table 1. The maximum birefringence values of 5CB, E7 and BNHR in the 0.2-1THz range are 0.168, 0.249 and 0.311, respectively, so the phase modulation of the LC cell by employing BNHR can be obviously enhanced due to its large birefringence in the THz regime.
3.3. Terahertz tunable wave retarder
To investigate the phase shifts, the effective birefringence can be obtained by ∆neff = ne(B)−no(B) = ny(B)−nx(B). The phase shift ∆δ(B) before and after applying the external magnetic field can be given by 
According to Eqs. (3) and (5), Fig. 4(a) presents the frequency-dependent phase shifts of the three kinds LCs at 30mT. A ∆δ tuning of π for 5CB, E7 and BNHR is achieved above 0.34, 0.23 and 0.2THz, and even a tuning of over 2π is achieved above 0.61, 0.45 and 0.35THz, respectively. The 3mm-thick BNHR layer is nearly allowed the cells to function as a half wave plate over the entire testing range (0.2-1THz). Then the voltage-dependent phase shifts for 5CB and E7 at the frequencies mentioned above are presented in Figs. 4(b) and 4(c). As expected, the phase shifts rises up continuously with the increasing of magnetic field intensity. Therefore, arbitrary polarization conversion could be performed above 0.61THz using the 5CB sample or above 0.45THz using the E7 sample by tuning the magnetic field.
Interestingly, the phase shift of BNHR is quite different with that of 5CB and E7 as shown in Fig. 4(d). There is a sharp change of phase shift for BNHR from 0 to 5mT, so that its phase shift at 5mT is much larger than that of 5CB and E7, and then the phase shift just slowly increases from 5 to 30mT, so it means that when the magnetic field is only as low as 5mT, the LC alignment is close to the homogeneous one at 30mT. Under a weak magnetic field of lower than 5mT, 3mm BNHR LC cell changes greatly from the isotropic medium to the uniaxial medium. Moreover, a 1.5π of phase shift is achieved above 0.35THz when the BNHR is driven under 5mT as shown in Fig. 4(d). These results show that the mm-thick randomly aligned LC cell can be effectively tuned the phase of THz signals in broad band by the low magnetic field, and the BNHR has a larger phase modulation depth and a lower driving magnetic field than that of traditional 5CB and E7 in the same LC cell.
3.4. Dynamic response of the BNHR
Finally, the dynamic response of abrupt phase shift of BNHR has been investigated. Figure 5(a) and 5(b) present the time-dependent phase shifts and absorption coefficient of BNHR at 0.35THz under a fixed magnetic field of 5mT and 15mT, respectively. As shown in Fig. 5(a), when the initial magnetic field is 5mT, the phase shift increases very slowly from 0 to 4min at first, and then sharply increases from 0.06π to 1.2π in the range of 4-6min. After 6min, it slowly reaches a saturated value of 1.5π after 10min. This means the BNHR need 10min to reach the steady state when the magnetic field of 5mT is applied. This is a long relaxation time because of three factors: the high viscosity γ of BNHR, the weak magnetic field and the mm-thickness of LC cell. During that abrupt increase of the phase shifts, the absorption coefficient also increases from 2.9cm−1 to 6.5cm−1, reaching a peak value. This large absorption peak originates from the strong scattering when the random LC molecules are dramatically changing. And then the absorption gradually returns to 3.9 cm−1 because the molecules tend to be uniform when reaching the steady state with magnetic field .
When the initial magnetic field of 15mT is applied, the similar dynamic response process of phase shift can be seen in Fig. 5(b). Clearly, the relaxation time becomes shorter to 5 min when the external magnetic field is increased. Because of higher driving magnetic field, the steady phase shift value reaches 1.73π corresponding to the one at 15mT in Fig. 4(d) and it has also a larger steady absorption coefficient. Therefore, for the BNHR, a larger magnetic field can significantly shorten the response time, but cannot effectively improve the phase shift value, and moreover it leads to a slightly larger absorption compared with that of 5mT. Although the response time of the BNHR cell is several minutes, it has a larger phase modulation depth and a lower driving magnetic field than that of traditional 5CB and E7 ones over the entire testing range (0.2-1THz). This kind of LC based THz devices can be used as tunable devices, which do not need real-time adjustment or high-speed modulation, such as tunable filter, phase retarder, tunable beam splitter, tunable THz absorber, active THz transducer, frequency-tunable device, etc [29, 30, 33–35]. The tunability and high phase modulation depth in a broad THz band, rather than its modulation speed, attract us which may greatly extend the scope of its application.
In conclusion, we have fabricated a 3mm-thick randomly aligned LC cell and investigated the tunable magnetic response of 5CB, E7 and BNHR under a weak magnetic field in the THz regime by the THz-TDS system. Three different LCs have been embedded in this LC cell as comparison. Experimental results show that the alignment of mm-thick randomly aligned LC cell can be effectively tuned in the THz regime by low magnetic field, and the BNHR cell has a larger phase modulation depth and a lower driving magnetic field than that of traditional 5CB and E7 ones in the same LC cell. The tunable wave retarder as a half wave plate can be realized by BNHR cell at 30mT over the entire testing range (0.2-1THz). The dynamic response process of BNHR on the magnetic field has also been investigated. When the initial magnetic field is applied, the refractive index and absorption of BNHR vary with time before reaching the steady state due to its high viscosity, and a larger magnetic field can significantly shorten the response time. The randomly aligned LC without pre-alignment treatments suggests a simple and low cost method to prepare a tunable THz phase controller with low driving magnetic field and high phase modulation depth in a broad THz band. Therefore, the randomly aligned LC based THz devices may have a wide application in spatial light modulation, filtering and tuning tasks.
This work was supported by the National Basic Research Program of China (Grant 2014CB339800), the National Natural Science Foundation of China (Grant 61171027, Grant 61505088), Natural Science Foundation of Tianjin (Grant 15JCQNJC02100), the Science and Technology Program of Tianjin (Grant 13RCGFGX01127), the Specialized Research Fund for the Doctoral Program of Higher Education(Grant 20131201120004).
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