Terahertz (THz) birefringence anisotropy of the polymer-dispersed liquid crystal (PDLC) doped with gold nanoparticles (Au NPs) is investigated by using terahertz time domain polarization spectroscopy. Controlled by the electric field, the change rate of refractive index for PDLC doped with Au NPs is 0.91% V−1 as the voltage increases, smaller than the pure PDLC, which indicates that the response of the PDLC doped with Au NPs to electric field is more uniform than that of pure PDLC. Therefore, the PDLC doped with Au NPs is more suitable for tunable phase shifters. Furthermore, we found that under the high-frequency alternating electric field, the anisotropic polarization effect of PDLC will disappear to this electric field, namely polarization relaxation phenomenon. However, the results show that the PDLC doped with Au NPs can respond to an electric field with higher alternating frequencies, and the relaxation frequency of PDLC with an Au NPs concentration of 0.2 wt% was improved over two times compared with the pure PDLC and four times higher than that of the precursor mixture without ultraviolet radiation. This work has the significance for the potential applications of tunable THz liquid crystal phase and polarization devices, providing a more uniform and faster relaxation response to the operating electric field.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
In recent years, Terahertz (THz) waves, typically defined as electromagnetic waves in the frequency range from 0.1 to 10 THz, have drawn much attention due to its superiority in security screening, nondestructive detection, wireless communication and material spectroscopy [1–4]. With the rapid development of THz technologies, THz sources and detectors are developing rapidly [5,6]. In order to construct compact and practical THz systems, high-performance THz functional devices, such as waveguides , filters , isolators , modulators , polarizers , and phase shifters , are also essential to control and modulate THz waves in an efficient way. Among these devices, the phase and polarization devices have led to an urgent demand for further development of THz technology and its application system.
Conventional polarization optical devices in the THz regime are limited due to their low birefringence, large loss, narrowband, and huge volume . Recently, the artificial metasurfaces, which have the advantages of flexible design and simple fabrication, provide a promising pathway for more flexible manipulation of THz wave in its phase and polarization . However, the limits of dispersion, bandwidth, and insertion loss always exist in these metasurfaces, and most of them cannot be actively manipulated once they are fabricated. Compared with these devices, the phase and polarization devices based on liquid crystals (LCs) have attracted great attention, because LCs have large optical anisotropy and can be flexibly manipulated by thermal, electrical, optical or magnetic field [15–18]. In recent years, the optical properties of LCs in the THz regime have been extensively studied. For example, Vieweg et al. proposed a nematic mixture BL037 with a high birefringence of about 0.2 from 0.3 to 2.5 THz . The ordinary and extraordinary indices of 5CB are 1.58 and 1.77 have been investigated by Pan et al., which gives rise to a birefringence of 0.20 ± 0.02 in the frequency range of 0.2-1.0 THz . Recently, Wang et al. reported a new LC mixture NJU-LDn-4 with a large birefringence 0.306 in a broad frequency range of 0.4-1.6 THz .
However, the required thickness of the THz LC cell should be several hundred micrometers to get enough phase shifts owing to the limited birefringence coefficient of the currently existing LCs. Therefore, there are several significant issues, such as high operating voltage, poor pre-alignment and slow response in the THz LC devices. To overcome these issues, some new transparent electrodes in the THz regime have been studied [22–24]. For example, Yang et al. have proposed a THz phase shifters by using highly transparent ITO nanowhisker electrodes, the transmittance of which reached is ∼78%, and the phase shift exceeding π/2 at 1.0 THz was achieved in a ∼517 µm thick cell . In addition, a tunable THz half-wave plate over 1.0 THz with highly transparent graphene electrodes has been obtained, of which the transmittance is more than 98% . Another strategy is to combine LCs with metasurfaces [25–28]. For example, Isić et al. proposed a compact metamaterial absorber based on nematic liquid crystals, which can display modulation depths above 23 dB, more than 15% spectral tuning, and 50-ms response times . Shen et al. proposed a dynamic Fano cloaking in a 250-µm-thick LC layer integrated THz metasurface. The modulation depth reaches over 50% in a broad frequency range of 660 GHz . Some work on the tunable beam steering using reconfigurable metasurfaces coupled with liquid crystals has been studied in recent years [27,28]. In our previous work, we proposed a phase shifter by combining LCs and magnetic nanoparticles, which can effectively enhance the manipulation of LCs, and its phase shift range at 1.45 THz up to π can be achieved over the whole tunable range . Furthermore, we investigated the dielectric anisotropic enhancement characteristics of the dual-frequency liquid crystal doped with carbon nanotube in the THz regime, of which a nearly perfect tunable quarter-wave plate can be achieved at 0.925 THz, while the pure dual-frequency liquid crystal cannot realize this function under the same conditions . Recently, Shen et al. proposed a compact and flexible platform for planar THz photonics based on photopatterned liquid crystal polymer films, which can work as multifunctional THz elements by designing the geometric phase of liquid crystal polymer elements freely .
Polymer-dispersed liquid crystal (PDLC), in which LC droplets with sizes ranging from nanometers to micrometers are embedded in the polymer matrix, were prepared by polymerization induced phase separation (PIPS) process using ultraviolet (UV) light. The PDLC has been drawing much attention in the electro-optic modulators due to its fast response [32,33]. The porous cellular structure of the polymer reduces the correlation length of LC molecules to the size of LC droplets, and allows the LC molecules to freely rotate inside the droplets under the influence of an external field. Nanoparticle-doping technology can effectively improve the working characteristics of LC devices . One of these characteristics is the electro-optic properties of LC devices, especially PDLC devices. Zhang et al. investigated the LC droplet size decreased with the concentration of Ag nanoparticles, which enhanced the response time of the PDLC . Hinojosa et al. reported that the transmittance and driving voltage of the PDLC were improved by doping Au NPs . Shim et al. studied the enhancement of frequency modulation response time for the PDLC by doping the ferroelectric nanoparticles of BaTiO3 . However, most works about the PDLC doped with nanoparticles were focused on the electro-optic modulators. Few studies have considered its application in phase and polarization devices in the THz regime.
In this paper, we experimentally investigated the THz birefringence anisotropy of the PDLC doped with Au NPs and its relaxation effect on the electric field with high alternating (AC) frequency by using terahertz time domain polarization spectroscopy (THz-TDPS) system. Thanks to the surface interaction and the polarization anchoring effect between Au NPs and LC molecules, the response of LC molecules to the electric field is more uniform for the PDLC doped with Au NPs. The results demonstrate that the change rate of refractive index for PDLC doped with Au NPs is 0.91% V−1 as the voltage increases, much smaller than pure PDLC with or without UV radiation. Therefore, the PDLC doped with Au NPs (0.2 wt%) is more suitable for tunable phase shifters. Besides, the polarization relaxation frequency of PDLC with an Au NPs concentration of 0.2 wt% is about 530 kHz, which is more than two times higher than pure PDLC and four times higher than the precursor mixture (no UV). The higher relaxation frequency of PDLC doped with Au NPs benefits from the polarization anchoring effect between Au NPs and LC molecules, which indicates that LC molecules can respond to the alternating electric field more quickly.
2.1 Sample preparation and characterization
The synthesis of Au NPs is known in the literature  and based on the reduction of gold salt in the presence of a stabilizer. The PDLC in this paper was obtained from Jiangsu Hecheng Technology Co., Ltd. (HPC21700-000, HCCH, China). The phase-transition temperature from LC state to isotropic state (TN→I) of pure LC was 114 °C, and its viscosity coefficient (γ) and birefringence were 68 mm2·s−1 and 0.263 (25 °C), respectively. The transmission electron microscopy (TEM) images shown in Figs. 1(a) and 1(b) indicate that the Au NPs are the spherical particles with uniform size. Figure 1(c) shows the UV/Visible absorption spectrum of Au NPs, meaning that there is only one absorption peak at the wavelength of 522 nm, which indicates the approximate particle size of Au NPs. Moreover, the distribution of Au NPs size is shown in Fig. 1(d) with an average diameter of 6.89 nm. The TEM images, UV/Visible absorption spectrum and nanoparticle size distribution of Au NPs all indicate the successful preparation of Au NPs. Then, Au NPs colloid solution was mixed with PDLC to form the mixed solution, and the mixed solutions with different concentrations from 0.1 wt% to 0.3 wt% are obtained. The mixed solution was baked for 12-16 h and ultrasonicated for 4-6 h to reach dispersion of Au NPs.
The mixed solution was added to fill a 0.5 mm-thick LC cell, which is fabricated by four parallel copper wires sandwiched within two 0.6 mm-thick fused silica substrates. The copper wires serve alternatively as positive and negative electrodes. The 4 mm gap between adjacent copper wires ensures the electric field intensity is uniform and that the electrodes do not affect the transmission of THz waves. The photo of the PDLC cell, and its cross-section and geometric parameters can clearly show the arrangement state of the electrodes, as shown by the inset in Fig. 2(b). Then, the encapsulated LC cell was irradiated by UV light with the wavelength of 365 nm and the power of 8 mW/cm2 for 5 min, under the temperature of 25°C to realize PIPS. Under the conditions of a certain thickness of LC cell and a certain UV light intensity, the irradiation time of 5 min is optimally selected in our experiment. When the irradiation time exceeds this time, the birefringence will no longer change. As shown in Fig. 1(e), in the absence of UV light irradiation, both the LC and the Au NPs are randomly distributed in the polymer matrix. After UV irradiating, the LC turns into a lot of droplets with sizes ranging from nanometers to micrometers embedded in the polymer matrix. Figure 1(f) shows the polarization microscopic image of the PDLC after UV irradiating, which indicates that the size of LC droplets is around several micrometers.
2.2 THz-TDPS system
Unlike the traditional THz time domain spectroscopy (THz-TDS) system, an additional polarizer was placed behind the sample to form the THz time domain polarization spectroscopy (THz-TDPS) system, as shown in Fig. 2(a). THz pulses are generated by a low temperature grown GaAs photoconductive antenna, which is excited by a femtosecond laser. The excitation source is a Ti:sapphire laser with 75 fs duration of 80 MHz repetition rate working at 800 nm. A ZnTe crystal is used for electro-optic sampling probe. The sample is settled at the focal point of the THz-TDPS system. A 70 mT constant magnetic field is used to pre-orientation treatment of LC molecules, and the variable DC or AC electric field is used to control the orientation of LC molecules. THz waves were focused into the PDLC device along the z-axis with a linear polarization (LP) light along the y-axis. The ZnTe crystal only detects the LP waves strictly along the y-axis. The additional polarizer is placed behind the sample, and can be rotated to obtain the +45° and −45° polarization components that pass through the sample, as shown in Fig. 2(b). In this method, we obtain the amplitude and phase of two orthogonal LP components of the output THz waves, so the output polarization state can be completely reconstructed.
2.3 Data processing
The time-domain pulse signals of the reference Er(t) and the sample Es(t) can be measured by THz-TDPS system. After Fourier transform, their amplitudes Er(ω), Es(ω) and phases δr(ω), δs(ω) of the reference and samples in the frequency domain are obtained, correspondingly. The transmission amplitude is A(ω) = Es(ω)/Er(ω) and the phase shift between the sample and the reference is Δδ = δs(ω) – δr(ω). Therefore, the effective refractive index n(ω) and absorption coefficient α(ω) can be calculated by 
The effective refractive index of the y-LP component is given by neffy(ω) = none/(no2cos2θ+ ne2sin2θ), where θ is the angle between the orientation of LCs and the y-axis, no and ne are the ordinary and extraordinary refractive index of LCs. Note that the signals we measured when the THz polarizer is fixed at 0° are just the results of the y-LP component, not the complete information of output polarization states. To obtain the output polarization states of samples, we measured the ±45° LP signals E+45°(t) and E−45°(t), so we can get A+45°(ω), A−45°(ω), and Δδ(ω) = δ+45°(ω) – δ−45°(ω). The terminal trajectory equation of electric vector E, also called as polarization ellipse, is obtained as follows: 
3. Results and discussions
3.1 THz anisotropy of PDLC with the Au NPs
First, we measured THz time domain signals of ±45° LP components for PDLC samples in the THz-TDPS system, as shown in Fig. 3(a). Figure 3(b) shows the output polarization states of the samples with different Au NP concentrations at 1.0 THz. There are some important cases for the ±45° LP components: first, if the time domain signals of ±45° LP components are overlapped, the output wave is still LP light along the y-axis, meaning that the optical axis of LC molecules is along the y- or x-axis; second, if the phase delay of the two signals is the same but their amplitudes are different, the output wave is an LP light by rotating a certain angle; the third one is that the output wave is an elliptically polarized light when there is a phase delay between the two signals.
As shown in Figs. 3(c)–3(e), the director of the LC droplet n is different from the director of LC molecules. Owing to the surface anchoring effect between the polymer matrix and the LC molecules, the LC molecules in the droplet exhibit an ordered bipolar configuration [41,42]. However, in the absence of an external electric field or magnetic field pre-orientation, the ellipticity of PDLC (0 wt%) is 0.591, meaning that the output wave is an elliptically polarized state. In this case, the PDLC without Au NPs shows a specific arrangement state rather than a strictly isotropic state, although the directors of the LC droplets are in an uncertain state, as shown in Fig. 3(c). As the red lines shown in Fig. 3(a), there is a slight phase difference between the time domain signals of ±45° LP components for the PDLC/Au NPs (0.2 wt%), suggesting that the output wave is an approximate LP state with a small ellipticity of 0.1268. Moreover, the ellipticity of PDLC/Au NPs (0.1 wt%) is 0.5764, which indicates that the output wave is an elliptically polarized state, and the ellipticity of PDLC/Au NPs (0.3 wt%) is 0.0472, leading to a more perfect LP light. Therefore, the output wave is closer to LP light with the increase of the Au NPs concentration, as shown in Fig. 3(b). The reason is that the surface vertical anchoring effect of Au NPs destroys the arrangement of the LC molecules in the LC droplets [43,44], resulting in a more random distribution of LC molecules (i.e. isotropic state), as shown in Fig. 3(d).
When applying a magnetic field pre-orientation of 70 mT along the x-axis, the phase delays of ±45° LP components are nearly the same, and their output polarization states are all very close to the LP, as shown by the blue lines in Fig. 3(a). Thus, as a pre-alignment, the magnetic field enables LC molecules to be uniformly arranged along the direction of the external magnetic field (i.e. x-axis), and the refractive index can be verified as no. On this basis, another external DC electric field is applied along the y-axis, and the output polarization states are also very close to the LP due to the same phase delays of −45° and +45° LP components, as shown by the green lines in Fig. 3(a). Consequently, LC molecules are oriented to the direction of the external electric field (i.e. y-axis) because the effect of the electric field on LC molecules is greater than the magnetic field, so the refractive index is ne in this case. The orientation of PDLC molecules with Au NPs dispersing in the presence of electric (or magnetic) field is shown in Fig. 3(e).
Then, we measured the THz birefringence anisotropy of the samples when applying a DC electric field in the THz-TDPS experimental setup. As shown in Fig. 4(a), the time domain signal delay is increased with the increase of the voltage, meaning that the refractive index becomes larger correspondingly. After Fourier transform and data processing, we can obtain the corresponding refractive index spectrum, as shown in Figs. 4(b)–4(d). For the precursor mixture (no UV) shown in Fig. 4(b), the refractive index increases sharply when the voltage increases from 30 V to 35 V. In contrast, the refractive index of the pure PDLC increases uniformly with the increase of the voltage, as shown in Fig. 4(c), which is due to the anchoring effect between the polymer matrix and the LC molecules. Moreover, the refractive index varies more uniform with the voltage for the PDLC doped with Au NPs than that of the above two samples, as shown in Fig. 4(d).
Figure 4(e) further compares the relationship between the refractive index and the voltage for the three samples at 1.0 THz. Here, the threshold voltage of the precursor mixture without UV radiation is about 20 V. In contrast, the threshold voltages of PDLC (0 wt%) and PDLC/Au NPs (0.2 wt%) are smaller, about 10 V and 15 V, respectively. Moreover, the three dashed lines are the tangent lines with the maximum tangent slope k of the three curves, and this slope represents the change rate of refractive index as the voltage increases. Note that the smaller the maximum slope k is, the more uniformly the refractive index varies with the voltage. Obviously, the change rate of refractive index k for the PDLC (0 wt%) is 1.14% V−1, less than the precursor mixture (no UV) (k = 1.40% V−1). This result indicates that the precursor mixture forms a distribution that LC droplets embedded in polymer matrix after the UV PIPS process, resulting in a better uniformity of the refractive index changing with the voltage. In contrast, the change rate for the PDLC doped with 0.2 wt% Au NPs is equal to 0.91% V−1, much less than the above two samples, meaning that its refractive index varies more uniformly with the voltage. As mentioned above, the arrangement of LC molecules is affected not only by the orientation force of the polymer surface, but also by the surface vertical orientation force of Au NPs when there is no external field, as shown in Fig. 3(d). When an electric field is applied, the additional polarization anchoring effect between Au NPs and LC molecules appears in the mixed system. There is the co-existence of three effects in the PDLC doped with Au NPs: the anchoring effect between the polymer matrix and the LC molecules, the surface interaction, and the polarization anchoring effect between Au NPs and LC molecules. The co-operation of the above three effects makes the uniform response of LCs to electric field. Therefore, the PDLC doped with Au NPs (0.2 wt%) is more suitable for continuously tunable phase shifters.
Figure 4(f) shows the absorption coefficient of the five samples for the ordinary axis and the extraordinary axis remains below 20 cm−1 across the frequency range of <1.1 THz. It is clear that the absorption coefficient curves of the five samples are basically coincident, indicating that the doping of Au NPs has a negligible effect on the absorption, scattering and reflection of the material, due to the very low doping concentration of Au NPs (0.1 ∼ 0.3 wt%).
3.2 Relaxation effect on alternating electric field with high frequency
We further studied the relaxation properties of the samples on high-frequency AC electric field. In this case, a square wave voltage (1 Hz-1 MHz, 0-100 V) is applied on the electrodes, and its AC frequency and intensity are controlled by the signal generator and voltage amplifier. The AC voltage is maintained as 80 V in our experiment. As shown in Fig. 5(a), the delay of time domain signal decreases with the increase of the AC frequency, which indicates that the refractive index is decreasing accordingly, and the corresponding refractive index spectra are shown in Figs. 5(b)–5(d). It is worth mentioning that the strong relaxation effect gradually eliminates the polarization of LC molecules as the AC frequency increases , which makes the orientation effect of electric field on PDLC molecules disappear gradually. Therefore, the director of LC molecule will gradually be pulled towards the initial direction of magnetic field. Figure 5(b) shows that the refractive index spectra of the precursor mixture (no UV) decrease as the AC frequency increases. A similar process can be observed in Figs. 5(c) and 5(d).
Furthermore, we obtained the refractive index of the five samples changes with the increase of the AC frequency at 1 THz, as shown in Fig. 5(e). Here, we defined the relaxation frequency as the frequency in which the polarization of LC molecules starts to decline. For example, the refractive index of the precursor mixture (no UV) decreases as the AC frequency increases from 130 kHz to 750 kHz, and thus its relaxation frequency is 130 kHz. While the relaxation frequency for the pure PDLC is 250 kHz, so this pure PDLC can respond to the electric field with higher AC frequencies due to the formation of polymer-coated LC droplets. Moreover, the relaxation frequency increases further when the PDLC doped with Au NPs, much larger than the above two samples. For example, the relaxation frequencies for the PDLC with the Au NPs concentration of 0.1 wt% to 0.3 wt% are 360 kHz, 530 kHz, and 630 kHz respectively. A clearer comparison of relaxation frequencies for the five samples can be found in Fig. 5(f). It is observed that the relaxation frequency of the PDLC doped with Au NPs is higher than that of the above two samples. Besides, the relaxation frequency increases gradually with the growing concentration of Au NPs. The relaxation time τ of LCs is related to the relaxation frequency fp, which can be calculated by τ = 1/(2πfp). Hence, the larger the relaxation frequency, the smaller the relaxation time. Therefore, the polarization effect of LC molecules for the PDLC doped with Au NPs can respond to the electric field with higher alternating frequencies than that of the pure PDLC. The higher relaxation frequency indicates a faster response of LC molecules to the alternating electric field.
When no electric field is applied, LC molecules are arranged perpendicular to the surface of Au NPs due to the surface vertical anchoring effect of Au NPs [43,44], as mentioned above. After applying the electric field, the generation of the induced charge on the surface of Au NPs leads to a polarization anchoring force between Au NPs and LC molecules [37,46], as shown in Fig. 6(c). On the one hand, the polarization anchoring force can effectively improve the local field strength, so it makes the LC molecules more orderly orient along the direction of the electric field. On the other hand, on account of the very fast relaxation response of Au NPs to the electric field with little relaxation loss, it leads to a faster relaxation response of the mixed solution by the polarization anchoring effect. Therefore, the mixed solution can respond to the electric field with a higher AC frequency. The response time to the electric field involves many factors, such as the viscosity coefficient of the LC, the thickness of the LC cell, and the driving voltage, and so on. Early research found that the response of the precursor mixture after the UV PIPS process is faster due to the increase of anchoring energy of polymer matrix and LC director in the droplet . Moreover, nanoparticle-doping technology can also effectively improve response time. For example, the literature  reported that doping BTO into PDLC drastically decreased the falling time from 334 to 94 ms, which is due to the increase of the polarization anchoring energy in the BTO-doped PDLC device. Therefore, the higher relaxation frequency of PDLC doped with Au NPs is also of great benefit for a faster response to the alternating electric field.
Finally, it is essential to confirm the output polarization state in this relaxation process with the increase of AC frequency. Here, we choose the PDLC (0 wt%) as an example. As shown in Fig. 6(a), the refractive index changes from ne to no here when only detecting the signal of y component with the increase of AC frequency. At the same time, the output polarization state changes from a LP to elliptical, and then back to a LP state. These experimental results suggest that the optical axis of LC molecules gradually rotates towards the direction of the magnetic field, excluding the case that the optical axis of LC molecules remains unchanged: 1. from the positive crystal to the isotropic state; 2. from the positive crystal to the negative one. The schematic diagrams of the refractive index for the PDLC (0 wt%) when the AC frequency increases from 1 kHz to 1 MHz are shown in Fig. 6(b).
We experimentally investigated and compared the THz birefringence and relaxation effect in the high frequency AC electric field of three different samples, that is the precursor mixture (no UV), the pure PDLC, and the PDLC doped with Au NPs. Some important conclusions are obtained: First, the change rate of refractive index for the PDLC doped with Au NPs is only 0.91% V−1 with the increase of voltage, resulting in a better uniformity of the refractive index changing with the voltage. This uniformity of PDLC doped with Au NPs response to electric field is favorable for the applications in tunable THz phase shifters. Second, the relaxation frequency of PDLC with an Au NPs concentration of 0.2 wt% is about 530 kHz, which is more than two times higher than pure PDLC and four times higher than the precursor mixture (no UV). The higher relaxation frequency indicates a faster relaxation response of LC molecules to the AC electric field. The enhanced uniformity and the faster relaxation response to the electric field show its utility in tunable THz phase and polarization devices.
National Key Research and Development Program of China (2017YFA0701000); National Natural Science Foundation of China (61671491, 61831012, 61971242); Natural Science Foundation of Tianjin City (19JCYBJC16600); Young Elite Scientists Sponsorship Program by Tianjin (TJSQNTJ-2017-12).
We would like to thank Xinmin Yue and Meng Meng (College of Pharmacy, Nankai University) for their assistance in the preparation of the gold nanoparticles.
The authors declare no conflicts of interest.
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