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Abstract
We demonstrate electrically tunable twisted nematic (TN) aligned liquid crystal (LC) terahertz phase shifters with a novel structure, in which a single LC composite polymer thin film is inserted in the middle of the LC cell. For designing such types of phase shifters, we have applied the Mauguin formalism used in LC-based switches for applications in the visible. Experimental results are in good agreement with those predicted by the theoretical model. Using this design, the phase shift has been increased by 14.3° at 1.2 THz in comparison to the conventional design (98.1°). The threshold voltage has been lowered from 0.81 VRMS to 0.48 VRMS while the driving voltage for quarter-wave (π/2) phase shift operation has been reduced from 8.4 VRMS to 6.3 VRMS at 1.2 THz. The dynamic response of devices also enhances significantly. Such design has also successfully been adopted to demonstrate a 2π phase shifter with similar improvement. Full-wave operation is achieved at a bias of 25 VRMS at 1.2 THz using a highly birefringent LC material. Order parameter calculations show that the polymer film improves significantly LC molecular alignment in the thick LC cell for THz applications. We have also compared the figure of merits (FOMs) of the present devices with previously reported THz π/2 and 2π phase shifters.
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1. Introduction
Terahertz (THz) technology is envisioned as a key wireless technology for communication networks sometimes referred to as “beyond fifth-generation (5G) networks” [1–3]. Advances in THz science and technology also enables a variety of new applications including spectroscopy, sensing, security imaging, and biomedical diagnostics [4–6]. In the applications mentioned above, electro-optical (EO) devices such as electrically tunable phase modulators are often required [7]. Nematic liquid crystals (LCs) are frequently material of choice in such devices due to their large electro-optical effect and capability of versatile configuration design tailored for the applications in the THz frequency band [8]. LC devices have been demonstrated to modulate THz electromagnetic wave for providing functions of beam shaping, beam steering, and polarization rotation [9]. In particular, the electrically controllable LC-based THz devices such as phase shifters are attractive as promising candidates in practical devices and instruments because of their simple structure, easily controllable dielectric properties, manufacturing maturity, and compatibility with complementary metal-oxide-semiconductor (CMOS) technology such that advanced, and integrated functions are possible [10,11]. Typically, LC layers in flat-panel displays are few microns in thickness. In contrast, LC-based THz phase shifters require thickness of a LC layer ∼over a few hundred microns for the purpose of providing sufficient optical phase shift for the sub-millimeter and millimeter waves [12]. However, thicker the LC layer is, poorer the alignment of LC molecules become. It leads to not-so-well-aligned orientations of LC molecules. As a result, the modulation performance of the phase shifter degrades. Thus, proposed new approaches of LC THz phase modulators, wherein improvements through the LC materials, LC layer thickness, and device designs are seriously pursued [13–15]. Previously, we have reported sandwich designs in which two LC cells were stacked together to enlarge phase shifts under low operating voltages, with the downside being lower transmittance [10]. More recently, LC activated subwavelength phase grating, and electrically tunable LC-based THz phase shifters integrated with metamaterials and metadevices are blooming [16–19]. About a decade ago, one of us (Lin) and co-workers proposed and demonstrated LC phase modulators with a thin polymer-separated double-layered structure in order to realize a large optical phase shift and remove polarization dependency and yet to lower the driving voltage and maintain dynamic response speed for visible and infrared applications [20,21]. Later on, this design was further developed by Lin’s group to fabricate multilayered LC phase modulators and realize polarizer-free LC lenses for ophthalmic application [22–25]. The common challenge in THz phase shifters and LC ophthalmic lenses is how to achieve a large polarization insensitive optical phase shift while maintaining the dynamic response speed under the constraints of LC birefringence and thickness originated from the material limitation of soft matter. In addition, the choice of LC material is critical: all the electro-optical properties of nematic LC govern the polarization of propagating electromagnetic wave through the material. The THz optical constant of several new types of nematic LCs with high birefringence and low loss have recently been explored for tunable microwave or THz components [26–30]. In another work, a numerical analysis has also been successfully used to explore the characteristics of tunable device embedded with high birefringence LC [31]. These are all potential candidates for enhancement of device performance.
Those considerations have motivated us to propose an electrically tunable THz quarter-wave (π/2) and full-wave (2π) phase shifters by introducing a twist nematic (TN) dual-layer LC cell structure, with an optically isotropic LC composite polymeric thin film in the middle of the LC cell. Preliminary results of a prototype π/2 phase shifter based on this concept have been reported in a conference paper [32] and patent disclosure [33]. Yet, the theoretical analysis and characteristics of this type of devices have not been fully explored. This critical element is a THz-transparent, isotropic and polarization insensitive LC composite polymer (LCP) thin film having alignment capability on both sides. The components and structure of the TNLC THz phase shifters were designed by following the Mauguin adiabatic equation [34]. Moreover, the Mauguin condition was considered to establish a theoretical model to predict the voltage-dependent phase shift at different THz frequencies. This theoretical model was further used to calculate the degree of alignment or order parameter (S) for understanding the twist deformation phenomena in a super thick TNLC cell. The figure-of-merit (FOM) of devices reported in this work and comparable ones in the literature are also calculated and compared. The impact of the proposed devices is not only in their high performance but also in their capability of further development of tunable, focusing LC lens arrays and Pancharatnam-Berry (PB) LC THz lens [35], which needs a half-wave phase shift. By a combination of N pieces of half-wave plates and N piece of PB lenses, one could realize a device with electrically tunable 2N-switching steps of focal lengths or a device with 2N multi-focal planes. A conceptual design of a multi-layered device is also presented.
2. Experimental methods
A LC composite solid polymer thin film was used as an intermediate partition in the LC cell in the devices reported here. The details of the preparation method can be found elsewhere [20–25]. Following is a brief summary, as shown schematically in Fig. 1(a). In the first step, two indium tin oxide (ITO) coated glass substrates with rubbed polyimide for homogeneous alignment were used in a sandwich structure filled with the LC mixture. The LC mixture was made by a combination of 20 wt% nematic LC (E7), 79 wt% reactive mesogen (RM257), and 1 wt% photoinitiator (IRG-184), all from Merck. A voltage (the waveform is sinusoidal) of approximately ∼350 VRMS with a frequency of 1 kHz was applied to align LC molecules in the mixture so that they were reoriented perpendicular to the glass substrates (see Fig. 1(a)) and then the cell was exposed for 1 hour to UV light with intensity of 3 mW/cm2 for photopolymerization in order to solidify the 50 µm-thick LC composite polymer film. Afterwards, we peeled off one ITO coated glass by the thermal releasing process whereas the other ITO-coated glass was still attached with the solidified LC polymer (LCP) thin film.
Fig. 1. The schematic illustration of (a) photopolymerization of polymer thin film and (b) the structure of bi-layer TN-LC THz phase shifter. [Red arrows indicates rubbing directions] (c) A photo of incomplete device (Arrows showing each distinct LC layer separated by LC composite polymer thin film). A schematic illustration of the (d) experimental setup and (e) the THz polarization wave emitted from PCA as detector and emitter. All abbreviations are explained in the text.
If it is used as alignment films for TN LC cells, the parallel alignment of LCP film can also be adopted. In such a configuration, the LCP film can possess alignment capability. The thickness of LC layer in the LCP film is about 50 µm, which is much higher than that of few layers of LC lie on near the both surface of LCP after photopolymerization. Thus, additional phase retardation from the 50µm-thick LCP with parallel alignment is expected. An irregular alignment of LC in LCP under applied voltage across TNCL cell can lead to scattering and hence will reduce phase shift. Thus we chose to polymerize the LCP in the vertically aligned state. Nonetheless, a few layers of LC molecules lie on near the both surface of polymer film even under applied electric force during the fabrication process. As a result, the films possess excellent alignment capability on both side of surface. The fabrication procedure was like used by one the co-authors (Lin et al.) in previous works [20–25].
The thickness of this film was chosen by taking into account: (I) transmittance in the frequency range of 0.4 to 1.2 THz must be sufficient high, (II) polarization free i.e. optically isotropic in the THz frequency band to eliminate additional phase shift experienced by this film and (III) mechanical hardness to support weight of LC molecules both side of the film. For example, thickness of this film was optimized to achieve transmittance high enough in a thick phase shifter. Meanwhile, THz transmittance of the film must be sufficiently high. Thinner film could increase THz transmittance but decrease the mechanical hardness and vise versa. The minimum thickness we can fabricate in the lab is 35 microns.
Next, we prepared two clean bare fused silica sheets as substrates. Pristine PEDOT: PSS and polyimide (PI) as the electrodes [36] and for LC alignment, respectively, were spin-coated on to those substrates. These were then subject to baking, cooling, and mechanical rubbing procedures in successful steps. The ITO-coated glass substrate with the LC composite polymer thin film was then stacked up-side-down onto a structure consisting of the 250µm-thick Mylar spacer layer/PI /pristine PEDOT: PSS/ fused silica substrate, keeping the rubbing orientation of LCP/ITO crosses at 45° with respect to the rubbing direction of the PI layer on the fused silica substrate. Following this, we removed the ITO glass substrate carefully without affecting the LC composite polymer thin film. This was also accomplished by the thermal releasing process. Henceforth, another substrate having a 250µm-thick Mylar spacer layer/PI/ pristine PEDOT: PSS was assembled onto the aforementioned structure. For the 2π phase shifter, the spacer used was twice as thick, i.e., 500µm-thick for each half of the dual-layer structure. Finally, we completed the π/2 or 2π phase shifter by injecting LC material MDA-00-3461 (Merck) and Mixture 1825 (Institute of Chemistry, Military University of Technology, Warsaw, Poland), respectively, into the cavity spaces of both sides of the polymer thin films. The thicknesses of phase shifters are designed according to the expression (Eq. (2).) as presented in a later section on the operating principles. The minimum thickness of TNLC cell required for LC with Δn ∼ 0.2 is larger than 315 µm and 625 µm for π/2 and 2π phase shifter, respectively. Yet, a range of thickness can be found in reported literature, ranging from 500 µm to 600 µm for π/2 phase shifters and from 1 mm to 1.6 mm for 2π phase shifter [9–12,16,17,36–39]. The LC layer thickness for phase shifters were thus chosen in this work to be 550 µm and 1050 µm for π/2 and 2π phase shifters, respectively. The schematic of the dual-LC-layer THz phase shifter with a single polymer intermediate layer is shown in Fig. 1(b). A photo of an incomplete device during the fabrication is shown in Fig. 1(c). The two halves of the device, separated by the LC composite polymer film can clearly be seen. For calibration, we prepared reference cells, i.e., an empty cell (without LC) and a sample cell (without the intermediate layer) with the same LC materials, both with the same thickness as the devices under test. These were used in order to null the effects of reflection by multiple interfaces for comparing the voltage-dependent transmittance and phase shift of devices under study.
The THz properties of the LCP layer, and phase-shifting characteristics of the π/2 and 2π phase shifters were characterized using a photoconductive antenna (PCA) based transmission-type THz time-domain spectrometer (THz-TDS) as described in our previous works [10,12]. In this arrangement, the incident THz wave is along the Z-axis and polarized in the Y-direction and normally incident on the TNLC phase shifter is shown in Fig. 1(d). The polarization of emitted THz wave is perpendicular to the strip lines of PCA as detector and emitter as shown in Fig. 1(e). The TN-LC-based THz phase shifter was biased by 1-kHz square waveform
3. Operating principles
The LC-embedded THz π/2 or 2π phase shifters presented to date utilized either homogenously aligned or TN LC cell [10,12,36]. These devices exhibited characteristics that agreed well with the theoretical predictions based on field-induced Fréedericksz transition, in general [40]. Additionally, the effect of geometry of the device due to boundary conditions has been taken into consideration in our earlier works [9–14]. In this paper, we extend our analysis by employing the Mauguin adiabatic equation [34,40] for normally black (NB) mode, i.e., TN cell is placed between a parallel arrangement of polarizations for the emitter and the detector in the THz-TDS setup. Hence, the Mauguin parameters (u) is expressed as [34,40]:
where, Δn = ne – no is the LC birefringence (0.2 for MDA-00-3461 and 0.4 for Mixture 1825 in the frequency range of 0.4-1.2 THz [36]); ne and no are refractive indices of the LC for e-ray and o-ray, respectively; dLC is the thickness of LC layer and λ is the wavelength of THz wave propagating through the TN-LC cell. Typically, dLC is of the order of several hundred microns in thickness, while λ ≈ 0.3 mm at 1 THz. For our dual-layer TNLC devices, the value of u ranged from 0.26 to 0.8 in the frequency range from 0.4 to 1.2 THz. Recalling that u > >1 for a device exhibiting perfect adiabatic nature [34,40], one can surmise that the effective ne for the LC materials in the thick LC THz phase shifter used is not equal to its typical value determined from measurement with a “thin” cell half as thick or less [36], because LC director misalignment leads to twist deformation at the middle in such a thick LC cell [11]. Thus, we define an effective refractive index for e-ray (ne-eff), for the predication of phase shift rather than using ne as in previous works [9,10,12,36]. We consider four different situations that might occur for LC molecule director alignment in the THz phase shifter, i.e. perfect, random (no order of LC director in a cell that was constructed without any alignment treatments on both substrate surfaces), effective alignment when the applied voltage is 0 VRMS, and LC molecule director at high driving voltage (VD), as schematically shown in Figs. 2(a) to 2(e).Fig. 2. The orientations of LC molecular directors are illustrated schematically for (a) perfect (b) random (c) effective alignment single-layer (d) effective alignment dual-layer at applied voltage 0 VRMS and (e) LC directors at high driving voltage (VD). The incident THz pulse is also depicted.
We assume that the TNLC THz LC cell exhibits the maximum phase shift when LC molecular directors are perfectly aligned (i.e. perfect alignment in Fig. 2(a)). The maximum phase shift (ΔΦmax), which is defined as the phase difference between Fig. 2(a) at VRMS =0 and Fig. 2(d) at VRMS > VD is expressed as [40,41]:
If LC molecular directors are randomly aligned throughout the TNLC THz phase shifters (Fig. 2 (b)), the phase shift (ΔΦran), the phase difference between Fig. 2(b) at VRMS =0 and Fig. 2(d) at VRMS > VD is given by [42–44]
where the refractive index of e-ray for the randomly aligned LC cell is ${n_{e - ram}} = ({2{n_o} + {n_e}} )/3$ [20,21]. Hence Eq. (3) can be rewritten asFrom Eqs. (2) and (4), it can be seen that ΔΦran = ΔΦmax/3. That is, the optical phase shift is three times smaller than the maximum optical phase shift due to the random alignment of LC directors. This is unavoidable because the anchoring energy of the polyimide is not large enough to maintain the LC alignment if the LC layer is very thick. For the situation of effective alignment of the LC director as is shown in Fig. 2 (c). Here we replace ne by ne-eff. The typical expression of temperature-dependent order parameter (S) is [45]:
where T is temperature, Tc is clearing point, $\beta$ is material parameter, $\Delta n(T)$ is temperature dependent birefringence and ${(\Delta n)_0}$ is the birefringence when the order parameter is 1. In a very thick LC cell, we assume the birefringence is ${(\Delta n)_0} = {n_e} - {n_o} \equiv \Delta n$ if the LC directors are aligned well. Thus (Δn)o ≈0.2 for MDA-00-3461 and 0.4 for Mixture 1825 in the frequency range of 0.4-1.2 THz, respectively [36]. On the other hand, $\Delta n(T) = \Delta {n_{eff.\max }}$. In this approximation, we write the order parameter as Eq. (5): where Δneff.max is the effective birefringence due to ne-eff at the effective tilt angle (θeff) experienced by the THz wave transmitting through the TNLC phase shifters [36–38], i.e., $\Delta {n_{eff.\max }} = \sqrt {({({{\cos }^2}{\theta_{eff}} \cdot n_o^{ - 2}) + (si{n^2}{\theta_{eff}} \cdot n_{e - eff}^{ - 2})} )} - n_o^2$. In this case, the value of S would be its maximum value, i.e., for the ideal situation and will decrease with increasing misalignment of LC molecule directors inside the phase shifters.We define the effective birefringence experienced by the THz wave propagating through the LC cell, Δneff at a bias of VRMS > VD as is shown in Fig. 2 (d). The corresponding maximum effective phase shift (ΔΦeff.max) can then be written as
Hence, by considering the electro-optical distortion and electromagnetic energy density in TNLC, the empirical formula for describing the correlation between the driving electric field (E) and the effective tilt angle (θeff) of the LC director at the effective middle position (dS/2) of the TNLC cell, can be written $\Delta {\Phi _{eff.\max }} = \frac{{2\pi \cdot \Delta {n_{eff}} \cdot {d_{LC}}}}{\lambda }$ as [36–38]
4. Results and discussions
In this section, we will summarize results on THz optical properties of the LC composite polymer thin film, phase shifting and transmission properties of the π/2 and 2π phase shifters investigated in this work. The figures of merits of devices studied are estimated and compared to those of similar devises.
4.1 THz optical properties of the LC composite polymer thin film
The transmittance, absorption coefficient, and refractive index of the LC composite polymer (LCP) thin film in the THz frequency band are shown in Fig. 3. The average THz transmittance attained for the polymer thin film is as high as 80% across a broad frequency range of 0.4-1.2 THz (see Fig. 3 (a)). The monotonically decreasing trend for transmittance with frequency could be attributed to the slow-varying broad-band frequency-dependent absorption of the film. Similar phenomena can also be seen in some other types of polymer such as bisphenol A carbonateco-4,40-diphenol carbonate (APC), poly bisphenol A carbonate (BPC), polymethyl methacrylate (PMMA), polystyrene (PS), polyethylene cyclic olefin copolymer (TOPAS), polytetrafluoroethylene (Teflon), and high-density polyethylene (HDPE), etc. [46,47]. The absorption coefficient of our LCP thin film (8.32 cm-1 at 1 THz, see Fig. 3(b)) is lower in comparison to those of APC (11.3 cm-1 at 1 THz), BPC (8.9 cm-1 at 1 THz), PMMA (13.6 cm-1 at 1 THz) and HDPE (13.54 cm-1 at 1 THz), making it more suitable than the aforementioned alternatives for passive broadband THz optical components such as phase shifters, etc. The extraordinary (ne) and ordinary (no) refractive indices of the film are also shown in Fig. 3 (b). For determining ne and no, the transmitted THz signal of the e-ray wave was measured while the LC alignment direction at near surface of LC polymer (LCP) films was mounted parallel to the THz field polarization, whereas the o-ray wave was obtained by simply rotating the LCP film by 90°. Note that both refractive indices are nearly identical in the frequency range of 0.4-1.2 THz. It indicates that the LC composite polymer thin film is isotropic in this frequency band. Therefore, the polymer thin film would not contribute to the voltage-dependent phase shift at THz frequencies. The average refractive index for this polymer layer is 1.46, slightly larger than that of Teflon (1.45) but somewhat smaller than that of TOPAS (1.52) [46,47].
Fig. 3. (a) The transmittance (black dots) of the polymer thin film as a function of frequency. (b) The refractive index and absorption coefficient (blue open circle) of the polymer thin film as a function of frequency. Dotted red line and dashed black line represent the ordinary and extraordinary refractive indices of the film, respectively.
4.2 Phase-shifting performance of QWPs
Next, we investigated the phase-shifting performance of a 550µm-thick TNLC THz phase shifter for π/2 phase operation with a dual-layer structure versus that for the same device with a single-layer structure. In Fig. 4(a) and (b), we show typical THz waveforms transmitted from these phase shifters at three different applied voltages. Besides the one for no bias, the driving voltages were chosen to correspond to (just above) the threshold voltage for LC molecular reorientation and the saturation voltage for quarter wave operation. From the relative time positions of the peaks, phase shifts by THz waves traversing the devices can be deduced.
Fig. 4. THz waveform transmitted from (a) single-layer π/2 phase shifter, (b) dual-layer π/2 phase shifter, (c) single-layer 2π phase shifter and (d) dual-layer 2π phase shifter, at three different applied voltages
The phase shifts as functions of the THz frequency at three different biases are shown in Fig. 5(a). The slopes for linear fit of the data varies from 21° /THz, 73° /THz and 85° /THz for single-layer π/2 phase shifter at the applied voltage of 2, 5 and 150 VRMS, respectively. On the other hand, the slopes for linear fit (the solid, dash, dot, dash dot, dash dot dot and short dash lines) varies from 45° /THz, 78° /THz and 103° /THz for dual-layer structure of TNLC THz π/2 phase shifter at the same three voltages above, respectively. Note that the slopes are in general significantly higher for the device with the dual-layer structure. This can be explained by looking at the role played by the order parameter, defined in Eq. (5). Higher value of order parameter corresponds to larger Δneff and results in increase in ΔΦeff.max at each THz frequency for the dual-layer structure. We will discuss this point further in a later section on the order parameter.
Fig. 5. Phase shifting properties of the dual-layer and single-layer TNLC THz π/2 phase shifter filled with LC material, MDA-00-3461; (a) phase shift versus frequency for various values of applied voltage and (b) phase shift versus applied voltage at different frequencies. The slope of the linear line fitting with experimental data is designated by m in (a). The square, circle, and triangle symbols stand for experimental data. The solid, dash, dot, dash dot, dash dot dot and short dash lines are linear fitting curves in (a) and theoretical curves in (b).
In Fig. 5(b), the phase shifts experienced by THz waves propagating through the single and dual-layer TNLC THz π/2 phase shifters as functions of applied root-mean-square voltage (VRMS) are plotted, at three different THz frequencies. The solid, dash, dot, dash dot, dash dot dot and short dash lines are theoretical curves predicted using Eq. (7). Note the agreements with the experimental data are excellent. The phase shift improves by 3.7° (31.3° from 27.6°) at 0.4 THz, 10.6° (68.7° from 58.1°) at 0.8 THz and 14.3° (112.4° from 98.1°) at 1.2 THz for dual-layer than for single-layer TNLC THz π/2 phase shifter at a bias of 150 VRMS. The corresponding electric field is 3 × 105 V/m. The driving voltage (VD-90°) for 90° of phase shift and threshold voltage (VTN−90°) at 1.2 THz in 550µm-thick dual-layer cell are estimated to be 6.3 VRMS and 0.48 VRMS, respectively. Whereas, VD-90° and VTN-90° of 550µm-thick single-layer π/2 phase shifter are much higher and approximately 8.4 VRMS and 0.81 VRMS, respectively.
The enhancement can also be explained with the capacitor model of the LC cell. The effective driving voltage for the dual-layer LC cell due to dielectric intermediate layer can be modeled as capacitors in series. For the same value of applied voltage across the single-layer device, the applied voltage in dual-layer LC cell with the polymeric layer placed at a distance of 250 µm from of the top substrate can be expressed as [48,49]:
4.3 Phase-shifting performance of 2π phase shifter
We also evaluated the performance of a 1.05mm-thick 2π phase shifter and compared its performance with a single-layer device of the same thickness but without the intermediate layer. The THz temporal waveforms at several bias voltages are shown in Fig. 4(b). In this case, both devices were filled with Mixture 1825 type of LCs materials [28–30,36], taking advantage of its high birefringence (Δn ∼ 0.4 in the frequency range of 0.4–1.2 THz). The phase shifts as functions of THz frequency at three different biases of 2, 7.5 and 150 VRMS are shown in Fig. 6(a). The corresponding slope (m) of linear fit (the solid, dash, dot, dash dot, dash dot dot and short dash lines) of the data increases from 3° /THz, 289° /THz and 304° /THz for single-layer to 17° /THz, 294° /THz and 365° /THz for dual-layer structure for TNLC THz 2π phase shifter.
Fig. 6. Phase shifting properties of the dual-layer and single-layer TNLC THz 2π phase shifters filled with LC material, Mixture 1825; (a) phase shift as a function of THz frequency at different values of applied voltage and (b) phase shift versus applied voltage at different THz frequencies. The slope of the linear fitting with experimental data is designated by m in (a). The square, circle, and triangle symbols stand for experimental data. The solid, dash, dot, dash dot, dash dot dot and short dash lines are linear fittings in (a), and show theoretical curves in (b).
The phase shifts experienced by THz waves while transmitted through the single- and dual-layer 2π phase shifters as functions of applied root-mean-square voltage (VRMS) are plotted at different THz frequencies in Fig. 6(b). The solid, dash, dot, dash dot, dash dot dot and short dash lines are theoretical curves calculated using Eq. (7). The phase shifts achieved are enhanced by 8.3° (98.7° from 90.4°) at 0.4 THz, 53.2° (261.1°from 207.9°) at 0.8 THz for dual-layer in comparison with single-layer THz phase shifter, at an applied voltage of 150 VRMS or an electric field of 1.5 × 105 V/m. Note that 2π phase shift (375° at 1.2 THz) can be achieved only using dual-layer THz 2π phase shifter at driving voltage (VD-360°) of 25 VRMS (electric field is 2.3 × 104 V/m). The threshold voltage (VTN-360°) of the dual-layer 2π phase shifter, 2.2 VRMS is also lower than that of the single-layer 2π phase shifter, 2.8 VRMS. Thus a huge enhancement was achieved in phase shift for the device employing the intermediate layer over that without. Further, the working frequency range of single-layer THz 2π phase shifter is limited to 0.8 THz, due to the low transmittance of the single-layer FWP at higher THz frequencies, which is to be discussed in a latter section. This is partly due to the high absorption coefficient of Mixture 1825 LCs materials beyond 0.8 THz and also imperfect alignment of LC molecules in a thick cell [28–30,36]. The latter can be understood through the order parameter (S) of both single and dual-layer 2π phase shifters, as will be shown in the next section.
4.4 LC order parameters
To understand better the effect of device structures on phase shifting performance, we have calculated the order parameters (S) by using Eqs. (2), (5) and (6) for different types of LC-based THz π/2 phase shifters at 0.8 THz. The S value for the present 550µm-thick single-layer TNLC THz π/2 phase shifter is 0.55. The corresponding S value for the dual-layer TNLC THz π/2 phase shifter of the same thickness is 0.71, about 20% higher. Similarly, we calculated that S ≅ 0.51 and 0.69 for the 1.05mm-thick single- and dual-layer 2π phase shifters, respectively, at the frequency of 0.8 THz. This agrees with our assertion that the degree of LC molecular director alignment has been improved significantly by incorporating LC composite polymer thin film that anchors the LC molecules in the middle of the thick LC cell.
It is interesting to examine S values for other types of reported single-layer TNLC and randomly aligned phase shifters. We notice that, the value of S is close to that of the present single-layer phase shifter with the same thickness (S = 0.55), and improves to 0.62 (MDA-00-3461) or 0.63 (Mixture-1825) by reducing the LC layer thickness to 250 µm [36]. However, the values of S of all the present TNLC phase shifters are very high compared with that for a randomly aligned single-layer LC phase controller of Sasaki et al. [37], i.e., 0.27. Particularly, the dual-layer TNLC π/2 phase shifter exhibits a superb value of S, 0.71. This is a remarkable outcome for the very long wavelength corresponding to THz frequency [in Eq. (6), ΔΦeff is inversely proportional to λ]. Hence, inserting a LCP thin layer in the LC cell has enhanced the effective birefringence significantly by improving the degree of alignment in a dual-layer TNLC π/2 and 2π phase shifters. To corroborate our argument further, we note that scatter in experimental data points in Figs. 5 and 6 for the single-layer devices is more substantial than for the dual-layer device. Similar phenomena also can be seen in THz phase shifters and waveplates reported previously [9,10,36]. Such scatter of experimental data were minimized either by separation of the thick LC cell into a dual-layer structure with the intermediate polymer thin film or by decreasing the LC layer thickness [36].
As has been noted earlier, in our devices the value of Mauguin parameter u varies from 0.26 to 0.8 in the frequency range from 0.4 to 1.2 THz, which is very low. Therefore, this type of configuration has been frequently used in black and white operation by modulating Δn·dLC in visible frequency range [51]. Thus, the present concept can potentially be applied to various devices for the operation at THz frequencies.
4.5 Transmission properties of the devices
Examining the waveforms shown in Fig. 4(a), one finds that the peak amplitudes of THz field at three different voltages are essentially the same for the single-layer π/2 phase shifter, whereas the peak amplitudes of THz filed of the dual-layer π/2 phase shifter decreased slightly from 1.0 to 0.9 a.u. as the bias was increased from 0 to 150 VRMS (Fig. 4(b)). In contrast, peak amplitudes of THz waveforms for both single- and dual-layer 2π phase shifters increased from 0.83 to 1 a.u. (Figure 4(c)) and 0.78 to 1 a.u. (Figure 4(d)), respectively, for the same bias voltages as above. Further, we calculated that the percentage of THz field intensity modulation (M) of all of the devices, defined as, M = [ (EV –E0)/E0 × 100] %, where, EV and E0 are peak amplitudes of transmitted THz field at applied voltage of 150 VRMS and 0 VRMS, respectively. We note that the transmittance in the frequency domain provides more information. This is discussed in later part of this section, with the corresponding figure (Fig. 7). The temporal waveforms clearly show phase shifting. These also shed additional light on the transmittance of the devices. The value of M is approximately -0.05%, -10.2%, 19% and 30% for the single-layer π/2 phase shifter, dual-layer π/2 phase shifter, single-layer 2π phase shifter and dual-layer 2π phase shifter, respectively. The different values of M for these devices strongly suggest the different degree of director alignment for LC molecule has been produced in different type of devices. Interestingly, the difference in M values for devices with single-layer and dual-layer structure is very close for either π/2 phase shifter (10%) or 2π phase shifter (11%). As the same LCP was used in π/2 and 2π phase shifters, the enhancement in orientation order of LC director under external bias is also about the same. The variation of THz waveform (EV –E0) could be attributed to the change of THz optical path length as the phase is changed under external bias. Similar phenomena have also been observed in a high-performance phase modulator demonstrated by Li et al. [11]. Their simulation study revealed that the peak amplitude of THz waveform reaches its maximum value when the LC molecular directors are perfectly oriented (Fig. 2(d)) under external bias. Due to alignment capabilities of the intermediate composite polymer layer in our dual-layer structure, the anchoring effect on the molecules throughout the LC cell is relatively well maintained. As a result, the LC molecular director orientations in the dual-layer cells are more uniform in response to external bias. In contrast, the change of peak amplitudes of THz fields remain negligible for the single-layer π/2 phase shifter due to either poor uniformity of LC molecular director orientation or negligible variation of optical path in response to external bias. This hypothesis is confirmed when one examines such characteristics for single-layer π/2 phase shifters reported previously [9,10,36].
Fig. 7. Frequency-dependent (a) transmittance and (b) change of transmittance with, for both single-layer and dual- layer π/2 phase shifters and 2π phase shifters biased at 150 VRMS. The theoretical fittings curve for π/2 phase shifter w/o intermediate polymer thin film (black solid), π/2 phase shifter w/- polymer intermediate thin film (black dash), 2π phase shifter w/o intermediate polymer thin film (red dash dot) and 2π phase shifter w/- intermediate polymer thin film (red dots) are shown in (a).
The THz frequency-dependent transmittance for both dual-layer and single-layer π/2 and 2π phase shifters are shown in Fig. 7(a). The bias voltage for these cases is 150 VRMS. The THz transmittance of the dual-layer and single-layer π/2 phase shifters are as high as 75% at 0.4 THz and exhibits a decreasing trend with frequency, down to ∼30% and 22%, respectively at 1.2 THz. In comparison, the average THz transmittance of the dual-layer and single-layer 2π phase shifter are lower, 62% and 64%, respectively at 0.4 THz and rapidly decreasing with frequency, down to ∼7% and 26%, respectively at 0.8 THz. Remarkably, the average THz transmittance of the dual-layer 2π phase shifter remains as high as 17% at 1.2 THz, just about 5% lower than that of the π/2 phase shifter. Besides, our data show that THz transmittance of the dual-layer 2π phase shifter declines fairly steeply with increasing frequency from 0.4-0.65 THz, then remains almost constant up to 1.2 THz.
Using the optical constants of all of the parts of the devices, we have estimated the transmittance expected. Fresnel reflections at various interfaces were taken into account. These are also shown in Fig. 7(a). The standard Fresnel formula for multi-layered media and absorption of each layer were employed to calculate transmittance for each device. However, we have not taken into account multi-beam interference. For normally incident polarized THz electromagnetic wave on the device, total Fresnel reflections (R) at the various interfaces (e.g., air to fused silica substrate) of the first half of a dual-layer device were calculated by [52]
where ${n_i}$ and ${n_j}$ are the ith and jth layer of the devices. The ${n_{sub}}$(∼ 1.95 [53]), ${n_{air}}$(= 1), ${n_{PI}}$(=1.72 [46,47]), ${n_{LC}}$(= 1.74 for MDA-00-3461 [36] and 1.96 for Mixture 1825 LC at 1.2 THz [27,28,36]) are the real part of refractive index of fused silica substrate, purged air, polyimide (PI) and LC, respectively and they are relatively constant in the frequency range from 0.4 to 1.2 THz); whereas ${n_{PEDOT}}$ and ${n_{LCP}}$ are the refractive index of electrode (PEDOT: PSS) and intermediate LC composite polymeric layer (LCP), respectively. The ${n_{PEDOT}}$ [54] and ${n_{LCP}}$ (Fig. 3(b)) varied from 26 to 15 and 1.54 to 1.39, respectively in the frequency range of 0.4 to 1.2 THz. Further, the incident THz wave for each layer were determined by where, ${T_{0i}}$ is the transmittance of initial THz wave before incident at ith layer. Further, we calculated absorption coefficient (α) of each layer using imaginary part of refractive index or extinction coefficient (κ) using the relationship where κi is the extinction coefficient of the ith layer and λ is the wavelength corresponding to THz frequencies. The transmittance of THz wave through ith layer is then approximated by where di is the thickness of ith layer in the device. That is, we calculated reflection (Eq. (1)) at each interface and the absorption by each component of the devices. Finally, we calculated total transmittance of the phase shifter by multiplying them all together. The absorption coefficient of fused silica substrate [53] and polyimides [46,47] is 0.35 mm-1 and 5 cm-1, respectively and they are relatively constant in the frequency range from 0.4 to 1.2 THz. The absorption coefficients of MDA-00-3461 LC [36] varied from ∼1 cm−1 to 4 cm−1, and ∼3 cm−1 to ∼10 cm−1for Mixture 1825 LC [27,28,36], in the frequency range of 0.4 1.2 THz. The absorption coefficient of LCP film (Fig. 3(b)) and PEDOT: PSS [54], on the other hand, varied from 0.2 to 8.4 cm-1 and from 10 to 6 cm-1, respectively. We note that data in Fig. 6(a) are transmittance with respect to the reference or empty cell. If we consider loss of the two fused silica substrates, the transmittance of devices reported will be lower.The theoretically calculated transmittance values for π/2 phase shifter with and without the intermediate thin film are 53% and 45%, respectively at 1 THz, and close to our experimental data (w/o: 55% and w/: 41%). On the other hand, the theoretically extracted transmittance values for 2π phase shifter with intermediate thin film are 32% at 1 THz, slightly higher than to our experimental data (23%). Whereas, theoretically calculated transmittance curves are much higher than that of experimental data for 2π phase shifter without intermediate thin film. The loss of transmittance for the single-layer device 2π phase shifter is likely attributed to the random alignment of LC director at the middle of the super thick (1050 µm) TNLC cell. Consequently, the working frequency range of the single-layer 2π phase shifter is cut short as compared to that of the dual-layer device. Nonetheless, the trends for theoretical and experimental values are consistent. Primarily, the decreasing trend of transmission of the devices with frequency is due to the frequency-dependent absorption of LC and others parts of the devices including substrate, alignment layer and electrode. This trend is clear in the theoretical curves shown in Fig. 7(a). Yet, there is significant difference between the experimental and theoretical data for 2π phase shifters that made of Mixture 1825 type LC (12.8% at 0.7 THz). The theoretical calculation was performed with absorption coefficient of extra-ordinary ray [36]. However, the absorption coefficient of ordinary ray of Mixture 1825 LC is also significantly high (absorption coefficient of ordinary ray and extra-ordinary ray are ∼9.7 cm−1 and ∼11.2 cm−1, respectively, at 1.2 THz). [36]. By considering absorption coefficient of ordinary ray as well, the error between experiment data and theoretical calculation is smaller. Further, the theoretical calculation is based on an approximate model as detailed above.
In Fig. 7(b), we have plotted for all devices studied their transmittance differential, defined as ΔT = [|(TV-T0)| × 100%], while the devices were operated at 0 VRMS and 150 VRMS as a function of THz frequency. Values of ΔT for the π/2 phase shifter with the intermediate layer is approximately 10% at 0.4 THz and reduced to 1.3% at 1.2 THz. Whereas, ΔT of the 2π phase shifter with and without the intermediate layer are estimated to be approximately 32.2% and 11.4% respectively at 0.4 THz. ΔT for the π/2 phase shifter without the intermediate layer is approximately 0.3%.
The applied voltage dependence of the THz transmittance of π/2 phase shifter and 2π phase shifter in Fig. 7 show the impact of orientation response of LCs molecules under bias in a device with a thick cell and the drastic improvement in transmittance is possible by employing the intermediate layer. It is likely that ΔT are affected by the responses of LC directors with applied bias for each type of devices studied. The transmittance change under bias is a significant merit for phase shifters used in the transmission mode, as referred in the section on figure-of-merit. In particular, this characteristic is an advantage in multi-cell configurations for imaging applications and tunable THz lens.
4.6 Figure of merit
We now turn to the figures of merit (FOM) of devices studied in this work. FOM of THz phase shifters is defined as [36,45]
where, VD-max (in V) and Tloss (in dB) are the driving voltage for achieving the maximum phase shift (ΔΦmax) and total transmittance loss, respectively, at 1 THz. Values of FOM value are listed in Table 1 for all types of single- and dual-layer THz-phase shifters reported to date.
Table 1. FOM values for different type of LC THZ WPs at 1 THz
We have compared the FOMs for various LC-based THz phase shifters, considering phase shift achieved, transmittance loss and driving voltage required. Those three variables are affected by the phase shifter design, especially loss of the LC layer as well as other component of devices. For example, thicker phase shifter can enhance phase shift but lead to higher transmittance loss. Similarly, highly-birefringent LC means a thinner cell. However, currently available LC with high-birefringence are usually accompanied by high viscosity and loss. A good electrode for the visible, namely indium tin oxide thin film, could ostensibly be ideal for THz phase shifters but it is hampered by high absorption coefficient in the THz frequency band. Since researchers are inclined to employ different components, e.g., LC, for their devices, it is desirable to have a common criterion for judging figure of merit for different designs. While we could compare FOMs employing the same LC, it is not unreasonable that π/2 phase shifters and 2π phase shifters need be optimized by themselves.
The FOMs for the present single-layer and dual-layer π/2 phase shifter are 2.74 and 2.17 deg·dB-1·V-1, respectively. The lower FOM obtained with dual-layer π/2 phase shifter is attributed to additional loss by the intermediate polymer composite thin film (Fig. 3(b)). Yet, this is much higher than those for single-layer π/2 phase shifter used the Au metallic grid (parallel orientation) [55] and one employing the combination of metallic grid and porous graphene [56], 0.07 deg·dB-1·V-1 and ∼0.92 deg·dB-1·V-1, respectively. Somewhat lower FOM values in these devices [55,56] are contributed by the inject of LC with higher absorption coefficients at the frequency of 1THz. On the other hand, the FOM for the present single-layer and dual-layer π/2 phase shifters are smaller than those employing ITO nanowhisker (4.96 deg·dB-1·V-1) [12], DMSO doped PEDOT: PSS [39] (2.49 deg·dB-1·V-1) and ITO finger type pattern (ITO-FTP) (3.56 deg·dB-1·V-1) [38] as electrodes. The superior FOM of these single-layer π/2 phase shifter [12,36,38,39] is primarily attributed to very low drive voltage needed. Meanwhile, FOM of the dual-layer design can be improved significantly by employing advanced electrode materials (Eq. (1)2) and/or thickness engineering of the intermediate polymer composite film to reduce loss.
It can be seen that the FOM value of 1.70 deg·dB-1·V-1 of the present dual-layer THz-2π phase shifter is slightly lower than that of dual-layer or sandwiched-structured ITO nanowhisker-Type A (2.66 deg·dB-1·V-1) in which two identical cells (four substrates) with four ITO nanowhiskers electrode layers were deposited. The higher FOM obtained by such type of device is attributed to extremely low driving voltage needed as the bias voltages were applied on both sides of LC layer individually. On the other hand, FOM value for the device in this work is much higher than those for dual-layer THz-2π phase shifters using ITO nanowhisker-Type B (a single cell made of three substrates with three ITO nanowhiskers electrode layers) [10], ITO nanowhisker-Type C (a single cell composed of three substrates with two ITO nanowhiskers electrode layers) [10] and porous graphene with metallic wire grid [56]. To the best of the authors’ knowledge, an electrically controlled single-layer 2π phase shifter based on NLC has not been explored in the range of 0.4 to 1.2 THz.
4.7 Dynamic response
The dynamic responses of THz phase shifters are important for certain applications. The rise times (voltage-ON) and fall times (voltage-OFF) of the devices fabricated in this work were measured in the THz-TDS setup by biasing the LC π/2 phase shifters with a step-like signal. The dynamic responses of the single- and dual-layer LC THz π/2 phase shifters are shown in Fig. 8. In analogy to thin LC- cells, we expected to see that time-dependent transmittance can be fitted by an exponential function [57,58]. The exponential fitting curves are also shown in Fig. 8.
Fig. 8. Dynamic responses of the QWPs: (a) Rise time and (b) Fall time. Solid and solid dash line are exponential fitting curve. Applied AC voltage of 10VRMS (1 kHz sinusoidal waveform)
The transmittance changes with and without bias is small (but observable). We have normalized the range of change to one to better show the dynamic response. In these experiments, the bias is sinusoidal at a frequency of 1 kHz as in all experiment. The bias of 10 VRMS was turned on instantaneously and the change was recorded over a short time interval, 7 seconds.
In principle, the dynamic response time scales with the square of the cell thickness for a particular LC embedded device [58,59]. Further, if performance of visible LC cells with intermediate layer can be used as an analogy, we expect response of the dual-layer cell to be similar to that of a single cell about half as thick. That is, they are expected to be four times as fast. Figure 8(a) shows that the 20% to 80% rise times of the single-layer and dual-layer π/2 phase shifters are 26 s and 7 s, respectively. This is in good agreement with the experimentally demonstrated trend for a phase modulator using a double-layered structure working at the wavelength of 633 nm [20].
The 20% to 80% fall time of the dual-layer-π/2 phase shifters is 106 s, also significantly faster than of single-layer-π/2 phase shifters which is about 180 s (Fig. 8(b)). In the thin-cell limit, 20% to 80% fall time is expected to be as short as 32 s for our dual-layer π/2 phase shifters. Tentatively, this discrepancy is attributed to long relaxation time of the ultra-thick LC layer, 500 vs several microns for cells used in visible applications. Previously, Altmann et al. [60] reported that the THz phase shifter made of polymer stabilized liquid crystal with thickness of 1600 µm exhibited a relaxation time of approximately 59 min. On the other hand, we showed that a 600µm-thick ITO-FTP (finger-tip-patterned)-based TN-LC phase shifter [38] exhibited 20% to 80% rise time and fall times of 26 and 126 s, respectively; while a 700µm-thick electrically controlled LC phase grating exhibited responses of 23 and 290 s. That is, all thick single-layer LC cells exhibit similar dynamic responses.
Our preliminary results verified that dual-layer structured LC cells incorporating polymer composite film can significantly improve the dynamic response properties of thick LC devices.
4.8 Discussion and future development
Currently, a lot of efforts has been made on metamaterials (MMs) and metasurfaces embedded with a few microns of thin LC layer for manipulating THz wave [13,14,18,61,62]. Because these devices were composed of periodic microstructure or artificial dielectric surface, one can tune key parameters such as transmittance and phase shift, and also an arbitrary value of electric permittivity and magnetic permeability can be designed. Further, a thin LC layer injected with these type of structure offers an unprecedented advantage such as reduced alignment issues, improved operating voltage and significantly decreased response time. For example, Buchnev et al. [63] reported the phase modulation of THz wave using an actively controlled large-area planar MMs combined with an optically thin Mixture 1825 LC layer (∼ 12 µm). The phase retardation of this type of device is associated with the shift of resonance frequency under an external electric field. As a result, a maximum phase shift of 40° was achieved at 0.77 THz when the cell was driven at 20 V with a fast response time of the order of milliseconds. In another work, Sasaki et al. [64] proposed a metasurface with a 40µm-thick LC layer (birefringence of 0.15) to achieve phase shift higher than 90° at 0.5 THz. The enhancement of phase shift is gained with combination of the artificial birefringence (∼ 0.90, six times higher than its intrinsic birefringence of 0.15) generated with the structure of metal mesh, and difference between the impedances of the free space and medium. These are significant advances in tunable THz LC devices. Yet, we note that these devices were not broadband and realizable only at the designed resonant frequency of the device. A relatively complicated procedure and hardware is required for fabricating, designing and optimizing such devices. Besides, the change of phase shift with change of resonant frequency is not sufficiently controllable for realization of THz phase shifter over a range of frequencies. Moreover, the driving voltage required is even higher than those for phase shifters using a sandwiched design of thick LC cell proposed in this work.
The phase shift experienced by the THz wave propagating through a sandwiched LC structure is directly proportional to the product of effective birefringence and thickness of the LC layer (Eq. (2)). The maximum birefringence of Mixture 1825 is approximately 0.4 in the THz frequency domain [28–32,36]. Using such kind of highly birefringence LC, we have previously demonstrated a π/2 phase shifter working at 1.2 THz with a 250µm-thick LC layer [36]. The operating voltage was improved by approximately 49% compared to that of a 550µm-thick LC cell with MDA-00-3461 (Δn≅ 0.2) [36]. The present work showed that with the 550µm-thick dual layer-structure, the operating voltage of the π/2 phase shifter was reduced by approximately 25% in comparison to that with the single-layer structure. Thus, operating voltage of a LC cell with thickness of 250 µm is expected to be further reduced by approximately 74% for a π/2 phase shifter working at 1.2 THz with a combination of a high birefringence LC and dual-layer structure. The estimated operating voltage of a π/2 phase shifter working at 1.2 THz in a dual-layer structure and injected with Mixture 1825 is estimated to be ∼ 4 VRMS. The rise and fall response time of such a device are estimated to be 1.7 s and 15.3 s, respectively with applied voltage of 10 VRMS [58,59]. Further, a multi-layer design as shown in Fig. 9 can be adopted so that the operating voltage, rise and fall response time can be as low as 2.7 VRMS, 0.424 s and 3.82 s, respectively. This is due to the reduced thickness of each LC layer in this type of architecture, as small as 62.5 µm.
Fig. 9. Schematic illustration for a TN-LC THz π/2 phase shifters with inserted multiple thin polymer layer (10 µm thick) having alignment capability on both surfaces as indicated by red arrows when biased at (a) VRMS = 0 and (b) VRMS > VTN. Phase change of THz temporal waveform shown for each layer.
For further improvement in response time, we could use still thinner LC-layer but that would adversely affect the achieved phase shift. Without reducing thickness of the LC layer, rapid relaxation time can also be obtained by fabricating electrodes with a large-area in-plane structure (IPS) on both of substrates, similar to those adopted in a number of optically thin LC loaded THz metamaterial devices or a single-substrate IPS LC cell [61,65]. Furthermore, dual-frequency LCs (DFLC) also can be employed. The use of such LCs, a very fast response time for the redshift and blueshift, 1.044 and 1.376 ms, respectively, was reported for a tunable THz metamaterial loaded with 50-µm-thick DFLCs [66,67]. Thus, the proposed dual- LC layer configuration can yield devices with attractive characteristics, i.e., low applied voltage and fast response time in the THz frequency band, with even a relatively thick cell. Besides, the device is broadband is straightforward to extend the present design of THz phase shifter by employing multiple LC composite thin polymer layers, each of which has an alignment capability on both surfaces. A conceptual design is shown in Fig. 9. Four 10µm-thick LC composite polymer thin films and five 100µm-thick LC layers can be seen in this example. As a single 50µm-thick LC composite polymer layer was used in the 550µm-thick LC π/2 phase shifters, the total amount of transmittance loss in the multi-layered LC device is expected to be the same. Yet, the alignment of LC molecules is expected to be improved significantly. Hence lower driving voltage is required, and misalignment-induced loss can be minimized. On the other hand, the dynamic responses of the multi-layer LC THz devices with intermediate LC composite polymer layer could be further improved if analogy can be drawn from the performance of the dual-layer device reported in this work.
5. Conclusion
In this paper, we have proposed and demonstrated a dual-layer TNLC THz π/2 phase shifters and 2π phase shifters. An isotropic LC composite polymer thin film, which can align LC molecules on both sides of the film is employed to separate the LC cell into two compartments. The transmittance of the LC composite polymer thin film is as high as 80% across a broad frequency range of 0.4-1.2 THz. The dual-layer TNLC π/2 phase shifter is capable of phase shift as high as 112.4° at 1.2 THz. This is much higher than that achieved for single-layer devices (98.1° at 1.2 THz). Besides, the threshold and driving voltage required for quarter-wave operation are lower for dual-layer TNLC π/2 phase shifter. Likewise, the dual-layer TNLC 2π phase shifter employing high-birefringence LCs materials (Mixture 1825) exhibits phase shift of 261.1° at 0.8 THz as compared to that of an identical single-layer cell (207.9°). Full-wave operation, phase shift of 375°, is achieved at 1.2 THz. Further, the modulation depths are improved by approximately 10% for dual-layer devices in comparison to that with the single-layer structure, irrespective of types of phase shifters.
The physics behind the enhanced performance is illuminated by examining the order parameters (S) for all type of THz LC devices studied. We find higher values of S for devices with dual-layer structure. This is correlated with higher transmittance (an improvement of ΔT = 20% at 1.2 THz for dual-layered FWP) as well as larger phase shift (more than 2π at 1.2 THz). These desirable characteristics are attributed to enhanced anchoring strength at interfaces and resulting uniformity of LC molecular director orientation in response to external bias. In this work, the S value of dual-layer π/2 phase shifter (0.71) and 2π phase shifter (0.69) are much higher than those of the single-layer π/2 phase shifter (0.55) and 2π phase shifter (0.51) at the frequency of 0.8 THz.
In addition, we show that the figure-of-merit (FOM) values of the present dual-layer THz-2π phase shifter is 1.70 deg·dB-1·V-1. This is superior to those for similar sandwich-structured LC THz-2π phase shifters using ITO nanowhisker-Type C (0.87 deg·dB-1·V-1) and porous graphene with metallic wire grid (0.61 deg·dB-1·V-1). The FOM for the present dual-layer QWP (2.17 deg·dB-1·V-1), however, is slightly lower than those of the single-layer π/2 phase shifter (2.74 deg·dB-1·V-1) presented in this work and reported existing literatures. This is primarily due to the additional loss raised by the 50µm-thick intermediate polymer layer. The FOM of dual-layer π/2 phase shifter can be improved by employing advanced electrode material and/or reducing thickness of intermediate polymer thin film for minimizing the loss.
The dynamic response of devices with dual-layer structure is also enhanced. The 20% to 80% rise times of the dual-layer and single-layer π/2 phase shifter are 7 s and 26 s, respectively. On the other hand, the 20% to 80% fall times of the dual-layer and single-layer π/2 phase shifter are 106 s and 180 s, respectively. A significant reduction of dynamic response time with dual-layer structure will open up a route to demonstrate fast response thick-LC based THz devices.
Moreover, a general theoretical model has been developed for the applications to LC based THz devices, such as phase shifters, waveplates, lenses, polarizers and spatial light modulator. Theoretically predicted thresholds, bias-dependent phase shifts are in excellent agreement with the theoretical model. Trends for transmission characteristics of the devices are also in good, qualitative agreement with the theory.
For the practical application of the proposed concept, the degree of alignment accuracy and the number of polymer layers or their thicknesses will be crucial parameters to fully control the phase shift performance. This work is an initial approach for further development and improvement of LC-based THz devices including lenses, modulators and polarizers. The proposed device design and theoretical formalism is also applicable to LC based phase shifter devices (such as Pancharatnam-Berry lens and tunable focusing lens) for THz imaging and sensing components.
Funding
Research funded by Ministry of Science and Technology, Taiwan (107-2112-M-009-019-MY3, 110-2112-M-003-012-MY3, 110-2112-M-A49-035).
Acknowledgments
The authors are thanks to Dr. Yu-Jen Wang and Dr. Hung-Chun Lin from National Yang Ming Chiao Tung University, Taiwan, for technical assistance
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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