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Despite the wide application of liquid crystals (LCs) in the visible frequency range, their properties in the terahertz range have not yet been extensively investigated. In this paper we have investigated the terahertz properties of LCs E7, BL037, RDP-94990 and RDP-97304 using terahertz time-domain-spectroscopy. We find that RDP-94990 has the largest birefringence and smallest absorption in the terahertz range compared to E7 and BL037. We highlight the importance of investigating all parameters, not just the birefringence, when designing fast, efficient and transmissive terahertz LC devices.
©2012 Optical Society of America
1. Introduction
In recent decades, terahertz applications ranging from spectroscopy of chemicals and explosives to bio-medical imaging of breast cancer and skin diseases have been explored [1]. For these and other applications using terahertz waves, optical devices such as waveplates and polarizers are essential components. Liquid crystals (LCs) have been studied for various applications at visible frequencies, such as displays, tunable optical elements, communications, signal processing and beam steering, because they typically have large birefringence and the orientation of the LCs can be externally controlled by electric or magnetic devices. LCs also provide an attractive option for optical devices at terahertz frequencies: phase shifters, Fabry-Perot filters, polarizers, phase gratings, Bragg switches and tunable metamaterials have already been demonstrated [2–4] and proposed [5,6]. However, the practical implementation of these devices is hampered by the relationships between birefringence, thickness and LC switching time. For example, the performance of a phase shifter is determined by the following equation relating the phase (δ) to the thickness (d) and birefringence (Δn) of the liquid crystal for a particular wavelength (λ):
Therefore, a phase shift of π at 1 THz (λ = 0.3 mm) for a typical birefringence of 0.15 would require an LC layer 1 mm thick. In comparison, the same phase shift at visible frequencies (e.g. green light at 550 nm) requires an LC layer only 1.8 μm thick. As a result, the absorption of the LC at terahertz frequencies becomes an important consideration. Furthermore, the response times increase with increasing thickness, such that the turn-on (τon) and turn-off (τoff) times are given by the following equations [7–9]: where Δε and V are the dielectric anisotropy of the LC mixture and the switching bias voltage of the cell respectively, γ1 is the rotational viscosity and Kx is the appropriate expression for the elastic constant of the LC mixture, which is dependent upon the alignment of the LC cell. Vth (Eq. (4)) is known as the threshold voltage of the LC cell. Given the squared dependency on thickness for both turn-on and turn-off times, fast devices at terahertz frequencies will require relatively high birefringence materials. Whilst the birefringence of LC mixtures is well documented at visible frequencies, very little is known about their properties in other frequency regions, including at terahertz frequencies.In this paper we report the terahertz properties of the LC mixtures: E7, BL037, RDP-94990 and RDP-97304. E7 and BL037 are from Merck (Merck KGaA, Darmstadt, Germany) and their terahertz optical properties have been previously studied by various groups [10,11]. RDP-94990 and RDP-97304 are from Dainippon Ink & Chemicals, Inc. (DIC, Tokyo, Japan) and they are both LC mixtures designed to have high optical birefringence and allow for fast switching modes. In addition, the elastic constants and rotational viscosity have been determined in order to calculate the switching times in potential terahertz LC devices.
2. Experimental setup
2.1 LC mixtures
The LC mixture E7, composed of 4-cyano-4’-n-pentyl-biphenyl (5CB), 4-cyano-4’-n-heptyl-biphenyl (7CB), 4-cyano-4’-n-octyl-biphenyl (8CB) and 4-cyano-4’-pentyl-p-terphenyl, has been widely used in LC devices due to its large birefringence (~0.2 in the visible range) and wide nematic temperature range (−10°C to 59°C). BL037 is similar to E7 except that the cyano moiety becomes an alkyl group and the biphenyl moiety becomes an alkoxy group. The mixture also consists of an LC substance with a biphenyl/cyclohexane ring system (BC) and terphenyls (TP). TPs are liquid crystals with three connected benzene rings, which typically provide a large anisotropy. BL037 has a large birefringence of Δn = 0.28 in the visible range and a stable nematic phase from ambient temperatures up to its clearing point at 109°C.
The detailed mixture information for RDP-94990 and RDP-97304 LCs are not provided by DIC due to confidentiality, but they are known to have relatively high birefringence at visible frequencies (0.252 and 0.270 respectively) which is larger than E7 (0.225) but smaller than BL037 (0.282).
2.2 Terahertz time-domain-spectroscopy (THz-TDS)
The measurements were performed using a conventional transmission geometry terahertz time-domain spectroscopy (THz-TDS) system at an ambient temperature of 294 K. The terahertz beam path was purged with dry air to remove the water vapour absorption lines present at terahertz frequencies, and had a bandwidth of 0.2-3 THz.
The LC sample cell consisted of the LC sandwiched between two 1 mm thick layers of fused silica substrate with a refractive index of 1.946 ± 0.001 and absorption of 0.2-12 cm−1 in the 0.2-2.0 THz range. Homogeneous alignment of the LC samples was achieved by rubbing the alignment layer on the substrate. The LC sample cell was rotated such that its director was either perpendicular or parallel to the polarization direction of the incident terahertz wave to measure the ordinary and extraordinary refractive indices and absorption coefficients. The LC sample cell reduced the bandwidth of the spectrometer to 0.2-2.0 THz for LC characterization.
2.3 Measurement of LC physical properties
To calculate the rotational viscosity (γ1) and splay elastic constant (K11) an antiparallel planar alignment LC cell was prepared. For such a cell, Kx in Eqs. (2)-(4) reduces to K11. Therefore, given the known value of the dielectric anisotropy (Δε) for the LC materials (obtained from manufacturer’s datasheet), measurement of the threshold voltage (Vth), turn-on (τon) and turn-off (τoff) times allows the calculation of these values. The bend elastic constant (K33) was calculated by measuring τoff and Vth of a twisted nematic cell (90° twist angle) prepared with the LC mixture of interest, as these parameters reduce to functions of K33 when the above constants are known [8,12]. Material parameters of RDP-97304, RDP-94990 and BL037 were calculated in this manner, whereas published literature values were used for E7 in the calculations of the LC cell performance.
3. Results and discussion
3.1 Terahertz optical properties
The refractive indices and absorption coefficients measured for the four LC samples between 0.2 and 2.0 THz are shown in Fig. 1(a) and Fig. 1(b) respectively. For all four LCs the refractive index for the extraordinary axis is higher than for the ordinary axis and the absorption coefficient for the ordinary axis is higher than for the extraordinary axis. The measured αe for each LC is comparable, and remains below 8 cm−1 across the frequency range. The smallest αe is measured from the RDP-94990 sample, and does not exceed 5 cm−1. RDP-94990 also displays the lowest αo, with values approximately half that of BL037 (which displays the highest αo values). Table 1 summarizes measurements for E7 and BL037 from previous researchers along with the present data for all four LCs. There are small differences between our data for E7 and BL037 and those by Yang et al. [10] and Vieweg et al. [11]. These differences are of the order 1-2% and could be due to subtle differences in experimental protocol or variation from batch to batch in the mixtures themselves.
Fig. 1 Refractive indices (a) and absorption coefficients (b) measured at 294 K: the ordinary and extraordinary axis data are represented with dot-dashed and solid lines respectively.
Table 1. Comparison of the terahertz properties of E7, BL037, RDP-97304 and RDP-94990 from the present work (in bold) and previous studies of E7 and BL037*
The different frequency dependent behaviour of the ordinary and extraordinary orientations has been noted by several previous studies of LCs in the far infrared [11]. For many LCs the absorption in this region has been attributed to strong torsional motions resulting in broad absorption bands, an effect known as Poley absorption [13]. The discrepancy in the relative absorption of the ordinary and extraordinary orientations (αo>αe) has been previously attributed in BL037 to the fact that rod-like liquid crystals can more easily move around their long axis than their short axes, resulting in the molecular vibrations excited by the extraordinary waves being more hindered [11]. The reason for the much reduced ordinary absorption in RDP-94990 when compared to the other three LCs is difficult to ascertain, particularly as the precise composition of the two RDP LCs are not known. We therefore determined γ1, Δε, K11 and K33 (presented in Table 2 ) to glean some insight as well as to enable us to calculate the switching times.
Table 2. LC material parameters and τon at 1 THz for a driving voltage of 1000 V (accuracy:+/− 5%)
The measured birefringences (Δn) of E7, BL037, RDP-94990 and RDP-97304 are shown in Fig. 2 for comparison. Both of the RDP LC mixtures display the highest birefringence values measured in the terahertz region to date, exhibiting a consistently higher birefringence than BL037. The higher birefringence will allow the use of thinner LC cells, thereby reducing the switching time and, as importantly, increasing the transmittance of the terahertz radiation.
3.2 Calculating the response time and transmittance of LC cells
From Table 2 we see that E7 has the largest rotational viscosity of the four LC materials, with a value over twice as large as that of the next most viscous (RDP-94990). BL037 has the largest dielectric anisotropy and bend and twist elastic constants, whereas both of the RDP LCs have relatively low values for these three constants. These values were put into Eqs. (1)-(4) to calculate τon assuming a vertically aligned (VA) LC cell configuration configured to produce a π phase shift of the incoming terahertz beam at a specific frequency. By both ignoring backflow and inertial effects, and assuming no pretilt angle and a strong anchoring energy, the effective elastic constant Kx in Eqs. (2) and (4) reduces to the following form [9]:
Figure 3(a) shows the evolution of the switching time with frequency on a semi-log scale. All four LCs show the same dependence with frequency, as the switching time here is strongly dependent on the birefringence. This is because the thickness of the LC cell is dependent on the birefringence and the frequency, as a larger birefringence and frequency will result in a thinner cell. The comparatively low birefringence of E7 is a disadvantage here, as it requires a thickness of 1.02 mm to produce the π phase change at 1 THz, whereas BL037, RDP-97304 and RDP-94990 only require thicknesses of 780 μm, 730 μm and 750 μm respectively.Fig. 3 τon as a function of (a) phase shifter frequency (using a driving voltage of 1000 V) and (b) driving voltage (using a frequency of 1 THz).
Despite the strong dependence on birefringence, the LC with the fastest switching time is not the most birefringent. Instead, BL037 is much faster because its bend and twist elastic constants exceed ten to twenty times that of the RDP mixtures: these over-compensate for its slightly lower value for the birefringence. Figure 3(b) shows the evolution of switching time with driving voltage: relatively large switching voltages are required to make useable devices. Recently a notch filter using a VA LC cell filled with BL037 was demonstrated with a design frequency of 0.35 THz [16]. The authors measured the switching time to be about one second using a driving voltage of 1000 V. From our measurements of the LC properties and above equations we calculate the switching time for their device to be 1.36 s which is in good agreement with the approximate measurement reported.
It is also important to consider the transmittance of an LC device, this will depend on the absorption of the LC mixture and the thickness used. Figures 4(a) and 4(b) show the resulting transmittance for a π phase shifter for the extraordinary and ordinary axes. RDP-94990 has the best transmittance which reaches over 80% at 0.3 THz and is above 50% across the whole range. In contrast the transmittance of BL037 and E7 along the ordinary axis is particularly poor – they transmit well under 40% across the frequency range. The poor transmittance of BL037 and E7 is due partly to the relatively large thicknesses required (for the E7) but also the significant absorption coefficients recorded for the ordinary axis orientation for these LC mixtures. In Table 3 we have constructed a table of merit to compare switching speed and transmission properties for the four LCs. As indicated in the table, if fast switching is the priority for the device then BL037 is the most suitable provided that moderate to low transmission is acceptable. If high transmission is the priority then RDP-94990 should be selected as long as the slower speed is tolerable.
Fig. 4 Transmittance of an LC cell made of the four LC mixtures producing a π phase change (a) extraordinary axis and (b) ordinary axis.
Table 3. Table of merit: matching LC materials to applications (ratings: best + + + + + ; worst + )
4. Conclusions
This paper presents a comprehensive study of the material and terahertz properties of E7, BL037, RDP-97304 and RDP-94990. In addition to the terahertz optical constants between 0.2 and 2.0 THz, the dielectric anisotropy, rotational viscosity and the bend and splay elastic constants were determined for these materials. The RDP LCs were found to have the highest birefringences measured so far at terahertz frequencies, yet comparatively small values for the other material parameters. The switching times for a VA LC cell were calculated and it was found that BL037 had the fastest response despite not having the highest birefringence, due to its elasticity constants being ten to twenty times greater than those of the other LCs. However, BL037 is significantly less transmissive, especially for the ordinary axis when compared to RDP-94990 and this will limit its usage to devices with low transmission requirements. For devices requiring high transmission and able to tolerate slower switching times, RDP-94990 would be the most suitable choice. These calculations highlight the importance of considering all of the LC mixture parameters, and not simply the birefringence alone, when choosing the mixture that will produce the fastest and usable LC devices.
Acknowledgments
The authors would like to acknowledge financial support from the Research Grants Council of Hong Kong (project codes 616611 and 612310) and DAG 09/10 EG01, the Shun Hing Institute for Advanced Engineering (SHIAE BME-p4/09), and the Basic Science Research Program of Korea (2009-0083512).
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