1. Introduction

Liquid crystals have long enjoyed widespread optical applications. Recently, the growth of THz technologies has stimulated interest in applications of liquid crystals in the THz band. A number of studies have been published reporting the THz optical properties of a variety of liquid crystals [1–17], focused primarily on identifying the material with the greatest birefrigence. With few exceptions, these employed THz time-domain spectroscopy (TDS).

In these studies crystal alignment was achieved using one of two techniques: a) coating the inner cell surface with rubbed polyimide [2–11]; or b) applying electric field via electrodes [11–17]. In both cases the crystal molecules were aligned parallel to the cell faces. It was observed that the investigated liquid crystals exhibited significant dichroism as well as birefringence.

Liquid crystal alignment using rubbed polyimide is widely used in optical devices. However, at THz frequencies, the cell thickness must be considerably larger. It has not been demonstrated that perfect alignment throughout the thickness of a THz cell can be reliably achieved by this technique. In contrast, an electric bias field can be increased to achieve saturation of the observed birefringence. In addition, it would be of interest to measure the optical parameters in crystal aligned perpendicularly to the cell faces and to compare them with those observed in parallel alignment.

The great majority of the studies employed cells made of silica or fused quartz [3–17]. This provides a cell with good rigidity and well-defined thickness, as well as offering optical transparency which is important in enabling uniform filling of the cell. Moreover, the technology for depositing and rubbing polyimide layer on silica is well known. However, the use of silica windows in the THz band is problematic. The most important disadvantage is absorption which increases steeply with frequency. This limits the available measurement range: none of the TDS studies using silica windows report measurements above 2.5 THz, and in many the bandwidth is considerably narrower.

Second, the THz refractive index of silica is ~1.95, which causes significant interface reflections at both inner and outer cell surfaces. These reflections contribute to further losses; and more importantly produce echoes in the time-domain signal. In order to minimize the loss and extend the measurement bandwidth, the cell walls and/or the cell thickness are commonly chosen to be thin, typically of the order of 1 mm or less. As a consequence, signal echoes impinge on the main signal peak, so that advanced data analysis is required to extract the measured parameters from the data [6,8,13,14,17].

In this paper we describe a liquid crystal cell using TPX polymer windows and furnished with biasing electrodes capable of aligning crystal either parallel of perpendicular to the cell faces. Two species of liquid crystal are studied: BL037, and GT3-23001.

2. Experimental

2.1 Liquid crystal cell

A schematic drawing of the liquid crystal cell is depicted in Fig. 1 . Polymethylpentene (TPX) was chosen as a material for cell windows, primarily because of its high THz transparency [18,19]. As an additional benefit, the refractive index of TPX in the THz band is 1.46 [18,19], which is close to those of liquid crystals studied, thus minimizing interface reflections within the cell. The thickness of the cell walls was 2 mm. Two pairs of copper electrodes 0.5 mm thick, arranged as shown in Fig. 1, acted as cell spacers. Having two pairs of electrodes made it possible to alternate between crystal orientations without re-positioning the cell in the THz beam. When the bias field was applied, the crystal would orient either parallel or perpendicular to the polarization of the THz beam. The electrodes were affixed to the TPX plates using chemically inert medical-grade double-sided adhesive film with uniform thickness of 55 μm (Adhesives Research Ireland, AR CARE – MH-8890). Channels between the electrodes allowed liquid crystal to be injected into the cell using a medical disposable syringe. The cell had a clear aperture of 20 mm, allowing measurements to be performed using a collimated THz beam.

 

Fig. 1 Schematic drawing of the liquid crystal cell.

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In addition to the copper electrodes internal to the cell, a thin layer of gold was evaporated onto the outer surfaces of the TPX plates. The thickness of this layer was such that it provided conductivity whilst remaining sufficiently transparent to permit transmission measurements. The mean transmission through the cell was ~30%, with weak frequency dependence. These orthogonal electrodes made it possible to align the crystal parallel to the axis of beam propagation. Similarly to the perpendicular alignment provided by the internal copper electrodes, the change in orientation could be performed without re-positioning the cell. Gold-coating the external surfaces of the electrodes – rather than the internal ones – greatly increased the time-separation of the echoes from the main signal peak, making parameter extraction simpler and more accurate.

The electrodes were biased with AC sinusoidal field at 1 kHz. In order to achieve maximum crystal alignment, the internal copper electrodes were biased with 1100 V, whilst the outer evaporated-gold electrodes were biased with 400 V.

The length of the optical path through the cell was determined by measuring the total thickness of the cell and subtracting the combined thickness of the TPX plates, and was found to be 650 ± 70 μm. In order to reduce the uncertainty in the optical pathlength, another type of cell was constructed, which allowed the thickness of the TPX cell to be calibrated. The second type of cell had fused silica walls 1 mm thick separated by a 1 mm thick silica spacer. The pathlength through this cell was determined to be 1.05 ± 0.02 mm, providing a much lower uncertainty than the TPX cell. The refractive indices of the liquid crystals in their non-aligned (unbiased) form were measured in this cell with high accuracy; then the measurements obtained in the TPX cell were normalized to that value.

All measurements were carried out at the ambient temperature of 21°C.

2.2 Liquid crystals

Two nematic liquid crystals were studied, BL037 and GT3-23001, both produced by Merck and designed for high birefrigence. BL037 is a well-known material that has been previously examined in the THz band [11,16]. The BL037 mixture consists of cyanobiphenyls substituted with alkyl and alkoxy groups, and a liquid crystal with a biphenyl/cyclohexane ring system and terphenyls [11,16]. GT3-23001 is a proprietary mixture whose composition has not been released to the public domain.

2.3 THz time-domain spectrometer measurements

The THz time-domain spectrometer (TDS) used a standard configuration incorporating a femtosecond laser, four off-axis parabolic mirrors, a biased GaAs emitter, and electro-optic detection with a ZnTe crystal and balanced photodiodes. The maximum dynamic range of the system was 2000 in amplitude [20], and the frequency resolution in the experiments was 7.5 GHz. The liquid crystal cell was placed in the collimated part of the THz beam, which had a diameter of 25 mm and was horizontally polarised. Measurements were carried out in dry air in order to eliminate water absorption lines from the recorded spectra. The amplitude and phase of the THz signal as a function of frequency were obtained from the measured time-domain data of THz electric field by applying the Fourier Transform using a standard FFT application (OriginPro 8). Reference data was obtained by measuring transmission through an empty cell and taking into account additional interface loss. Loss coefficients (α) and refractive indices (n) of the liquid crystal were calculated using the equations [21]:

The uncertainty in the absorption coefficients was estimated using the method described by Tripathi et al. [22], and was approximately 5%. The uncertainty in the refractive index data is traceable to the uncertainty in the thickness of the silica cell, via $\Delta n=\Delta d(n-1)/d$.

3. Results

3.1 BL037

Figure 2 shows the refractive indices and absorption coefficients of the liquid crystal mixture BL037. The values of parameters at 2 THz are listed in Table 1 . For comparison, values from literature [11,16] are also listed.

 

Fig. 2 Refractive indices (a) and absorption coefficients (b) of the liquid crystal BL037.

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Table 1. Optical Constants of Liquid Crystals BL037 and GT3-23001 at 2 THz^*

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It is notable that the values of the refractive indices and α_o at 2 THz obtained in this work are similar to those presented in Refs [11,16], although the frequency-dependent profiles appear to be substantially different. In contrast, the value of α_e is significantly different from those found in [11] and [16], which also differ significantly from each other. It may be speculated that material properties of BL037 may vary due to different handling history in a way that affects α_e particularly strongly. Extraordinary absorption α_e arises from oscillations orthogonal to the long axis of the molecule, which would be liable to be affected by the configuration and distribution of the attached groups.

The extended measurement range reveals features at higher frequencies, in particular the distinct absorption peaks at 3.2 THz for the ordinary beam, at 1.8 THz for the extraordinary beam, and a combined band at 1.8-3.6 THz for the crystal aligned parallel to the beam axis. Notably, birefringence increases at higher frequencies, from 0.05 at 0.5 THz, and reaching 0.20 at 4 THz. This is due to the fact that the extraordinary refractive index increases with frequency, whilst the ordinary refractive index decreases. The different frequency dependence of n_o and n_e is related, via the Kramers-Kronig relationship, to the different absorption functions for the two beams. As a matter of practical utility it may also be of interest that the refractive index difference between the non-aligned (no bias) state and that oriented parallel to the beam axis varies between 0.12 and 0.21, so that birefringence may be accessed even more effectively by switching the bias on-off.

Dichroism in liquid crystals has been observed by numerous workers [2,4,7,8,10–17], and is generally ascribed to Poley absorption [23,24]. Poley absorption is caused by torsional oscillations around the long axis of the liquid crystal molecule. When the molecule is aligned with its long axis perpendicular to the THz beam polarization (α_o), the induced dipole and the molecular oscillations can be larger than for parallel orientation (α_e). The effect is increased further when the molecule is aligned with its long axis parallel to the direction of beam propagation (α_p), such that all transverse oscillations can be activated. This is reflected in the combined absorption band at 1.8-3.6 THz seen in this crystal orientation.

The refractive index and absorption curves of the non-aligned state of the crystal are of interest because they appear to be unrelated to those of aligned crystal. The refractive index is higher than for any of the aligned states, and the absorption is lower. This may be attributed to the effects that crystal alignment has on polarizability and oscillation activity.

3.2 GT3-23001

GT3-23001 is a relatively new liquid crystal mixture specially designed for microwave and THz applications. Figure 3 presents the refractive indices and absorption coefficients of this material.

 

Fig. 3 Refractive indices (a) and absorption coefficients (b) of the liquid crystal GT3-23001.

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GT3-23001 was designed to be strongly birefrigent, and indeed its maximum birefringence at 1.2 THz is 0.32. However, the birefrigence is frequency dependent, being only 0.05 at its minimum (at 0.5THz), due to the variations in the ordinary and extraordinary refractive indices. The refractive index difference n_nb-n_p is almost as large and varies much less, between 0.12 and 0.25. The differences between the ordinary refractive index n_o and the index observed with the crystal axis aligned parallel to beam propagation n_p may be attributed to the geometrical configuration of the liquid crystal. In the case of n_o the rod-like crystal molecules are aligned parallel to the coherent THz wavefront, so that the induced oscillation has the same phase along the length of the molecule. In the case of n_p, in contrast, the molecules are aligned perpendicularly to the wavefront, so that the phase of the oscillation induced by the travelling wave varies along the length of the molecule.

The absorption spectra are notable by the presence of two large peaks in the ordinary and extraordinary absorption at 0.9 THz and 2.7 THz. These peaks are much weaker in the non-aligned state; whilst in the state aligned parallel to the beam axis a broad band is present peaking at 2.9 THz. Therefore GT3-23001, like BL037, is seen to be strongly dichroic. In the case of GT3-23001, the molecule undergoes similar oscillations when it is aligned with its long axis perpendicular (α_o) or parallel (α_e) to the THz beam polarization; but these oscillations are suppressed when it is aligned parallel to the beam axis (α_p). Also like in BL037, the unbiased state has the lowest absorption.

In view of the fact that in GT3-23001 the non-aligned state and the state oriented parallel to the beam axis have the lowest absorption loss, and the refractive index difference n_nb-n_p is both large and varies less strongly than birefringence, switching between these two states appears to be preferable for device applications. I.e., in devices employing GT3-23001, bias should be applied parallel to the beam propagation, and switching accomplished by turning it on-off. In such a biasing scheme, GT3-23001 would be a superior material to BL037, owing to its larger birefringence and greatly reduced losses.

4. Conclusion

Two liquid crystal materials, BL037 and GT3-23001, were examined in the range 0.4-4 THz using THz time-domain spectroscopy. Refractive indices and absorption coefficients were measured for the ordinary and extraordinary rays by applying electric bias orthogonally to the axis of the traversing beam. In addition, the optical constants were also measured for crystal orientation parallel to the beam axis. In both materials it was found that optical constants in the orientation parallel to the traversing beam differ greatly from those for the ordinary and extraordinary rays. GT3-23001 was shown to have a larger birefringence and lower loss than BL037, provided that biasing parallel to the traversing beam is employed.