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We propose an electrically tunable phase shifter for terahertz frequencies. The device is based on a polymer stabilized liquid crystal which allows for a simple device geometry. The polymer stabilized liquid crystal enables continuous tuning of the introduced phase shift with only one pair of electrodes. By characterizing the device with terahertz time-domain spectroscopy we demonstrate a phase shift up to 2.5 terahertz, only slightly changed properties of the neat liquid crystal and significantly reduced response times.
©2013 Optical Society of America
1. Introduction
Liquid crystals (LCs) are anisotropic fluids, thermodynamically located between the common isotropic liquid and the three dimensionally ordered solid [1–3]. They combine the fluidity of a liquid with the anisotropic properties of a crystal. This has been largely exploited in the display industry by the design of displays, flat panel TVs, and smaller devices, but also in adaptive optics, through the design of electrically addressed lenses, optical spatial light modulators and the like. Despite their wide use in the optical frequency range the terahertz (THz) properties are much less studied [4–7]. Yet, THz devices such as waveguides, amplitude or phase-modulators and filters could benefit from LCs as base materials [8–11]. While semiconductor based devices typically exhibit short response times, the achievable modulation depth is rather low. LC based components in comparison often show a much stronger modulation but suffer from longer response times, which can be reduced with polymer stabilization.
2. Sample preparation
A substantial number of individual liquid crystal phases are distinguished each exhibiting different amounts of self-organized order. The simplest LC phase is the nematic phase, which solely exhibits orientational order of the long axis of rod-like molecules, as it is employed in this study. The molecules spontaneously orient along an average direction, called the director n, which is at the same time the uniaxial optic axis of the system. The director field n(r) can easily be influenced and made homogeneous at large scales, via the boundary conditions applied at the substrate surfaces. It can then be altered by the application of external fields. In the present case, planar boundary conditions (director parallel to the substrate) are employed, and the nematic liquid crystal can be switched into a homeotropic orientation (perpendicular to the substrate plane), due to its positive dielectric anisotropy (switching on). This effect is referred to as Freedericksz transition.
Being a dielectric reorientation process, which is independent of the electric field polarity, the reorientation back to the planar orientation needs to be accomplished by the elastic interactions between the substrate and the liquid crystal at turned off field (switching off). Exactly this is the problem for liquid crystal based switchable THz devices, because the field-off reorientation is extremely slow, as very large cell gaps have to be employed [12,13]. A solution to this problem is the use of polymer stabilized liquid crystals [14,15]. This allows for device construction without complicated electrode design, and reduces the response time for very thick samples by several orders of magnitude, often from minutes or hours (even days), down to a few seconds or hundreds of milliseconds.
Polymer stabilized liquid crystals (PSLCs) are fabricated by mixing a small amount (<10%) of a photo-sensitive bifunctional (often liquid crystalline) monomer into the oriented liquid crystal host phase, which then acts as a template and transfers its self-organized order onto the monomers. The neat LC mixture 1852b comprises several isothiocyanato compounds. The transition from the crystalline into the nematic phase occurs below −30 °C while the isotropic phase is reached between 162.9 °C and 168.6 °C. The system is then UV polymerized in the presence of a small amount of photo-initiator. A phase-separated cross-linked polymer network is formed, which resembles the structure of the liquid crystal phase and director field it was formed in (see Fig. 1). Due to its huge surface area, the polymer network has a much larger elastic contribution to the reorientation process of the enclosed liquid crystal than just the substrates in standard devices. The switching on process is controlled by the electric field amplitude, the switching off process is controlled by the polymer network. In order to proof the uv-stability of our sample we verified a stable clearing temperature under incident ultra-violet light.
Fig. 1 Photograph of the polymer network after forming with ultra-violet light. The sample is heated slightly into the liquid crystals isotropic phase in order to enhance the visibility of the polymer network via the residual birefringence.
The polymer stabilized configuration (95% liquid crystal, 5% polymer) has significant advantages over recently reported THz devices based on polymer dispersed liquid crystals, which employ a large amount of polymer (up to 40% polymer and 60% liquid crystal) [16–18]. (i) Our system uses considerably more volume fraction of the actually addressable material, as only the liquid crystal is dynamically modulating the received THz response, not the stationary surrounding polymer. (ii) Index matching is not really a main issue, (iii) scattering phenomena is less pronounced.
Thus we present a dynamically switchable THz device, without significant loss of performance, but with a much simpler addressing geometry, and considerably faster response times than equivalent devices.
3. Experimental characterization
The presented device is based on a sandwich like structure with the PSLC being placed between two fused silica plates which are fixed to each other by a uv-curing adhesive (see Fig. 2). The two fused silica plates have a thickness of 0.7 mm and are separated by 1.6 mm, which also defines the thickness of the PSLC-layer. A metallic wire grid is attached to the top and bottom plate and acts as both, an electrode to align the LC molecules and a polarizer to ensure linear polarization of the THz wave. If a voltage is applied to the electrodes the LC aligns itself along the electrical field between the plates and the propagating THz wave experiences the LC’s ordinary refractive index. After removing the voltage the polymer network pulls the molecules back into their initial state and a propagating wave experiences the extraordinary refractive index component. Due to the birefringence of the liquid crystal a phase shift is introduced. The elastic interactions between the LC and the polymer network allow for a continuously tuning of this phase shift.
Fig. 2 Schematic drawing of the device. The upper and lower plate are made from fused silica and kept in place by a uv-curing adhesive (not shown). The PSLC is aligned by a) the applied voltage to the metallic wire grid or b) the elastic interactions between the LC and the polymer network.
The dielectric properties of both, the pure LC and the PSLC are determined with a standard THz time-domain spectrometer [19]. First a measurement without the sample in place is performed as a reference. Second we insert the sample and the time trace for the extraordinary axis was recorded. And third we align the PSLC by applying a voltage of 100 V to the electrodes and recorded a waveform for the ordinary axis (see Fig. 3). The dielectric values are extracted from the time domain values by a very precise data extraction algorithm including the properties of the fused silica windows [20,21].
Fig. 3 Measured THz Transmission of the sample. Recorded signal amplitude for the reference (black line) and both sample measurements, ordinary (grey) and extraordinary (light grey) direction of the LC molecules in the a) time-domain and b) frequency-domain.
The extracted material parameters in the range from 500 GHz up to 2.5 THz are shown in Fig. 4. The slightly decreased birefringence can easily be explained by the introduced amount of polymer and as a result the lowering of the effective extraordinary refractive index. Since there are no known measurements for the dielectric function of the employed monomer (RM257) it is assumed that the change in absorption is caused by either the additional material itself or interactions between the LC and the polymer network. However, the reduced dicroism will be helpful for future devices.
Fig. 4 Measured material parameters for the PSLC. Calculated values for a) the refractive index and b) absorption coefficient of the mixture in the frequency range from 500 GHz to 2,5 THz. Each in comparison to the values calculated for the pure liquid crystal (black).
By tuning the voltage the refractive index can be adjusted seamlessly between the values for ordinary and extraordinary orientation. As can be seen from Fig. 5(a) the threshold voltage is about 5 V and the transition from one orientation to the other is finished at around 45 V. A full 360 ° phase shift is introduced for a minimum frequency of 684 GHz (dashed line in Fig. 5(a). Figure 5(b) depicts the introduced phase shift versus frequency for selected voltages and clearly shows a nearly linear behavior of the phase shift up to 2.5 THz.
Fig. 5 Dependency of the introduced phase shift. The introduced phase shift is plotted a) versus the applied voltage for selected frequencies and b) versus the frequency for selected values of the applied voltage
In order to determine the relaxation time of the PSLC we performed dynamic measurements using the same setup as employed for the static experiments. Two reference points were selected to detect the transition from the on-state (voltage applied) into the off-state (polymer stabilized) (see Fig. 6(a)). Starting at the on-state the voltage was switched off and the signal amplitude was recorded. The exponential behaviour of the transition becomes clearly observable in a semi-logarithmic plot of the signal amplitude versus time (see Fig. 6(b)). The observed response time is in the order of 7 seconds. Though literature gives no reference value for the passive transition of such a thick LC layer it is assumed to be in the order of hours or days without the presence of a polymer network, which was qualitatively confirmed on non-stabilized samples. A numerical estimation for this value can be performed using
Here γ1 represents the rotational viscosity, d the LC layer thickness and K11, K22 and K33 are Frank’s constants for splay, twist and bend [22]. Since these values are not given for the actually used LC mixture we will use the values for 5CB instead [23, 24] which results in a relaxation time of τrelax = 3352 s or approximately 59 minutes. Since this formula is only valid for very thin sample cells it is assumed that the actual value is several times larger.Fig. 6 Measured relaxation time for the polymer stabilized Liquid Crystal. a) Reference points for the transition measurement from the on-state (black curve) to the off-state (grey curve) and b) the normalized signal amplitude versus time to determine the transition time
4. Conclusion
In conclusion we have presented a simplified structure for liquid crystal based THz or millimetre wave devices and the first measurements for a phase shifter up to 2.5 THz. The combination of a polymer stabilized liquid crystal and a THz phase shifter holds great potential for future applications. The less complicated electrode geometry allows for multi-pixel applications such as phased arrays or a THz display. By changing the composition of the PSLC or reducing the layer thickness the relatively low response time can also be improved.
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