Parameters of fused silica and the NLC E7.
We review our theoretical and experimental studies on a class of liquid crystal (LC) photonic devices, i.e., terahertz (THz) phase gratings and beam steerers by using LCs. Such gratings can function as a THz polarizer and tunable THz beam splitters. The beam splitting ratio of the zeroth-order diffraction to the first-order diffraction by the grating can be tuned from 10:1 to 3:5. Gratings with two different base dimensions were prepared. The insertion loss is lower by approximately 2.5 dB for the one with the smaller base. The response times of the gratings were also studied and were long (tens of seconds) as expected because of the thick LC layer used. Accordingly, the devices are not suitable for applications that require fast modulation. However, they are suitable for instrumentation or apparatuses that require precise control, e.g., an apparatus requiring a fixed beam splitting ratio with occasional fine tuning. Schemes for speeding up the device responses were proposed. Based on the grating structure, we also achieved an electrically tunable THz beam steerer. Broadband THz radiation can be steered by 8.5° with respect to the incident beam by varying the driving voltages to yield the designed phase gradient.
- liquid crystals
- liquid crystal devices
- phase grating
- grating arrays
- beam splitter
- submillimeter wave
- THz radiation
- tunable circuits and devices
- ultrafast optics
- beam steering
Terahertz (THz) science and technology have advanced significantly over the last 3 decades. Applications are abundant in topics such as material characterization, data communication, biomedicine, 3D imaging, and environmental surveillance [1, 2, 3, 4, 5]. These developments were hampered as crucial quasi-optic components such as phase shifters [6, 7, 8, 9], phase gratings [10, 11, 12], modulators [13, 14], attenuators , polarizers [16, 17], and beam splitters [18, 19, 20, 21] in the THz range are still relatively underdeveloped.
To control the properties of electromagnetic waves at all wavelengths, periodic structures such as gratings are frequently employed. In the THz frequency range, gratings with various periods have been used for tailoring few-cycle pulses . Gratings have also been used as couplers and filters . Tunable THz devices based on an optically and electrically controlled carrier concentration in quantum-well structures have been demonstrated. However, these devices have a limited range of tunability and must be operated at cryogenic temperatures far below room temperature [24, 25, 26]. The potential of gratings with liquid-crystal-enabled functionalities was recognized 2 decades ago . Recently, the focus has been on various tunable THz devices, such as phase shifters, filters, and switches that are controlled electrically or magnetically, employing liquid crystals, primarily nematic liquid crystals (NLCs) [6, 7, 8, 9, 10, 15, 16, 18, 27, 28, 29, 30, 31, 32, 33]. Previously, we demonstrated a magnetically controlled phase grating for manipulating THz waves . This is based on magnetic-field-induced birefringence of the NLCs employed . Nonetheless, electrically controlled phase gratings are generally regarded as desirable for many applications. Therefore, we also proposed and demonstrated an electrically controlled phase grating involving NLCs for THz waves . However, the theoretical analysis was not described in detail and the issue of insertion loss was not touched upon in the previous communication.
Besides, there is an urgent need for THz beam steering devices for scanning the THz beam over the surface of targets to get full topological and spectral information, a metamaterial-based beam steerer has been demonstrated and achieved a maximal deflection angle of 6° . Other groups employed highly-doped semiconductors, such as Indium antimonide (InSb)  and GaAs , so that the propagation properties of surface plasmons mode in highly-doped semiconductor slits can be tailored by changing the carrier density there . On the other hand, the development of a reconfigurable THz antenna , which can electrically steer the THz beam or vary the beam shapes, are useful for applications, such as adaptive wireless, satellite communication networks, and automobile radar systems. The use of LC to construct a phase array for beam steering in millimeter wave range has also been reported recently .
In this chapter, we report our comprehensive experimental studies on a phase grating for THz waves. In particular, we analyzed the insertion loss in such gratings and devised an approach for improving the loss by 2.5 dB over existing designs. Further, we demonstrated an electrically tunable phase shifter array to modulate the phase of THz beam. By applying different voltages on each part of the phase array, we can achieve a gradient in phase shift. Finally, it is shown that the incident THz wave can be steered toward a selected direction.
2. Theoretical and experimental methods
2.1. Operation principles of the phase grating
We designed a binary phase grating consisting of alternating sections of two materials (fused silica and LCs) with different refractive indices. Figure 1 shows the schematic of a generic binary phase grating. The grating is periodic along the x-direction. The THz wave is assumed to be polarized along the x-axis and propagates along the y-direction. Each section of the grating can be considered a retarder that introduces a phase shift. The Jones matrix  associated with a particular retarder can be written as
For our design, we set
In Eq. (4),
For an ideal binary phase grating, the diffraction efficiency
Because of the THz wavelength and THz beam size, the grating can have only a finite number of grooves. Further, the number of grooves
Let the frequency of the THz be centered at 0.3 THz or a wavelength of 1 mm, we designed
When the relative phase difference between adjacent groves is tuned between π and 2π, the diffracted signals between the zeroth order and the first order have the maximal tunable range. This is illustrated in Figure 3 for a grating with 10 periods. For Δ
2.2. Construction of the grating
The design of the grating was based on the structure of the electrically controlled THz phase grating reported in our previous study . This is shown schematically in Figure 4. The incident THz wave was assumed to be polarized in the y-direction. Orientations of the LC molecules for two possible configurations are shown (See Figure 4). The device was designed such that the frequency band of 0.3–0.5 THz would exhibit the highest zeroth-order diffraction efficiency.
Parallel grooves with a period of 2.0 mm, width of 1.0 mm, and groove depth of 2.5 mm were formed by stacking indium tin oxide (ITO)-coated fused silica substrates; the refractive index of these substrates is 1.95 in the sub-THz frequency region (0.2–0.8 THz). The surfaces of the fused silica substrates were coated with polyimide (SE-130B, Nissan) and then rubbed for homogenous alignment. The grooves were filled with NLCs (E7, Merck) and sealed with a sheet of fused silica coated with N,N-dimethyl-N-octadecyl-3-aminopropyltrimethoxysilyl chloride. At room temperature, E7 is a birefringent material with positive dielectric anisotropy. The LC molecules tend to be aligned parallel to the direction of the applied electric field when the applied voltage is greater than a threshold voltage. The effective refractive index of E7 ,
2.3. Transmission measurements
A photoconductive (PC) antenna-based THz time-domain spectrometer (THz-TDS) [32, 44], was used for measuring the zeroth-order diffraction spectra of the device. Briefly, the pump beam from a femtosecond mode-locked Ti:sapphire laser was focused on a dipole antenna fabricated on LT-GaAs for generating a broadband THz signal, which was collimated and collected through the THz phase grating by using off-axis parabolic gold mirrors. A pair of parallel wire-grid polarizers (GS57204, Specac) was placed before and after the device under test. The zeroth-order diffraction of THz radiation was coherently detected by another PC antenna of the same type as that of the THz-TDS and grated by ultrafast pulses from the same laser.
In the second set of experiments, the broadband THz signal was filtered by using a metallic hole array to obtain a quasi-monochromatic wave centered at 0.3 THz and with a line width of 0.03 THz . The diffraction pattern of this beam produced by a grating with various nematic LC orientations was detected and mapped by a liquid-helium-cooled Si bolometer, which was at a distance of 20 cm from the device and located on a rotating arm that could be swung with respect to the fixed grating. The bolometer had an aperture with a diameter of approximately 2.5 cm.
2.4. Insertion loss
To estimate the insertion loss of the THz grating, we regarded the device as a stack of parallel-plate waveguides. The ITO conductive film was not an ideal conductor. We recently showed that for a conductivity of 1500–2200 Ω−1·cm−1, the complex refractive indices of ITO are 20−70 for
2.5. Electrically controlled steering of the THz beam
We have also designed an electrically tunable phase shifter array which can function as the THz beam steerer. Figure 5 shows the structure of the phase shifter array, which is constructed by alternately stacking a number of NLC layers and electrodes. Voltage sources are connected to the electrodes to apply control voltages to each NLC layer. The effective refractive index,
The device was designed such that, when no voltage was applied, the NLC molecules are aligned along the y-direction. In this case, the effective refractive index equals to that of the ordinary component of light in the LC,
where λ is the corresponding wavelength of THz wave. Accordingly, the THz wave can be steered by the control voltage. The phase shift Δ
In this work, we used the 550-μm-thick Teflon sheet as the spacer and the 100-μm-thick copper foil as the electrode. The copper foil was coated with PI Nissan SE-130B on both sides and rubbed for homogeneous alignment along y-direction before applying the voltage. The 18 NLC layers and 19 electrodes were stacked up alternately. The total thickness of the device was 12.1 mm, which corresponded to the size of the aperture,
The threshold voltage
For studying THz beam steering, we modified the THz-TDS by employing a 1 m-long single mode fiber (F-SF-C-1FC, from Newport Corp.) to guide the femtosecond laser directly to the detecting antenna. This way, the optical path remained fixed when the detecting arm was moved as the THz beam was steered. The schematic diagram of the setup is shown in Figure 6. The detection assembly was 20 cm away from the device and located on a rotation arm that can be swung with respect to the fixed device. This system was much more stable and convenient to use than the one employing the bolometer.
3. Results and discussions
3.1. Phase grating
We studied zeroth-order diffracted THz pulses by the phase grating for both ordinary and extraordinary waves were described in Ref. .
Experimentally, the diffraction efficiency of diffracted signals,
In the FDTD simulation, we analyzed the grating structure as a stack of rectangular-shaped waveguides. Neglecting conductive and magnetic loss of the materials involved, the Maxwell-Faraday and Maxwell-Ampere equations can be expanded in the Cartesian coordinates as
To illustrate performance of the grating, experimental and FDTD simulation results of the zeroth-order diffraction efficiencies of the phase grating operated at four values of applied voltage are plotted as a function of frequency in Figure 8 (reproduced from  with permission). Note that the experimentally measured diffraction efficiency was the highest near 0.3 THz, in agreement with the designed frequency. For an ordinary wave at 0.3 THz, the phase difference between fused silica and E7 was close to 2π. Therefore, the transmission of the grating was higher. The THz wave was mainly concentrated in the zeroth order. By contrast, for extraordinary waves, the phase difference was close to π. Furthermore, the diffraction efficiency was lower for the zeroth order because the THz wave was mostly diffracted into the first order.
The experimental and FDTD simulation results are in general agreement. In Figure 8(a, b), there are, however, some discrepancies in efficiencies and peak positions. This is expected as the thickness of the fused silica plates in the grating assembly varies by ±0.1 mm. To check, we calculated diffraction efficiencies of gratings with dimensions of 2.4, 2.5, and 2.6 mm using the FDTD software for the o-ray and e-ray, respectively. Further, a structure with random arrangement of sections with deviations of 0.1 mm centered around 2.5 mm was also studied. The results are shown in Figure 9. Clear shifts are observed in the curves. Therefore, we inferred that the experimental results are reliable.
Because of the periodically arranged ITO films in the grating, our device could be considered a wire-grid polarizer for the THz wave. Only a THz wave polarized perpendicular to the grooves could pass through the electrically tuned phase grating. The measurement result is shown in Figure 10. The extinction ratio of the device shows the ratio of the transmitted THz signals polarized parallel and perpendicular to the grooves is better than 1:100 at ~ 0.3 THz.
3.2. Bolometer measurement results
In Figure 11, we present the intensity profiles of the diffracted 0.3 THz beam polarized in the y-direction. Data are shown for the grating biased from 0 to 90 V. The corresponding effective indices of refraction vary from 1.58 to 1.71. A diffraction maximum was detected at
When the E7 molecules were aligned such that the refractive index was
Figure 12(a, b) show the diffraction efficiencies of the zeroth and first orders as a function of the refractive index of E7 and
Alternatively, these results indicate that the beam splitting ratio can be tuned and varied as a function of the refractive index of the nematic liquid crystal, E7. This is illustrated in Figure 13.
The theoretical calculation results and the experimental results are shown by the curve and dot symbols, respectively in Figure 13. The results indicate that the beam splitting ratio of the zeroth order to the first order can be tuned from 10:1 to 3:5.
3.3. Insertion loss
Insertion loss is a critical parameter for THz devices. We have experimentally and theoretically studied the insertion loss of two classes of devices. Figure 14(a) shows the diffraction efficiency of a grating with a thicker base (
The thickness of the ITO film we used was approximately 200 nm. According to , the conductivity
|Material||Fused silica||E7 (
The estimated loss value was obtained from Eqs. (9) and (10). For the grating with a larger base component (
|Driving voltage||0 V (
||90 V (
||0 V (
||90 V (
|(Estimated insertion loss)
|Measured value||8.0 dB||10 dB||6.1 dB||7.4 dB|
Therefore, if a grating device without a base (
3.4. Device response times
For gratings using LCs, the response time of the device is a concern. The voltage-on and voltage-off times were measured by subjecting the device to a pulse signal. Figure 15(a, b) shows the normalized power as a function of the driving voltage in the voltage-on and voltage-off states, respectively. We defined the rise time as the duration for which the driving voltage was turned on for reducing the power to 37% of the maximum. The fall time was defined as the duration for which the driving voltage was turned off for increasing the power to 63% of the maximum. The rise and fall times of the grating were found to be approximately 23 and 290 s, respectively. The phase grating responded slowly because of the thick LC layer used. Consequently, the present device is not suitable for applications that require fast modulation. However, the device is appropriate for instrumentation or apparatuses that require, for example, a fixed beam splitting ratio with occasional fine tuning.
The response time of the voltage-off state depended only on the material properties and cell thickness. Therefore, it cannot be shortened by applying a higher electric field. To shorten the response time, LCs with birefringence than E7 can be used. Alternatively, dual-frequency LCs can be employed; the use of dual-frequency LCs has been discussed in previous papers [51, 52, 53, 54]. Dual-frequency LCs show high dielectric dispersion, and their dielectric anisotropy is frequency dependent, resulting in a change in sign at the crossover frequency. Dual-frequency materials in which the crossover frequency is a few kilohertz and changes markedly over the range are commercially available. Dual-frequency LCs would enable the operation of phase gratings in a nonzero applied voltage state.
3.5. Phase shifting and beam steering
We have studied the phase shift experienced by the THz wave propagating through the grating in which the control voltages were applied equally to all NLC layers. Figure 16 shows the measured THz waveforms for biasing voltages varied from 0 to 28.8 Vrms. It is obviously that the pulses delay increase as applying voltages increased, as the NLC molecules re-orientate gradually from ordinary to extraordinary refractive index.
By applying Fourier transform on the waveforms in Figure 16, we obtained the phase shift as a function of frequency. This is shown in Figure 17. The phase shift increased with increasing applying voltages as expected. Figure 18 is a plot the phase shift at 0.3 THz as a function of the control voltage. Above the threshold voltage, 1.20 Vrms, the phase shift rapidly increases with the applying voltage. The maximum phase shift reached approximately 11.24 rad. This value is in close agreement with the calculated value.
We measured the beam steering characteristics of the phase-shifting array with the modified THz-TDS shown in Figure 6. Although the applying voltage should be adjusted layer-by layer for beam steering, only nine values of control voltages were available to be applied to each NLC block consisting two NLC layers. As the phase shift Δ
|Applied voltage (Vrms)||Phase shift (rad) at 0.3 THz|
The experimental results demonstrating beam steering are shown in Figure 19.
In the above figure, (a) shows the THz signal before transmitted to the device, and (b) and (c) show the THz signal transmitted through the device with ordinary and extraordinary refractive indices at
In this work, we review our theoretical and experimental studies on electrically controlled LC-based phase gratings for manipulating THz waves. This device can be used as a tunable THz beam splitter, and the beam splitting ratio of the zeroth-order diffraction to the first-order diffraction can be tuned from 10:1 to 3:5. An FDTD simulation was performed to investigate the diffraction effect of the phase grating. The experimental and simulation results were in general agreement. The signal losses of the device were discussed. It was observed that the insertion loss could be reduced by reducing the thickness of the fused silica plates in the base component of the device. The rise and fall times of the grating are approximately 23 and 290 s, respectively. The slow response could be accounted for because of the thick LC layer employed. Consequently, it is not suitable for applications that require fast modulation. However, the device is appropriate for instrumentation or apparatuses that require, for example, a fixed beam splitting ratio with occasional fine tuning. The use of highly-birefringent NLCs or dual-frequency LCs could alleviate the problem somewhat. Besides, we demonstrated a grating-structured phase shifter array that can be used as the THz shifter and THz beam steerer. A phase shift as large as 11.24 rad was achieved. Using a designed voltage gradient biasing on the grating structure, broadband THz signal below 0.5 THz can be steered by as much as 8.5°. The experimental results are in good agreement with theoretical predictions.
This work was partly supported by the National Science Council of Taiwan (104–2221-E-007-093-MY3), the Academic Top University Program of the Taiwan Ministry of Education, and the U.S. Air Force Office of Scientific Research (FA2386–13–1-4086). Chia-Jen Lin is now with Taiwan Semiconductor Manufacturing Company. Contributions by Mr. Chuan-Hsien Lin are gratefully acknowledged.
Ferguson B, Zhang X-C. Materials for terahertz science and technology. Nature Materials. 2002; 1:26-33
Tonouchi M. Cutting-edge terahertz technology. Nature Photonics. 2007; 1:97-105
Zhang X-C, Xu J. Introduction to THz Wave Photonics. New York: Springer; 2010
Nagatsuma T, Ducournau G, Renaud CC. Advances in terahertz communications accelerated by photonics. Nature Photonics. 2016; 10:371-379
Alonso-González P, Nikitin AY, Gao Y, Woessner A, Lundeberg MB, Principi A, Forcellini N, Yan W, Vélez S, Huber AJ, Watanabe K, Taniguchi T, Casanova F, Hueso LE, Polini M, Hone J, Koppens FHL, Hillenbrand R. Acoustic terahertz graphene plasmons revealed by photocurrent nanoscopy. Nature Nanotechnology. 2017; 12:31-35
Yang C-S, Tang T-T, Chen P-H, Pan R-P, Yu P, Pan C-L. Voltage-controlled liquid-crystal terahertz phase shifter with indium-tin-oxide nanowhiskers as transparent electrodes. Optics Letters. 2014; 39(8):2511-2513
Yang C-S, Tang T-T, Pan R-P, Yu P, Pan C-L. Liquid crystal terahertz phase shifter s with functional indium-tin-oxide nanostructures for biasing and alignment. Applied Physics Letters. 2014; 104:141106
Yang C-S, Kuo C, Tang C-C, Chen JC, Pan R-P, Pan C-L. Liquid-crystal terahertz quarter-wave plate using chemical-vapor-deposited graphene electrodes. IEEE Photonics Journal. 2015; 7(6):2200808
Pan CL, Pan RP, Yang CS, Yu P, Voltage-controlled 2 liquid-crystal terahertz phase shifter with indium-tin-oxide (ITO) nanowhiskers as transparent electrodes. In: The XXXI General Assembly of the International Union of Radio Science, paper DFC01.6, Beijing, China. Aug 16–13, 2014
Lin C-J, Li Y-T, Hsieh C-F, Pan R-P, Pan C-L. Manipulating terahertz wave by a magnetically tunable liquid crystal phase grating. Optics Express. 2008; 16:2995-3001
Lin C-J, Lin C-H, Li Y-T, Pan R-P, Pan C-L. Electrically controlled liquid crystal phase grating for terahertz waves. IEEE Photonics Technology Letters. 2009; 21:730-732
Mirzaei B, Silva JRG, Luo YC, Liu XX, Wei L, Hayton DJ, Gao JR, Groppi C. Efficiency of multi-beam Fourier phase gratings at 1.4 THz. Optics Express. 2017; 25:6581-6588
Chen H-T, Padilla WJ, Cich MJ, Azad AK, Averitt RD, Taylor AJ. A metamaterial solid-state terahertz phase modulator. Nature Photonics. 2009; 3:148-151
Nouman MT, Kim H-W, Woo JM, Hwang JH, Kim D, Jang J-H. Terahertz modulator based on metamaterials integrated with metal-semiconductor-metal varactors. Scientific Reports. 2016; 6:26452
Wang M, Vajtai R, Ajayan PM, Kono J. Electrically tunable hot-silicon terahertz attenuator. Applied Physics Letters. 2014; 105:141110
Hsieh C-F, Lai Y-C, Pan R-P, Pan C-L. Polarizing terahertz waves with nematic liquid crystals. Optics Letters. 2008; 33:1174-1176
Farid A, Laurita NJ, Tehrani B, Hester JG, Tentzeris MM, Armitage NP. Inkjet printed wire-grid polarizers for the THz frequency range. Journal of Infrared, Millimeter and Terahertz Waves. 2017; 38:276-282
Park J-H, Yu C-J, Kim J, Chung S-Y, Lee S-D. Concept of a liquid-crystal polarization beamsplitter based on binary phase gratings. Applied Physics Letters. 2003; 83:1918-1920
Berry CW, Jarrahi M. Broadband terahertz polarizing beam splitter on a polymer substrate. Journal of Infrared, Millimeter and Terahertz Waves. 2012; 33:127-130
Ung BS-Y, Fumeaux C, Lin H, Fischer BM, Ng BW-H, Abbott D. Low-cost ultra-thin broadband terahertz beam-splitter. Optics Express. 2012; 20(5):4968-4978
Mo G-Q, Li J-S. Compact terahertz wave polarization beam splitter using photonic crystal. Applied Optics. 2016; 55:7093-7097
Filin A, Stowe M, Kersting R. Time-domain differentiation of terahertz pulses. Optics Letters. 2001; 26:2008-2010
Garet F, Coutaz J–L, Narzarov M, Bonnet E, Parriaux O, Racine G, THz time-domain spectroscopy study of grating couplers and segmented grating filters. In: IEEE 2004 Joint 29th Int. Conf. on Infrared and Millimeter Waves and 12th Int. Conf. on Terahertz Electronics. Oct 2004. pp. 181-182
Kersting R, Strasser G, Unterrainer K. Terahertz phase modulator. Electronics Letters. 2000; 36:1156-1158
Kleine-Ostmann T, Dawson P, Pierz K, Hein G, Koch M. Room-temperature operation of an electrically driven terahertz modulator. Applied Physics Letters. 2004; 84:3555-3557
Libon IH, Baumgärtner S, Hempel M, Hecker NE, Feldmann J, Koch M, Dawson P. An optically controllable terahertz filter. Applied Physics Letters. 2000; 76:2821-2823
Chen J, Bos PJ, Vithana H, Johnson DL. An electro-optically controlled liquid crystal diffraction grating. Applied Physics Letters. 1995; 67:2588-2590
Chen CY, Hsieh CF, Lin YF, Pan RP, Pan CL. Magnetically tunable room-temperature 2π liquid crystal terahertz phase shifter. Optics Express. 2004;12:2625-2630
Wu HY, Hsieh CF, Tang TT, Pan RP, Pan CL. Electrically tunable room-temperature 2π liquid crystal terahertz phase shifter. IEEE Photonics Technology Letters. 2006; 18:1488-1490
Chen C-Y, Hsieh C-F, Lin Y-F, Pan C-L, Pan R-P. Liquid- crystal-based terahertz tunable Lyot filter. Applied Physics Letters. Mar. 2006; 88:101107
Ho I-C, Pan C-L, Hsieh C-F, Pan R-P. Liquid- crystal- based terahertz tunable Solc filter. Optics Letters. 2008; 33:1401-1403
Ghattan Z, Hasek T, Wilk R, Shahabadi M, Koch M. Sub- terahertz on–off switch based on a two-dimensional photonic crystal infiltrated by liquid crystals. Optics Communication. 2008; 281:4623-4625
Jewell1 SA, Hendry E, Isaac TH, Sambles JR. Tuneable Fabry–Perot etalon for terahertz radiation. New Journal of Physics. 2008; 10:033012
Pan R-P, Hsieh C-F, Chen C-Y, Pan C-L. Temperature- dependent optical constants and birefringence of nematic liquid crystal 5CB in the terahertz frequency range. Journal of Applied Physiology. 2008; 103:093523
Neu J, Beiggang R, Rahm M. Metamaterial-based gradient index beam steerers for terahertz radiation. Applied Physics Letters. 2013; 103:041109
Xu B, Hu H, Liu J, Wei X, Wang Q, Song G, Xu Y. Terahertz light deflection in doped semiconductor slit arrays. Optics Communication. 2013; 308:74-77
Xu Z, Mazumder P. Terahertz beam steering with doped GaAs phase modulator and a design of spatial-resolved high-speed terahertz analog-to-digital converter. IEEE Transactions on Electron Devices. 2014; 61:2195-2202
Bin Shams MI, Jiang Z, Qayyum J, Rahman S, Fay P, Liu L. A terahertz reconfigurable photo-induced fresnel-zone-plate antenna for dynamic two-dimensional beam steering and forming. In: Microwave Symposium (IMS), 2015 IEEE MTT-S International, Phonenix, AZ. May 2015. pp. 1-4
Kamoda H, Kuki T, Fujikake H, Nomoto T. Millimeter-wave beam former using liquid crystal. In: Microwave Conference, 2004. 34th European, Amsterdam, The Netherlands. Oct 2004. pp. 1141-1144
Brosseau C. Fundamentals of Polarized Light. New York: Wiley; 1998
Goodman JW. Introduction to Fourier Optics. 2nd ed. McGraw-Hill; 1996
Fowles JR. Introduction to Modern Optics. 2nd ed. Holt, Rinehart and Winston; 1975
Yang C-S, Lin C-J, Pan R-P, Que CT, Yamamoto K, Tani M, Pan C-L. The complex refractive indices of the liquid crystal mixture E7 in the terahertz frequency range. Journal of the Optical Society of America B: Optical Physics. 2010; 27:1866-1873
Yang C-S, Lin M-H, Chang C-H, Yu P, Shieh J-M, Shen C-H, Wada O, Pan C-L. Non-Drude behavior in indium-tin-oxide nanowhiskers and thin films by transmission and reflection THz time-domain spectroscopy. IEEE Journal of Quantum Electronics. 2013; 49:677-690
Pan C-L, Hsieh C-F, Pan R-P, Tanaka M, Miyamaru F, Tani M, Hangyo M. Control of enhanced THz transmission through metallic hole arrays using nematic liquid crystal. Optics Express. 2005; 13:3921-3930
Chen C-W, Lin Y-C, Chang C-H, Yu P, Shieh J-M, Pan C-L. Frequency-dependent complex conductivities and dielectric responses of indium tin oxide thin films from the visible to the far-infrared. IEEE Journal of Quantum Electronics. 2010; 46:1746-1754
Kamoda H, Kuki T, Fujikake H, Nomoto T. Millimeter-wave beam former using liquid crystal. In: Proc. 34th European Microwave Conf., Amsterdam, Netherlands. 2004. pp. 1141-1144
Cheng DK. Field and Wave Electromagnetics. 1st ed. Addison-Wesley; 1983. p. 465
Ku C-P, Shih C-C, Lin C-J, Pan R-P, Pan C-L. THz optical constants of the liquid crystal MDA-00-3461. Molecular Crystals and Liquid Crystals. 2011; 541:303-308
Kamoda H, Kuki T, Nomoto T. Conductor loss reduction for liquid crystal millimeter-wave beam former. IEICE Electronics Express. 2005; 2:471-476
Jewell SA, Taphouse TS, Sambles JR. Rapid switching in a dual-frequency hybrid aligned nematic liquid crystal cell. Applied Physics Letters. 2005; 87:021106
Golovin AB, Shiyanovskii SV, Lavrentovich OD. Fast switching dual-frequency liquid crystal optical retarder, driven by an amplitude and frequency modulated voltage. SID 03 Digest. 2003; 2(1472):55
Hsieh CT, Huang CY, Lin CH. In-plane switching dual-frequency liquid crystal cell. Optics Express. 2007; 15:11685-11690
Chen C-C, Chiang W-F, Tsai M-C, Jiang S-A, Chang T-H, Wang S-H, Huang C-Y. Continuously tunable and fast-response terahertz metamaterials using in-plane-switching dual-frequency liquid crystal cells. Optics Letters. 2015; 40:2021-2024