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OPTICS LETTERS / Vol. 40, No. 7 / April 1, 2015
Universal polarization terahertz phase controllers using randomly aligned liquid crystal cells with graphene electrodes Tomoyuki Sasaki,1,* Kohei Noda,1 Nobuhiro Kawatsuki,2 and Hiroshi Ono1 1
Department of Electrical Engineering, Nagaoka University of Technology, 1603-1 Kamitomioka, Nagaoka, Niigata 940-2188, Japan 2
Department of Materials Science and Chemistry, Graduate School of Engineering, University of Hyogo, 2167 Shosha, Himeji, Hyogo 671-2280, Japan *Corresponding author: [email protected] Received February 4, 2015; revised March 10, 2015; accepted March 11, 2015; posted March 11, 2015 (Doc. ID 233838); published March 30, 2015
We present a universal polarization terahertz (THz) phase controller using a randomly aligned liquid crystal (LC) cell with graphene electrodes. The LC cell was fabricated using a nematic LC and two quartz substrates that were coated with a monolayer of graphene as the transparent electrode. The LC in the cell was prepared without any alignment treatments and was randomly aligned. The size of the random domains and the width of the disclination lines in the LC layer were several tens of microns. These textures disappeared when an alternating voltage was applied to the LC through the graphene layers. Using a THz time domain spectroscopic technique, we investigated the complex transmittance of the LC cell. The LC cell was highly transparent in the THz frequency range, and there was little change in the transmittance with the applied voltage. This indicated that the scattering loss originating in the randomly aligned LC molecules was small for the THz waves. We also demonstrated that the THz phase shift could be controlled by the applied voltage. The amplitude of the phase shift was explained by the ordinary and extraordinary refractive indices of the LC. These LC cells with graphene electrodes can be used to realize universal polarization THz phase controllers because of the random alignment. © 2015 Optical Society of America OCIS codes: (230.3720) Liquid-crystal devices; (260.5430) Polarization; (300.6495) Spectroscopy, terahertz; (310.7005) Transparent conductive coatings. http://dx.doi.org/10.1364/OL.40.001544
Terahertz (THz) technologies have received considerable attention in various fields [1,2]. For widespread adoption of THz technologies, we should develop not only highpower light sources and highly sensitive detectors, but functional THz elements as well [3–14]. Chen et al. presented an active metamaterial device capable of efficient real-time control and manipulation of THz radiation [6]. Nagai et al. reported an achromatic THz wave plate composed of stacked parallel metal plates with a hole array [11]. These studies demonstrated that the propagation of THz waves can be manipulated using artificial structures [3,4,6–8,11]. There have also been several studies on THz devices employing liquid crystal (LC) materials [5,9,10,12–14]. LCs are excellent media for various optical applications because they are highly transparent in the visible range, have a large optical anisotropy, and respond to external fields [15,16]. Recent studies on the optical constants of LCs in the THz frequency range have shown that LCs are potentially useful for functional THz devices [17–20]. For LC optical devices, including LC displays, indium tin oxide (ITO) films are widely used as transparent electrodes [16]. However, ITO films are opaque in the THz frequency range [13]. When thin ITO films are used to increase the transmittance, the electrical resistivity increases significantly [13]. Therefore, transparent electrodes in the THz frequency range are under considerable investigation to realize electrically controllable THz devices using LCs [9,10,13]. Wu et al. studied voltage-controlled THz phase shifters using LC cells with graphene layers as the electrodes [9]. Graphene THz modulators by ionic liquid gating were also reported [21]. Graphene exhibits good electrical conductivity, chemical stability, and mechanical strength [22,23]. Additionally, graphene is highly transparent in 0146-9592/15/071544-04$15.00/0
a wide frequency range [22,23]. We believe that graphene has considerable promise as transparent electrodes for LC devices in the THz frequency range. In previous studies on LC THz phase shifters, LC molecules in the cells were oriented using alignment films that were coated on the substrates [5,9,10,13,14]. To obtain sufficient phase shifts using an LC cell, the thickness of the LC layer should be increased compared with optical applications. This is because THz waves are in the sub-millimeter range, which is several hundred times longer than visible light waves. However, it is difficult to fabricate homogeneously aligned LC cells with a submillimeter-thick LC layer using common polymeric alignment films. For optical applications, inhomogeneously or randomly aligned LCs cause scattering losses because of the domain textures and the defects. However, the scattering loss may be reduced in the THz frequency range because the sizes of the scattering textures in the LC layer are small in comparison to the THz waves. Therefore, we believe that highly transparent LC phase shifters can be realized without the use of special alignment treatments. Additionally, the random alignment means that the device is polarization independent unlike previously reported LC THz elements that require an initial alignment. These universal polarization THz phase shifters will be useful for various THz applications such as in spatial phase modulators and interferometers. In the present study, we propose a universal polarization THz phase controller using an LC cell with graphene electrodes. The LC cell was fabricated without the use of alignment layers to obtain the random alignment. Based on optical observations, we investigated the texture of the LC layer, control of the alignment using voltage, and the dependence on the polarization. The © 2015 Optical Society of America
April 1, 2015 / Vol. 40, No. 7 / OPTICS LETTERS
the domain texture and the disclination lines gradually disappeared with increased applied voltage [Figs. 1(a)–1(c)]. When a sufficiently high voltage was applied to the LC cell, a dark-field image was observed as shown in Fig. 1(d). This result indicates that the LC molecules were reoriented perpendicularly to the substrates by the applied voltage. This means that the graphene layers can be used as electrodes for the LC cell. Figure 2 shows transmittance spectra in the visible range. These data were measured using randomly polarized light at normal incidence. The detector was placed 5 cm away from the LC cell. When voltage was not applied to the cell, the transmittance was relatively low (below 50%). This is because the visible light was scattered by the domain structure and the disclination lines, which are larger than the wavelengths of the visible light. However, the transmittance increased when the applied voltage increased. For V 0 100 V, we observed transmittance above 85% at 800 nm. This result indicates that the LC molecules are unidirectionally oriented, and the domain structure and the disclination lines disappeared by applying a sufficiently high voltage. Figure 3 shows the waveforms of the THz pulse transmitted through the LC cell. The THz time-domain spectra were measured for normal incidence under parallel 100
V0 (V) Transmittance (%)
complex transmittance in the THz frequency range was measured using a THz time-domain spectroscopic technique. By analyzing the data, we demonstrated that the randomly aligned LC cell with graphene electrodes was applicable for use as voltage-controlled THz phase shifters. The amplitude of the THz phase shift was discussed on the basis of the ordinary and extraordinary refractive indices of the LC. An empty cell was fabricated using two quartz substrates that were coated with a monolayer of graphene (Graphene Platform, Japan). Graphene was transferred on the whole face of the quartz substrates with the area of 25 mm × 25 mm. A nematic LC, 4-pentyl-4′-cyanobiphenyl (5CB, Wako, Japan), filled the empty cell by capillary action. The sheet resistance of the graphene substrate was 0.6 kΩ∕sq. The thickness of the quartz substrates was 0.5 mm. The thickness of the LC layer was adjusted to 0.10 mm using film spacers. The texture of the fabricated LC cell was observed using a polarizing optical microscope (ECRIPS E200, Nikon, Japan) with crossed nicols. We measured transmittance spectra of the LC cell in the visible and THz frequency ranges using a visible spectrometer (HR4000, Ocean Optics) and a THz time-domain spectrometer (TAS7500TS, Advantest, Japan) with the time resolution of 2 fs. In the experiments, the voltage V 0 with a square wave and a frequency of 1 kHz was applied to the LC through the graphene layers. Here, V 0 represents the amplitude. All measurements were conducted at room temperature. Figure 1 shows the observed microscope images. When the voltage was not applied to the LC cell, we observed multiple domains and disclination lines. These can be seen in Fig. 1(a) as marble-like textures and line defects [24]. Therefore, we conclude that the LC molecules between the graphene layers were randomly aligned because the cell was fabricated without alignment layers. The size of the domains and the width of the disclination lines were several tens of microns, which is one order of magnitude smaller than the THz waves. The wavelength of a 1-THz wave is 300 μm. The brightness of the observed image decreased when the applied voltage increased. Additionally,
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0 40 20 0 400
500
600
700
800
Wavelength (nm) Fig. 2. range.
Transmittance spectra of the LC cell in the visible
0.2
Amplitude (arb. unit)
0.20
V0 (V)
0.15
100, 0
0.1
0.10 0.05
0.0 0.5
1.0
0.00 −0.05 −0.10 −0.15 0
Fig. 1. Polarizing optical microscope images under the crossed nicols. The applied voltage, V 0 , is (a) 0, (b) 10, (c) 20, and (d) 100 V. The length of the white bar corresponds to the 1-THz wavelength.
1
2
3
4
Time (ps) Fig. 3. Amplitude of the THz pulse transmitted through the LC cell. The inset is an enlarged image at the positive peak.
OPTICS LETTERS / Vol. 40, No. 7 / April 1, 2015
nicols. As shown in the inset of Fig. 3, shifts in the time domain were clearly observed with the application of the voltage. We can calculate the transmittance and the phase shift by taking the Fourier transform of the observed THz waveforms in the time domain. Figure 4(a) shows the calculated phase shifts at the frequency, f , of 0.5, 1.0, or 1.5 THz. Here, the phase shift was defined as the difference in the case of V 0 0. The phase shift decreased with the increase of the applied voltage. This means that the average refractive index of the LC layer for the THz waves decreased with the increase of the applied voltage. In the THz frequency range, the ordinary refractive index of the LC (no ) is smaller than the extraordinary one (ne ) [18]. Denoting the spatially averaged refractive index in the LC layer for normal incidence as nV 0 , we can write as no < n0 < ne as the LC molecules are randomly aligned at V 0 0. When a sufficiently high voltage is applied to the LC cell (when the LC molecules are oriented perpendicular to the substrates), we can also write as n ≅ no . Therefore, the decrease of the phase shift can be qualitatively explained by considering the refractive index change in the LC layer. The observed phase shift for V 0 ≥ V th was fitted using the equation
(a)
0.00
Phase shift (rad)
0.5 −0.05
1.0
−0.10
1.5 f (THz)
−0.15 0
20
40
60
80
100
Applied voltage (V)
(b)
0.00
Phase shift (rad)
0.5 −0.05
V − V th ϕV 0 Δϕ exp − 0 −1 ; Vτ
(1)
where Δϕ is the maximum amplitude of the phase shift, V th is the threshold voltage, and V τ is the saturation voltage [16]. The phase shift, Δϕ, can be written as Δϕ
2πd 2πd n0 − no ≡ Δn; λ λ
(2)
where d is the thickness of the LC layer, and λ is the wavelength of the THz wave [16]. The ordinary and extraordinary refractive indices of 5CB are no 1.585 0.015 and ne 1.695 0.005 for the frequency range of 0.5–1.5 THz [19]. For the randomly aligned nematic LC, the average refractive index is approximately given by [16] s n2e 2n2o : (3) n¯ 3 ¯ we can obtain as Δn 0.038 Assuming n0 n, 0.019 using Eqs. (2) and (3). However, the experimentally observed Δn, which was estimated based on the fitted data, was 0.032, 0.033, and 0.036, at 0.5 THz, 1.0 THz, and 1.5 THz, respectively. Here, we assumed d 0.10 mm in the calculations. The other parameters were as follows: V th 4.5V and V τ 7.9 V at f 0.5 THz, V th 4.0 V and V τ 9.3 V at f 1.0 THz, and V th 4.7 V and V τ 7.4 V at f 1.5 THz. The experimental results are in agreement with the theoretical value. This demonstrates that the LC cell is applicable for use as a voltage-controlled THz phase shifter. In the experimental system, the THz wave was linearly polarized. We also investigated the polarization dependence of the phase shift by rotating the sample around the propagation direction. There was very little dependence on the polarization state. The result was summarized in Fig. 4(b). Figure 5 shows the observed transmittance spectra in the THz frequency range. The ripples were attributed to multiple interference originating in the cell structure. We cannot observe these ripples in Fig. 2 because of the cell thickness, which is substantially larger than the wavelengths of the visible light, and the strong scattering. The
1.0
60
0 −0.10
Transmittance (%)
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−0.15 0
45
90
135
180
Rotation angle (deg) Fig. 4. Phase shifts in the THz range. (a) Dependence on the applied voltage. The plots represent the measured data. The lines are the curves fitted using Eq. (1). We assumed that ϕV 0 < V th 0 for the fits. (b) Dependence on the polarization state. The plots represent the measured data for V 0 100 V. The lines show the mean value. The random error for the phase shift was about 0.02 rad.
40
100 20
V0 (V) 0 0.5
1.0
1.5
Frequency (THz) Fig. 5. range.
Transmittance of the LC cell in the THz frequency
April 1, 2015 / Vol. 40, No. 7 / OPTICS LETTERS
transmittance in the THz frequency range showed little change with the applied voltage in contrast with the visible range (Figs. 2, 5). This can be explained by considering that the scattering loss originating in the random alignment is significantly reduced for the THz waves. This is because the sizes of the scattering textures mentioned above are small in comparison with the wavelengths of the THz waves. However, as shown in Fig. 5, the average transmittance was reduced when voltage was applied. This result may be understood by considering the absorption in the LC layer. In the THz frequency range, the absorption coefficient for the ordinary wave is larger than the extraordinary one [18]. Quantitative evaluations considering the absorption and multiple interference are in progress to characterize the transmittance spectra. Additionally, there was very little dependence of the transmittance on the polarization state independent of the applied voltage. In conclusion, using the randomly aligned LC cell with graphene electrodes, the THz phase shifts could be electrically controlled. The transmittance of the LC cell in the THz frequency range was several tens of percent. Additionally, the transmittance showed very little change with the applied voltage. This indicates that there was no scattering loss originating in the random-domain texture and the disclination lines in the LC layer. Using the 0.1-mm-thick cell, we obtained a phase shift of 0.11 rad at 1.5 THz. When alignment layers are not used, thicker LC cells can be fabricated. Therefore, large THz phase shifts will be obtained by employing this LC cell structure. The presented THz phase controller has polarization universality because of the random alignment in the initial state. To our knowledge, universal polarization LC THz phase shifters have not been reported. This is a useful property for various THz applications including spatial phase modulators and interferometers. This research was supported by the Konica Minolta Imaging Science Encouragement Award of the Konica Minolta Science and Technology Foundation. References 1. P. H. Siegel, IEEE Trans. Microw. Theory Tech. 50, 910 (2002). 2. M. Tonouchi, Nat. Photonics 1, 97 (2007).
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3. I. H. Libon, S. Baumgärtner, M. Hempel, N. E. Hecker, J. Feldmann, M. Koch, and P. Dawson, Appl. Phys. Lett. 76, 2821 (2000). 4. T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pandry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004). 5. T.-R. Tsai, C.-Y. Chen, R.-P. Pan, C.-L. Pan, and X.-C. Zhang, IEEE Microw. Wireless Compon. Lett. 14, 77 (2004). 6. H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, Nature 444, 597 (2006). 7. J.-B. Masson and G. Gallot, Opt. Lett. 31, 265 (2006). 8. P. Weis, O. Paul, C. Imhof, R. Beigang, and M. Rahm, Appl. Phys. Lett. 95, 171104 (2009). 9. Y. Wu, X. Ruan, C.-H. Chen, Y. J. Shin, Y. Lee, J. Niu, J. Liu, Y. Chen, K.-L. Yang, X. Zhang, J.-H. Ahn, and H. Yang, Opt. Express 21, 21395 (2013). 10. C.-S. Yang, T.-T. Tang, R.-P. Pan, P. Yu, and C.-L. Pan, Appl. Phys. Lett. 104, 141106 (2014). 11. M. Nagai, N. Mukai, Y. Minowa, M. Ashida, J. Takayanagi, and H. Ohtake, Opt. Lett. 39, 146 (2014). 12. A. Chopik, S. Pasechnik, D. Semerenko, D. Shmeliova, A. Dubtsov, A. K. Srivastava, and V. Chigrinov, Opt. Lett. 39, 1453 (2014). 13. C.-S. Yang, T.-T. Tang, P.-H. Chen, R.-P. Pan, P. Yu, and C.-L. Pan, Opt. Lett. 39, 2511 (2014). 14. D. C. Zografopoulos, K. P. Prokopidis, R. Dabrowski, and R. Beccherelli, Opt. Mater. Express 4, 449 (2014). 15. I. C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (Wiley, 1995). 16. P. Yeh and C. Gu, Optics of Liquid Crystal Displays (Wiley, 1999). 17. T. Nose, S. Sato, K. Mizuno, J. Bae, and T. Nozokido, Appl. Opt. 36, 6383 (1997). 18. T.-R. Tsai, C.-Y. Chen, C.-L. Pan, R.-P. Pan, and X.-C. Zhang, Appl. Opt. 42, 2372 (2003). 19. N. Vieweg, M. K. Shakfa, B. Scherger, M. Mikulics, and M. Koch, J. Infrared Millim. Terahz Waves 31, 1312 (2010). 20. L. Wang, X.-W. Lin, X. Liang, J.-B. Wu, W. Hu, Z.-G. Zheng, B.-B. Jin, Y.-Q. Qin, and Y.-Q. Lu, Opt. Mater. Express 2, 1314 (2012). 21. Y. Wu, C. La-o-vorakiat, X. Qiu, J. Liu, P. Deorani, K. Banerjee, J. Son, Y. Chen, E. E. M. Chia, and H. Yang, Adv. Mater. 27, 1874 (2015). 22. A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, Rev. Mod. Phys. 81, 109 (2009). 23. K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J.-H. Ahn, P. Kim, J.-Y. Choi, and B. H. Hong, Nature 457, 706 (2009). 24. I. Dierking, Texture of Liquid Crystals (Wiley, 2003).
OPTICS LETTERS / Vol. 40, No. 7 / April 1, 2015
Universal polarization terahertz phase controllers using randomly aligned liquid crystal cells with graphene electrodes Tomoyuki Sasaki,1,* Kohei Noda,1 Nobuhiro Kawatsuki,2 and Hiroshi Ono1 1
Department of Electrical Engineering, Nagaoka University of Technology, 1603-1 Kamitomioka, Nagaoka, Niigata 940-2188, Japan 2
Department of Materials Science and Chemistry, Graduate School of Engineering, University of Hyogo, 2167 Shosha, Himeji, Hyogo 671-2280, Japan *Corresponding author: [email protected] Received February 4, 2015; revised March 10, 2015; accepted March 11, 2015; posted March 11, 2015 (Doc. ID 233838); published March 30, 2015
We present a universal polarization terahertz (THz) phase controller using a randomly aligned liquid crystal (LC) cell with graphene electrodes. The LC cell was fabricated using a nematic LC and two quartz substrates that were coated with a monolayer of graphene as the transparent electrode. The LC in the cell was prepared without any alignment treatments and was randomly aligned. The size of the random domains and the width of the disclination lines in the LC layer were several tens of microns. These textures disappeared when an alternating voltage was applied to the LC through the graphene layers. Using a THz time domain spectroscopic technique, we investigated the complex transmittance of the LC cell. The LC cell was highly transparent in the THz frequency range, and there was little change in the transmittance with the applied voltage. This indicated that the scattering loss originating in the randomly aligned LC molecules was small for the THz waves. We also demonstrated that the THz phase shift could be controlled by the applied voltage. The amplitude of the phase shift was explained by the ordinary and extraordinary refractive indices of the LC. These LC cells with graphene electrodes can be used to realize universal polarization THz phase controllers because of the random alignment. © 2015 Optical Society of America OCIS codes: (230.3720) Liquid-crystal devices; (260.5430) Polarization; (300.6495) Spectroscopy, terahertz; (310.7005) Transparent conductive coatings. http://dx.doi.org/10.1364/OL.40.001544
Terahertz (THz) technologies have received considerable attention in various fields [1,2]. For widespread adoption of THz technologies, we should develop not only highpower light sources and highly sensitive detectors, but functional THz elements as well [3–14]. Chen et al. presented an active metamaterial device capable of efficient real-time control and manipulation of THz radiation [6]. Nagai et al. reported an achromatic THz wave plate composed of stacked parallel metal plates with a hole array [11]. These studies demonstrated that the propagation of THz waves can be manipulated using artificial structures [3,4,6–8,11]. There have also been several studies on THz devices employing liquid crystal (LC) materials [5,9,10,12–14]. LCs are excellent media for various optical applications because they are highly transparent in the visible range, have a large optical anisotropy, and respond to external fields [15,16]. Recent studies on the optical constants of LCs in the THz frequency range have shown that LCs are potentially useful for functional THz devices [17–20]. For LC optical devices, including LC displays, indium tin oxide (ITO) films are widely used as transparent electrodes [16]. However, ITO films are opaque in the THz frequency range [13]. When thin ITO films are used to increase the transmittance, the electrical resistivity increases significantly [13]. Therefore, transparent electrodes in the THz frequency range are under considerable investigation to realize electrically controllable THz devices using LCs [9,10,13]. Wu et al. studied voltage-controlled THz phase shifters using LC cells with graphene layers as the electrodes [9]. Graphene THz modulators by ionic liquid gating were also reported [21]. Graphene exhibits good electrical conductivity, chemical stability, and mechanical strength [22,23]. Additionally, graphene is highly transparent in 0146-9592/15/071544-04$15.00/0
a wide frequency range [22,23]. We believe that graphene has considerable promise as transparent electrodes for LC devices in the THz frequency range. In previous studies on LC THz phase shifters, LC molecules in the cells were oriented using alignment films that were coated on the substrates [5,9,10,13,14]. To obtain sufficient phase shifts using an LC cell, the thickness of the LC layer should be increased compared with optical applications. This is because THz waves are in the sub-millimeter range, which is several hundred times longer than visible light waves. However, it is difficult to fabricate homogeneously aligned LC cells with a submillimeter-thick LC layer using common polymeric alignment films. For optical applications, inhomogeneously or randomly aligned LCs cause scattering losses because of the domain textures and the defects. However, the scattering loss may be reduced in the THz frequency range because the sizes of the scattering textures in the LC layer are small in comparison to the THz waves. Therefore, we believe that highly transparent LC phase shifters can be realized without the use of special alignment treatments. Additionally, the random alignment means that the device is polarization independent unlike previously reported LC THz elements that require an initial alignment. These universal polarization THz phase shifters will be useful for various THz applications such as in spatial phase modulators and interferometers. In the present study, we propose a universal polarization THz phase controller using an LC cell with graphene electrodes. The LC cell was fabricated without the use of alignment layers to obtain the random alignment. Based on optical observations, we investigated the texture of the LC layer, control of the alignment using voltage, and the dependence on the polarization. The © 2015 Optical Society of America
April 1, 2015 / Vol. 40, No. 7 / OPTICS LETTERS
the domain texture and the disclination lines gradually disappeared with increased applied voltage [Figs. 1(a)–1(c)]. When a sufficiently high voltage was applied to the LC cell, a dark-field image was observed as shown in Fig. 1(d). This result indicates that the LC molecules were reoriented perpendicularly to the substrates by the applied voltage. This means that the graphene layers can be used as electrodes for the LC cell. Figure 2 shows transmittance spectra in the visible range. These data were measured using randomly polarized light at normal incidence. The detector was placed 5 cm away from the LC cell. When voltage was not applied to the cell, the transmittance was relatively low (below 50%). This is because the visible light was scattered by the domain structure and the disclination lines, which are larger than the wavelengths of the visible light. However, the transmittance increased when the applied voltage increased. For V 0 100 V, we observed transmittance above 85% at 800 nm. This result indicates that the LC molecules are unidirectionally oriented, and the domain structure and the disclination lines disappeared by applying a sufficiently high voltage. Figure 3 shows the waveforms of the THz pulse transmitted through the LC cell. The THz time-domain spectra were measured for normal incidence under parallel 100
V0 (V) Transmittance (%)
complex transmittance in the THz frequency range was measured using a THz time-domain spectroscopic technique. By analyzing the data, we demonstrated that the randomly aligned LC cell with graphene electrodes was applicable for use as voltage-controlled THz phase shifters. The amplitude of the THz phase shift was discussed on the basis of the ordinary and extraordinary refractive indices of the LC. An empty cell was fabricated using two quartz substrates that were coated with a monolayer of graphene (Graphene Platform, Japan). Graphene was transferred on the whole face of the quartz substrates with the area of 25 mm × 25 mm. A nematic LC, 4-pentyl-4′-cyanobiphenyl (5CB, Wako, Japan), filled the empty cell by capillary action. The sheet resistance of the graphene substrate was 0.6 kΩ∕sq. The thickness of the quartz substrates was 0.5 mm. The thickness of the LC layer was adjusted to 0.10 mm using film spacers. The texture of the fabricated LC cell was observed using a polarizing optical microscope (ECRIPS E200, Nikon, Japan) with crossed nicols. We measured transmittance spectra of the LC cell in the visible and THz frequency ranges using a visible spectrometer (HR4000, Ocean Optics) and a THz time-domain spectrometer (TAS7500TS, Advantest, Japan) with the time resolution of 2 fs. In the experiments, the voltage V 0 with a square wave and a frequency of 1 kHz was applied to the LC through the graphene layers. Here, V 0 represents the amplitude. All measurements were conducted at room temperature. Figure 1 shows the observed microscope images. When the voltage was not applied to the LC cell, we observed multiple domains and disclination lines. These can be seen in Fig. 1(a) as marble-like textures and line defects [24]. Therefore, we conclude that the LC molecules between the graphene layers were randomly aligned because the cell was fabricated without alignment layers. The size of the domains and the width of the disclination lines were several tens of microns, which is one order of magnitude smaller than the THz waves. The wavelength of a 1-THz wave is 300 μm. The brightness of the observed image decreased when the applied voltage increased. Additionally,
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0 40 20 0 400
500
600
700
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Wavelength (nm) Fig. 2. range.
Transmittance spectra of the LC cell in the visible
0.2
Amplitude (arb. unit)
0.20
V0 (V)
0.15
100, 0
0.1
0.10 0.05
0.0 0.5
1.0
0.00 −0.05 −0.10 −0.15 0
Fig. 1. Polarizing optical microscope images under the crossed nicols. The applied voltage, V 0 , is (a) 0, (b) 10, (c) 20, and (d) 100 V. The length of the white bar corresponds to the 1-THz wavelength.
1
2
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Time (ps) Fig. 3. Amplitude of the THz pulse transmitted through the LC cell. The inset is an enlarged image at the positive peak.
OPTICS LETTERS / Vol. 40, No. 7 / April 1, 2015
nicols. As shown in the inset of Fig. 3, shifts in the time domain were clearly observed with the application of the voltage. We can calculate the transmittance and the phase shift by taking the Fourier transform of the observed THz waveforms in the time domain. Figure 4(a) shows the calculated phase shifts at the frequency, f , of 0.5, 1.0, or 1.5 THz. Here, the phase shift was defined as the difference in the case of V 0 0. The phase shift decreased with the increase of the applied voltage. This means that the average refractive index of the LC layer for the THz waves decreased with the increase of the applied voltage. In the THz frequency range, the ordinary refractive index of the LC (no ) is smaller than the extraordinary one (ne ) [18]. Denoting the spatially averaged refractive index in the LC layer for normal incidence as nV 0 , we can write as no < n0 < ne as the LC molecules are randomly aligned at V 0 0. When a sufficiently high voltage is applied to the LC cell (when the LC molecules are oriented perpendicular to the substrates), we can also write as n ≅ no . Therefore, the decrease of the phase shift can be qualitatively explained by considering the refractive index change in the LC layer. The observed phase shift for V 0 ≥ V th was fitted using the equation
(a)
0.00
Phase shift (rad)
0.5 −0.05
1.0
−0.10
1.5 f (THz)
−0.15 0
20
40
60
80
100
Applied voltage (V)
(b)
0.00
Phase shift (rad)
0.5 −0.05
V − V th ϕV 0 Δϕ exp − 0 −1 ; Vτ
(1)
where Δϕ is the maximum amplitude of the phase shift, V th is the threshold voltage, and V τ is the saturation voltage [16]. The phase shift, Δϕ, can be written as Δϕ
2πd 2πd n0 − no ≡ Δn; λ λ
(2)
where d is the thickness of the LC layer, and λ is the wavelength of the THz wave [16]. The ordinary and extraordinary refractive indices of 5CB are no 1.585 0.015 and ne 1.695 0.005 for the frequency range of 0.5–1.5 THz [19]. For the randomly aligned nematic LC, the average refractive index is approximately given by [16] s n2e 2n2o : (3) n¯ 3 ¯ we can obtain as Δn 0.038 Assuming n0 n, 0.019 using Eqs. (2) and (3). However, the experimentally observed Δn, which was estimated based on the fitted data, was 0.032, 0.033, and 0.036, at 0.5 THz, 1.0 THz, and 1.5 THz, respectively. Here, we assumed d 0.10 mm in the calculations. The other parameters were as follows: V th 4.5V and V τ 7.9 V at f 0.5 THz, V th 4.0 V and V τ 9.3 V at f 1.0 THz, and V th 4.7 V and V τ 7.4 V at f 1.5 THz. The experimental results are in agreement with the theoretical value. This demonstrates that the LC cell is applicable for use as a voltage-controlled THz phase shifter. In the experimental system, the THz wave was linearly polarized. We also investigated the polarization dependence of the phase shift by rotating the sample around the propagation direction. There was very little dependence on the polarization state. The result was summarized in Fig. 4(b). Figure 5 shows the observed transmittance spectra in the THz frequency range. The ripples were attributed to multiple interference originating in the cell structure. We cannot observe these ripples in Fig. 2 because of the cell thickness, which is substantially larger than the wavelengths of the visible light, and the strong scattering. The
1.0
60
0 −0.10
Transmittance (%)
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1.5 f (THz)
−0.15 0
45
90
135
180
Rotation angle (deg) Fig. 4. Phase shifts in the THz range. (a) Dependence on the applied voltage. The plots represent the measured data. The lines are the curves fitted using Eq. (1). We assumed that ϕV 0 < V th 0 for the fits. (b) Dependence on the polarization state. The plots represent the measured data for V 0 100 V. The lines show the mean value. The random error for the phase shift was about 0.02 rad.
40
100 20
V0 (V) 0 0.5
1.0
1.5
Frequency (THz) Fig. 5. range.
Transmittance of the LC cell in the THz frequency
April 1, 2015 / Vol. 40, No. 7 / OPTICS LETTERS
transmittance in the THz frequency range showed little change with the applied voltage in contrast with the visible range (Figs. 2, 5). This can be explained by considering that the scattering loss originating in the random alignment is significantly reduced for the THz waves. This is because the sizes of the scattering textures mentioned above are small in comparison with the wavelengths of the THz waves. However, as shown in Fig. 5, the average transmittance was reduced when voltage was applied. This result may be understood by considering the absorption in the LC layer. In the THz frequency range, the absorption coefficient for the ordinary wave is larger than the extraordinary one [18]. Quantitative evaluations considering the absorption and multiple interference are in progress to characterize the transmittance spectra. Additionally, there was very little dependence of the transmittance on the polarization state independent of the applied voltage. In conclusion, using the randomly aligned LC cell with graphene electrodes, the THz phase shifts could be electrically controlled. The transmittance of the LC cell in the THz frequency range was several tens of percent. Additionally, the transmittance showed very little change with the applied voltage. This indicates that there was no scattering loss originating in the random-domain texture and the disclination lines in the LC layer. Using the 0.1-mm-thick cell, we obtained a phase shift of 0.11 rad at 1.5 THz. When alignment layers are not used, thicker LC cells can be fabricated. Therefore, large THz phase shifts will be obtained by employing this LC cell structure. The presented THz phase controller has polarization universality because of the random alignment in the initial state. To our knowledge, universal polarization LC THz phase shifters have not been reported. This is a useful property for various THz applications including spatial phase modulators and interferometers. This research was supported by the Konica Minolta Imaging Science Encouragement Award of the Konica Minolta Science and Technology Foundation. References 1. P. H. Siegel, IEEE Trans. Microw. Theory Tech. 50, 910 (2002). 2. M. Tonouchi, Nat. Photonics 1, 97 (2007).
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3. I. H. Libon, S. Baumgärtner, M. Hempel, N. E. Hecker, J. Feldmann, M. Koch, and P. Dawson, Appl. Phys. Lett. 76, 2821 (2000). 4. T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pandry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004). 5. T.-R. Tsai, C.-Y. Chen, R.-P. Pan, C.-L. Pan, and X.-C. Zhang, IEEE Microw. Wireless Compon. Lett. 14, 77 (2004). 6. H.-T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, Nature 444, 597 (2006). 7. J.-B. Masson and G. Gallot, Opt. Lett. 31, 265 (2006). 8. P. Weis, O. Paul, C. Imhof, R. Beigang, and M. Rahm, Appl. Phys. Lett. 95, 171104 (2009). 9. Y. Wu, X. Ruan, C.-H. Chen, Y. J. Shin, Y. Lee, J. Niu, J. Liu, Y. Chen, K.-L. Yang, X. Zhang, J.-H. Ahn, and H. Yang, Opt. Express 21, 21395 (2013). 10. C.-S. Yang, T.-T. Tang, R.-P. Pan, P. Yu, and C.-L. Pan, Appl. Phys. Lett. 104, 141106 (2014). 11. M. Nagai, N. Mukai, Y. Minowa, M. Ashida, J. Takayanagi, and H. Ohtake, Opt. Lett. 39, 146 (2014). 12. A. Chopik, S. Pasechnik, D. Semerenko, D. Shmeliova, A. Dubtsov, A. K. Srivastava, and V. Chigrinov, Opt. Lett. 39, 1453 (2014). 13. C.-S. Yang, T.-T. Tang, P.-H. Chen, R.-P. Pan, P. Yu, and C.-L. Pan, Opt. Lett. 39, 2511 (2014). 14. D. C. Zografopoulos, K. P. Prokopidis, R. Dabrowski, and R. Beccherelli, Opt. Mater. Express 4, 449 (2014). 15. I. C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (Wiley, 1995). 16. P. Yeh and C. Gu, Optics of Liquid Crystal Displays (Wiley, 1999). 17. T. Nose, S. Sato, K. Mizuno, J. Bae, and T. Nozokido, Appl. Opt. 36, 6383 (1997). 18. T.-R. Tsai, C.-Y. Chen, C.-L. Pan, R.-P. Pan, and X.-C. Zhang, Appl. Opt. 42, 2372 (2003). 19. N. Vieweg, M. K. Shakfa, B. Scherger, M. Mikulics, and M. Koch, J. Infrared Millim. Terahz Waves 31, 1312 (2010). 20. L. Wang, X.-W. Lin, X. Liang, J.-B. Wu, W. Hu, Z.-G. Zheng, B.-B. Jin, Y.-Q. Qin, and Y.-Q. Lu, Opt. Mater. Express 2, 1314 (2012). 21. Y. Wu, C. La-o-vorakiat, X. Qiu, J. Liu, P. Deorani, K. Banerjee, J. Son, Y. Chen, E. E. M. Chia, and H. Yang, Adv. Mater. 27, 1874 (2015). 22. A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, Rev. Mod. Phys. 81, 109 (2009). 23. K. S. Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J.-H. Ahn, P. Kim, J.-Y. Choi, and B. H. Hong, Nature 457, 706 (2009). 24. I. Dierking, Texture of Liquid Crystals (Wiley, 2003).
