730 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 21, NO. 11, JUNE 1, 2009
Electrically Controlled Liquid Crystal Phase Grating
for Terahertz Waves
Chia-Jen Lin, Chuan-Hsien Lin, Yu-Tai Li, Ru-Pin Pan, and Ci-Ling Pan, Senior Member, IEEE
Abstract—This work demonstrates the feasibility of electrically
controlled liquid-crystal-based phase grating for manipulating the terahertz (THz) waves. This device can be utilized as a THz beam splitter and the beam splitting ratio of the zeroth- to the first-order diffractions can be tuned from 10 : 1 to 1 : 1.
Index Terms—Liquid crystal devices, phase grating,
submil-limeter wave, terahertz (THz) radiation, tunable circuits and devices, ultrafast optics.
I. INTRODUCTION
Q
UASI-OPTICAL components for submillimeter or tera-hertz (THz) waves are in high demand due to the recent rapid progress in THz science and technology [1], [2]. For control of properties of electromagnetic waves at all wave-lengths, periodic structures such as gratings were widely used for applications such as couplers and filters [3], [4]. The poten-tial for gratings with liquid-crystal-enabled functionalities was also recognized two decades ago [5]. Of late, various tunable THz devices employing nematic liquid crystals (NLCs), such as phase shifters, filters, and switches that are controlled ei-ther electrically or magnetically, were demonstrated [6]–[12]. By changing the effective refractive index of the NLC [13], we recently demonstrated a magnetically controlled phase grating for manipulating THz waves [14]. Nonetheless, electrically con-trolled phase gratings are deemed desirable for many applica-tions. In this work, we propose and demonstrate an electrically controlled phase grating using NLC for THz waves. Perfor-mance of the device is in good agreement with theoretical pre-dictions.II. OPERATIONPRINCIPLES ANDEXPERIMENTALSETUPS
The present device is designed as a binary phase grating. It contains alternate sections of two materials with different re-fractive indices. The electric fields of electromagnetic waves that pass through these two materials, and , and the total
Manuscript received December 15, 2008; revised February 26, 2009. First published March 27, 2009; current version published May 15, 2009. This work was supported in part by the National Science Council (NSC) through various grants including NSC 96-2221-E-009-131-MY3, PPAEU-II, and by the ATU program of the Ministry of Education, Taiwan, Republic of China.
C.-J. Lin and C.-H. Lin are with the Department of Electrophysics, National Chiao Tung University, Hsinchu, Taiwan (e-mail: [email protected]; [email protected]).
Y.-T. Li and C.-L. Pan are with Department of Photonics and the Institute of Electro-Optical Engineering, National Chiao Tung University, Hsinchu, Taiwan (e-mail: [email protected]; [email protected]).
R.-P. Pan is with the Department of Electrophysics, National Chiao Tung University, Hsinchu, Taiwan (e-mail: [email protected]).
Color versions of one or more of the figures in this letter are available online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/LPT.2009.2017382
Fig. 1. Schematic drawing of the electrically controlled THz LC phase grating. The dimensions of the structure are shown. P: polarizer; PI: polyimide;V : threshold voltage.
field, detected at an angle of from the incident beam can be written as
and
(1) where is the amplitude of the incident electric field, is the diffraction angle, is the wave number of the electromagnetic wave in free space, is the width of each material (assumed to be equal), is the thickness of the grating, and and are complex refractive indices of materials 1 and 2, respectively.
Fig. 1 is a schematic drawing of the electrically controlled THz phase grating. The incident THz wave is polarized in the y-direction. Orientations of the LC molecules for two possible configurations are also shown. The device is designed such that the zeroth-order diffraction efficiency would be highest in the band around 0.3–0.5 THz. Parallel grooves having a period of 2.0 mm, a width of 1.0 mm, and a groove-depth of 2.5 mm are made by stacking indium tin oxide (ITO) coated fused silica plates with a refractive index of 1.95 in the sub-THz frequency region (0.2–0.8 THz). The fused silica surfaces are coated with polyimide (PI, SE-130B by Nissan), and then rubbed for ho-mogenous alignment. The grooves are filled with a room tem-perature NLC (E7, Merck) and sealed with a fused silica plate
LIN et al.: ELECTRICALLY CONTROLLED LIQUID CRYSTAL PHASE GRATING FOR THz WAVES 731
Fig. 2. (a) Time-domain and (b) spectral-domain characteristics of the device. Explanations of the various curves are given in the text.
coated with DMOAP (N, N- dimethyl-N-octadecyl-3-amino-propyltrimethoxysilyl chloride). Due to its positive dielectric anisotropy, the E7 molecules tend to be aligned parallel to the direction of the applied electric field when the applied voltage is lager than the threshold voltage. The effective refractive index of E7 [6], , can be tuned from the value for the ordinary wave to that for the extraordinary wave by varying the applied voltage.
The zeroth-order diffraction spectra of the device are de-tected with a photoconductive antenna-based THz time-domain spectrometer (THz-TDS) described previously [15]. A stack of ITO-coated fused silica plates identical in dimension to that of the grating is prepared as the reference for the THz-TDS. In the second set of experiments, the broadband THz signal is filtered by using a metallic hole array as a filter to yield a quasi-monochromatic wave centered at 0.3 THz with a line width of 0.03 THz [15]. The diffraction pattern of this beam by the grating with various NLC orientations is detected and mapped by a liquid-helium-cooled Si bolometer, 20 cm away from the device and located on a rotation arm that can be swung with respect to the fixed grating. The bolometer has an aperture about 2.5 cm in diameter.
III. RESULTS ANDDISCUSSION
The zeroth-order diffracted THz pulses transmitted through the phase grating for both ordinary and extraordinary waves, (black and red curves), are shown in Fig. 2(a). For comparison, we also plotted the incident and the transmitted THz waveforms through the reference (the cyan and blue curves). The inset of
Fig. 3. (a) Experimental and (b) FDTD simulation results of the frequency de-pendence of the zeroth-order diffraction efficiencies of the phase grating oper-ated at four applied voltages.
Fig. 2 shows a magnified view of the black, red, and blue curves. The spectral characteristics for all cases discussed in Fig. 2(a) are illustrated in Fig. 2(b).
The inset in Fig. 2(a) clearly shows oscillating components arriving 3.0 and 1.9 ps before the main pulse for ordinary and ex-traordinary waves, respectively. These are attributed to the prop-agation time difference between the waves through fused silica and NLC. The calculated times, , where is the differ-ence of the refractive indices between fused silica and NLC, is groove depth and is the speed of light in vacuum, are 3.1 and 2.0 ps, respectively. These are very close to the experimental observed time difference.
The diffraction efficiencies in the frequency domain can be determined by normalizing the diffracted signals in the fre-quency domain with respect to that of the reference. Fig. 3(a) shows the experimentally determined diffraction efficiencies as a function of frequency with the device operating at 0, 15, 20, and 90 V. A finite-difference time-domain (FDTD) algorithm (RSoft Design Group, Inc.) is employed to simulate the diffrac-tion of THz waves transmitted through the device. In the FDTD simulation, the size of the grid is 10 m 10 m while the time step is s. The experimental and FDTD simula-tion results are in general agreement [see Fig. 3(b)]. There are, however, some discrepancies in efficiencies and peak positions. This is acceptable, as the thickness of the fused silica plates in the grating assembly varies by 0.1 mm. Further FDTD simu-lations show such variations could change efficiencies by 0.05 and the peak positions by 0.02 THz.
The experimental diffraction efficiency is highest near 0.3 THz, in agreement with the designed frequency. For or-dinary wave at 0.3 THz, the phase difference between fused silica and E7 is close to . Therefore, the transmission of the grating is higher. The THz wave is mainly concentrated in the zeroth order. In contrast, the phase difference is close to for extraordinary waves. The diffraction efficiency is smaller for
732 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 21, NO. 11, JUNE 1, 2009
Fig. 4. Diffraction efficiency as a function of diffraction angle for the 0.3-THz beam.
the zeroth order, because the THz wave is mostly diffracted into the first order.
Fig. 4 illustrates the intensity profiles of the diffracted 0.3-THz-beam polarized in the y-direction. A diffraction maximum is detected at , which corresponds to the first-order diffracted beam that is predicted by the grating equation. The measured diffraction efficiencies for zeroth and first orders are also in good agreement with the theoretical values predicted by (1), taking into account the finite dimension of the grating and acceptance angle of the bolometer ( 3 ).
When the E7 molecules are aligned with equal to , the phase difference is close to . Most of the THz signal prop-agates in the direction of the zeroth-order diffraction. Experi-mentally, we find the diffraction efficiencies are 0.62 and 0.06 for the zeroth and first orders, respectively. On the other hand, when is equal to , the phase difference is close to . The THz wave propagates mostly as the first-order diffracted beam. The diffraction efficiencies are 0.18 and 0.25 for the zeroth and first orders, respectively. The grating would then function as a variable beam splitter. Varying the applied voltage, the beam splitting ratio of the zeroth to the first orders can be tuned from 10 : 1 to 1 : 1.
Overcoming the mechanical constraint of rotating the magnet without obstruction the THz wave in the previously reported magnetically tuned device [14], we are now able to vary the beam splitting ratio of the current device over a broader range. However, the transmittance of the electrically tuned phase grating is about half of the magnetically tuned one.
The stacked ITO-coated plates can be regarded as a wave-guide that causes additional loss in transmittance. The energy of the incident THz pulse mainly distributed between 0.2 and 0.8 THz, much higher than the cutoff frequency of our device, 0.08 THz. According to the way we excited the waveguide and considering the resistive properties of the ITO layer, it was the TM mode traveling through the device. Following [16], the con-ductor losses are estimated to be 2.3 and 2.4 dB at 0.3 THz, for o-wave and e-wave, respectively, while the corresponding di-electric losses are 3.2 and 3.0 dB. The attenuation due to ab-sorption and reflection at interfaces is about 1.5 dB. Thus the estimated total loss of the device is about 7 dB. Experimentally, the insertion loss of the grating for the zeroth-order diffracted wave at 0.3 THz is about 7–10 dB. The discrepancy could be due to finite collection efficiency of the detection system. By decreasing the thickness of fused silica plates in the base of the
device from 17.5 to 2.5 mm, the insertion loss can be reduced to 3–4 dB.
The periodic arranged ITO film can be considered as a wire-grid polarizer. Only the THz wave polarized perpendicular to the grooves can pass through the electrically tuned phase grating. The extinction ratio is 100 : 1 at 0.3 THz.
The turn-on and turn-off times of the grating are about 23 and 290 s, respectively. As a result, the present device is not suitable for applications that require fast modulation. Instead, the device is excellent for instrumentation or apparatus that require, e.g., a fixed beam splitting ratio with occasional fine tuning.
IV. CONCLUSION
We have demonstrated the feasibility of diffracting THz wave by an electrically controlled liquid crystal phase grating. The experimental results fit well with the FDTD calculation and theoretical prediction. This device can also be used as a beam splitter. The ratio of the zeroth- to first-order diffracted THz-beams (0.3 THz) polarized in a direction perpendicular to that of the grooves of the grating can be tuned from 10 : 1 to 1 : 1.
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