1488 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 18, NO. 14, JULY 15, 2006
Electrically Tunable Room-Temperature 2
Liquid
Crystal Terahertz Phase Shifter
Hsin-Ying Wu, Cho-Fan Hsieh, Tsung-Ta Tang, Ru-Pin Pan, and Ci-Ling Pan, Senior Member, IEEE
Abstract—Tunable phase shift up to 360 at 1 THz is demon-strated using electrically controlled birefringence in a vertically aligned nematic liquid crystal (E7) cell, 1.83 mm in thickness. The driving voltage and corresponding field required for a phase shift of 360 at 1 THz are 100 V and 90.5 V/cm, respectively.
Index Terms—Liquid crystal (LC) devices, submillimeter wave phase shifters, tunable circuits and devices, ultrafast optics.
I. INTRODUCTION
R
ECENTLY, terahertz (THz) technology and its appli-cations have advanced rapidly [1]–[3]. Nonetheless, essential quasi-optic components such as tunable THz phase shifters are relatively under-developed. Several groups have demonstrated tunable phase shifters based on optically or elec-trically controlled carrier concentration in quantum-well struc-tures [4]–[6]. These quantum-well-based THz phase shifters, however, have limited range of tunability and in general need to be operated at temperatures far below room temperature [4], [5]. Using magnetically controlled birefringence [7], [8] in a sandwiched dual nematic liquid crystal (NLC) cell, 3 mm in total thickness, a tunable room-temperature THz phase shifter capable of more than 360 of phase shift at 1 THz was realized [9], [10]. Following initial demonstration of less than 5 of phase shift in a homogeneously aligned 38.6- m-thick NLC cell [11], we recently report electrically tunable phase shifts be-yond 90 at 1 THz in a homeotropically aligned 570- m-thick NLC cell driving at 125 V or 105 V/cm [12]. The operation of the device as a THz quarter-wave plate was also verified. Scaling of the electrically tuned liquid crystal (LC) phase shifter from 90 of phase shifter to 360 is not straightforward, however. It would require an NLC cell about 2 mm in thickness. For such thick cells, alignment of LC molecules in the bulk of the cell is not assured. The uniformity of electric field within the thick cell is also a concern. In this work, we demonstrate that the LC tunable terahertz phase shifter can indeed be scaled by increasing the cell thickness up to nearly 2 mm. Tunable phase shift up to at 1 THz is realized.Manuscript received February 9, 2006; revised April 23, 2006. This work was supported in part by various grants from the National Science Council of the Republic of China.
H.-Y. Wu, C.-F. Hsieh, and R.-P. Pan are with the Department of Electro-physics, National Chiao Tung University, Hsinchu, Taiwan, R.O.C.
T.-T. Tang and C.-L. Pan are with the Department of Photonics and the Institute of Electro-Optical Engineering, National Chiao Tung Uni-versity, Hsinchu, Taiwan, R.O.C. (e-mail: [email protected]; [email protected]).
Digital Object Identifier 10.1109/LPT.2006.877579
Fig. 1. Schematic drawing of the electrically tunable LC2 THz phase shifter. Conoscopic patterns of 1.5-mm (upper inset) and 2-mm (lower inset) LC cells are shown. (Color version available online at http://ieeexplore.ieee.org.)
II. DESIGN ANDOPERATIONPRINCIPLES
The configuration of this device is shown in Fig. 1(a). The cell was constructed by sandwiching the E7 (Merck) layer be-tween two fused silica substrates. Two copper pieces (purity of 99.94%) worked both as spacers and electrodes for the cell. They were parallel to each other and separated by
mm. The substrates were coated for vertical or homeotropic alignment [13]. The thickness of the E7 layer is 1.83 mm. A square-wave ac voltage at 1 kHz was applied to the electrodes to avoid domain formation. The applied voltages quoted in this letter are all root-mean-square values.
The vertical alignment is confirmed by conoscopic measure-ments as shown in the inset of Fig. 1. Up to a cell thickness of 1.5 mm, the cell is well-aligned (top inset of Fig. 1). Although characteristic brushes and interference fringes can still be seen for the 2-mm-thick cell (lower inset of Fig. 1), the center part of the pattern changes slowly with time. The 1.83-mm-thick cell used in this work is near the limit of good alignment. This is sufficient for device application demonstrated in this work. The phase shifting properties of this device was characterized by
WU et al.: ELECTRICALLY TUNABLE ROOM-TEMPERATURE 2 LC THz PHASE SHIFTER 1489
a photoconductive-antenna-based THz time-domain spectrom-eter [14]. The measurements were done at room temperature
( C).
The usual analysis of electrically controlled birefringence of an NLC cell used applied voltage. It implied that the expression is a good approximation. Because of the thick cell used in this work, the uniformity of the electrical field is a concern. We have, thus, taken a more general approach and formulated phase shift as a function of electrical field.
The threshold field (the Fréedericksz transition) required for reorienting the E7 molecules in the bulk of cell will be reoriented toward the applied electric field is , where and are the bend elastic constant, dielectric anisotropy, and electric permittivity of free space, re-spectively. For our device, we calculated that V/cm,
with mm, , and
(from Merck). The phase shift experienced by the THz beam transmitted through the cell biased at an electric field is given by
(1) where is the frequency of THz wave, is the speed of light in vacuum, and is the change of effective birefrin-gence for NLC at a position along the propagation direction of the THz beam. The effective birefringence can be written as
(2) where and are ordinary and extraordinary indices of refraction of NLC and is the reorientation angle of NLC molecules from the initial orientation. For , the angle at any point in the cell can be computed using the relation [13]
(3)
where , and for E7) is
the splay elastic constant of NLC. The angle is the maximum reorientation angle located at . It is related to by
(4) In a uniform electric field approximation, can be written as . Equations (3) and (4) allow us to calculate the profile of molecular orientation in the cell for a given applied electric field [13].
III. RESULTS ANDDISCUSSION
The temporal waveforms of the THz pulse transmitted through an empty cell and the device at several applied voltages are shown in Fig. 2.
Fig. 2. Temporal waveforms of the THz pulse transmitted through the empty and LC cell at various applied voltages. (Color version available online at http:// ieeexplore.ieee.org.)
Fig. 3. Spectral phase shift for several driving voltages of the NLC cell. (Color version available online at http://ieeexplore.ieee.org.)
The dispersion of the LC cell due to the LC layer and fused silica substrates are negligible in the THz range. Transmittance of the LC cell was 34% for e-ray. Scattering and absorption account for the attenuation of the 1.8-mm-thick LC cell. The transmitted THz pulses exhibit clearly larger delay and higher peak field at higher applied voltages. This trend is explained by taking into account Fresnel reflections at the two interfaces between NLC layer ( at 0.3 THz) [9] and quartz substrate ( at 0.3 THz). The theoretically calculated value was 1.11, assuming an ideal plane wave and neglecting scattering losses.
The transmitted THz spectra are deduced from the temporal profiles of the THz pulse with fast Fourier transform algorithms. The spectral phase shifts can then be determined. According to (1), a larger phase shift is expected at higher frequencies. This is confirmed in Fig. 3, in which we plot the phase shifts from 0.2 to 1.0 THz by varying the driving voltages. For a given voltage,
1490 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 18, NO. 14, JULY 15, 2006
Fig. 4. Phase shift as a function of driving voltage for four frequencies. The curves are theoretically predicted phase shifts. (Color version available online at http://ieeexplore.ieee.org.)
the measured phase shift varied linearly with frequency, with a slope of 346.8 /THz at 100 V.
Fig. 4 shows the phase shifts as a function of driving voltage. Over 360 of phase shift was achieved at 1.0 THz when the cell was driven at 100 V or 90.5 V/cm. The theoretically pre-dicted phase shift is 376 . The curves are theoretical predictions according to (1)–(4). Far above threshold, the NLC molecules are essentially aligned with the electrical field. The theoretical curves are in good agreement with the experiments. For ap-plied voltage near and about threshold, the theoretical phase shift values tend to be larger than those of the experimental ones. The experimental threshold voltage and the corresponding field were found to be 16.3 V and 14.7 V/cm, respectively, higher than the theoretically predicted values, 7.1 V and 6.4 V/cm. This is reasonable, as the actual electric field reorienting the NLC molecules in the thick cell is lower than the average electric field given by . We have calculated the field distribution in our device using FEMLab (a finite-element software by COMSOL, Inc.). Within more than 80% of the 1.0-cm-diameter THz beam area, the actual electric field is smaller than the average elec-tric field. At the center of the cell, the actual elecelec-tric field is 95% of . Because the average electric field is used in the theoretical calculation, the theoretical phase shifts according to (1)–(4) will be larger than the experimental values. Furthermore, there are significant slow fluctuations of the NLC director for smaller than or near and a cell thicker than 1.5 mm. This is confirmed by long-term monitoring of the conoscopic pattern of the LC cell thicker than 1.5 mm. For , this is not so severe as the molecules are forcefully aligned along the direc-tion of the applied electric field.
Although the electrically controlled NLC THz phase shifter has many advantages, we should point out that it is difficult to tune the desired phase shift accurately near the threshold. Fur-ther, the response of the device is slow, due to its thickness. It is,
thus, not suitable for applications that require fast modulation. Instead, the device is excellent for instrumentation or apparatus that require a fixed phase with occasional fine tuning.
Equations (1)–(4) provide the needed mathematics for de-signing the LC THz phase shifter. First, an LC with large bire-fringence and acceptable loss in the frequency of interests is chosen. Using , required for the desired maximum phase shift is estimated. Cell thickness should fall within the range of acceptable thickness for good LC alignment. The threshold field and the phase shift versus operating voltage are calculated, as il-lustrated in Fig. 4.
IV. CONCLUSION
In summary, we have demonstrated an electrically tuned THz phase shifter by using a 1.83-mm-thick vertically aligned NLC cell. A maximum phase shift of 360 at 1 THz has been achieved by using electrically controlled birefringence in an NLC driven at 100 V or 90.5 V/cm. The phase shift can be tuned electrically by controlling the effective refractive index of NLC layer. Measured results are in agreement with theoret-ical predictions.
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