This article was downloaded by: [National Chiao Tung University 國立交通大學] On: 24 April 2014, At: 18:55
Publisher: Taylor & Francis
Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK
Molecular Crystals and Liquid Crystals
Publication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/gmcl20
THz Optical Constants of the Liquid
Crystal MDA-00-3461
Cheng-Pin Ku a , Chih-Chang Shih a , Chia-Jen Lin a , Ru-Pin Pan a & Ci-Ling Pan b
a
Department of Electrophyics , National Chiao Tung University , Hsinchu, Taiwan, R. O. C.
b
Department of Physics , National Tsing Hua University , Hsinchu, Taiwan, R. O. C.
Published online: 30 Jun 2011.
To cite this article: Cheng-Pin Ku , Chih-Chang Shih , Chia-Jen Lin , Ru-Pin Pan & Ci-Ling Pan (2011)
THz Optical Constants of the Liquid Crystal MDA-00-3461, Molecular Crystals and Liquid Crystals, 541:1, 65/[303]-70/[308], DOI: 10.1080/15421406.2011.570149
To link to this article: http://dx.doi.org/10.1080/15421406.2011.570149
PLEASE SCROLL DOWN FOR ARTICLE
Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content.
This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions
THz Optical Constants of the Liquid Crystal
MDA-00-3461
CHENG-PIN KU,
1CHIH-CHANG SHIH,
1CHIA-JEN LIN,
1RU-PIN PAN,
1AND CI-LING PAN
21
Department of Electrophyics, National Chiao Tung University, Hsinchu, Taiwan, R. O. C.
2
Department of Physics, National Tsing Hua University, Hsinchu, Taiwan, R. O. C.
We have measured the far infrared optical constants of MDA-00-3461 at 25C by using terahertz time-domain spectroscopy. The extraordinary and ordinary refrac-tive indices of MDA-00-3461 are ne 1.74 and no 1.54, or a birefringence of
0.20 from 0.3 to 1.4 THz. The extinction coefficient of MDA-00-3461 is relatively small. There are no absorption peaks in the frequency range investigated.
Keywords Absorption; birefringence; liquid crystal; refractive index; terahertz; time-domain spectroscopy
1. Introduction
The knowledge of the frequency dependence and the magnitude of the refractive indices of liquid crystals (LCs) is important for fundamental studies and practical applications of LCs. Applications of LCs in many fields are well-known. Following rapid development of terahertz science and technology in the past decade, terahertz optics and functional elements are in great demand. Recognizing the need for tun-able LC terahertz photonic elements, we explored the optics, electro-optic and magneto-optics of LC in the terahertz frequency range [1]. Using terahertz time-domain spectroscopy (THz-TDS) [2], we have determined the complex indices of refraction of nematic liquid crystals, 5CB, PCH5 and E7 from 0.2 to beyond 1 THz [3–8]. Significantly, the birefringences of 5CB [3] and E7 [8] at terahertz fre-quencies are found to be comparable to their values in the visible regime, while the absorption is negligible. These works paved the way for the realization of func-tional LC tetrahertz optical elements such as 0–2p tunable tetrahertz phase shifters [9], control of enhanced transmission [10], polarizers [11], phase gratings [12], broadly tunable birefringent filters of the Lyot [13] and Solc types [14], etc.
Address correspondence to Ru-Pin Pan, Department of Electrophyics, National Chiao Tung University, Hsinchu, Taiwan 30010, R. O. C. Tel.: 886-3-5731989; Fax: 886-3-5725230; E-mail: rpchao@mail.nctu.edu.tw
ISSN: 1542-1406 print=1563-5287 online DOI: 10.1080/15421406.2011.570149
65=[303]
MDA-00-3461 is a relatively new liquid crystal by Merck, intended to replace currently widely-used LC mixture, E7. According to Merck’s data sheet, the new LC exhibits a clearing point of 92C, visible birefringence of0.26 at 20C [15].
In this work, we employ THz-TDS to determine the refractive indices of LC MDA-00-3461 from 0.3 to 1.4 THz, for the first time to our knowledge.
2. Experimental Methods
We employed two types of cells, a homogeneously aligned LC cell and a reference cell, in this work. They are schematically shown in Figure 1. The LC cell was pre-pared by sandwiching MDA-00-3461 (Merck) between two fused silica windows as substrates. The thickness of the LC layer was controlled by Mylar spacers and was measured by subtracting the total thickness of substrate windows from the total thickness of the LC cell. The total thickness of substrate windows of the LC cell is 6348 1 mm. The thickness of the LC layer is 255 1 mm. Homogeneous alignment was achieved by spin coating the polyimide films on inner surfaces of the substrates of the LC cell, followed by mechanical rubbing [16]. The reference cell was fabricated by two fused silica windows and in contact with each other. The thickness of the ref-erence cell is 6334 1 mm. The measurement temperature was set at room tempera-ture (25 0.1C).
An antenna-based THz-TDS system with a collimated terahertz beam at the sample position [17] had been used. A schematic of the THz-TDS system is shown in Figure 2. The mode-locked Ti: Sapphire laser beam in the THz-TDS system is div-ided into two beams, a pump and a probe. Terahertz pulses, generated by femtosecond-laser-excited dipole antenna fabricated on low-temperature-grown GaAs, were collimated by an off-axis paraboloidal mirror and propagated through the sample at normal incidence. The terahertz fields of extraordinary wave (e-wave) and ordinary wave (o-wave) are parallel and perpendicular to the rubbing direction of LC cell, respectively. The transmitted terahertz pulses were focused on another dipole-like antenna and oriented to detect terahertz waves polarized parallel to the incident terahertz wave polarization. The beam size of the terahertz wave through the sample is about 0.8 cm in diameter.
Figure 1. Sketches of (a) the reference cell and (b) the LC cell. The substrates are fused silica window and the alignment of LC cell is homogeneous and its geometry respect to the incident terahertz wave. (Figure appears in color online.)
66=[304] C.-P. Ku et al.
Several absorption lines of water vapor in the frequency range of 0.2–1.4 THz were observed [18]. Our THz-TDS system could be purged with nitrogen and kept the relative humidity at (4.0 0.5)%. The terahertz time-domain signals and frequency signals before and after purging are shown in Figures 3(a) and 3(b), respectively.
3. Determination of Optical Constants
We assume that the terahertz signal is a monochromatic plane wave passing through the cell at normal incidence. The electric field of the terahertz wave transmitted through the reference cell at an angular frequency x, can be written as
ERefðxÞ ¼ E0ðxÞ gðxÞ PAirðx; dÞ; ð1Þ where E0(x) is the electric field of the incident THz wave. The parameter g(x) takes
into account the Fabry-Perot effect due to the Fresnel reflection of the tetrahertz
Figure 2. The schematic experimental setup for THz-TDS. BS: beam splitter. (Figure appears in color online.)
Figure 3. (a) The terahertz time-domain signals before (solid line) and after (dash line) purging. (b) The power spectra of the terahertz signals before (solid line) and after (dash line) purging. Several absorption lines of water vapor appear before purging evidently. The relative humidities before and after purging are 54% and 4%, respectively.
wave at the window-air interfaces and its propagation in fused silica. The propagation coefficient in air over a distance d is denoted by PAirðx; dÞ ¼ exp ði~½ nnAirxdÞ=c, where ~nnAir is the complex refractive index of air and the value of 1þ 0i is assumed in this work. The length d is chosen to be the same as that of the LC layer (see Fig. 1). Similarly, the electric field of the THz wave transmitted through the LC cell can be written as
ELCðxÞ ¼ E0ðxÞ gðxÞ TWLCðxÞ PLCðx; dÞ TLCWðxÞ FPLCðx; dÞ; ð2Þ where TWLCðxÞ ¼ ð2 ~nnWÞ=ð~nnWþ ~nnLCÞ and TWLCðxÞ ¼ ð2 ~nnLCÞ=ð~nnLCþ ~nnWÞ are the transmission coefficients of the window-LC and LC-window interfaces, respec-tively; ~nnW is the complex refractive index of fused silica (~nnW¼ 1:951 þ 0i in the frequency range of 0:2 1:4 THzÞ and ~nnLC is either the ordinary index ð~nno¼ no ijoÞ or extraordinary index ð~nne¼ ne ijeÞ of the LC layer. PLCðx; dÞ ¼ exp½ði~nnLCxdÞ=c and FPLC(x, d) are propagation and Fabry-Perot coefficients in
the LC layer with a thickness of d. The coefficient, g(x) for the LC cell is the same as that for the reference cell because of the thicknesses of the fused silica windows used are the same. The complex transmittance T(x) of the LC layer can be obtained by dividing ELC(x) by ERef(x):
TðxÞ ¼ELCðxÞ ERefðxÞ
¼ 4 ~nnLC ~nnW ð~nnLCþ ~nnWÞ2
exp ið~nnLC ~nnAirÞ x d
c
FPLCðx; dÞ; ð3Þ For optically thick samples, such as ours, the echoes of tetrahertz waves from the multiple reflections of the sample are temporally well separated from the main signal. These can be easily removed without affecting accuracies of the measure-ments. Thus we can set FPLC(x, d)¼ 1 in Eq. (3) [19] without considering the
Fabry-Perot effect [20]. We set FPLC(x, d)¼ 1 when we calculated the optical
con-stants. In this work, T(x) is experimentally measured. On the right of Eq. (3), only ~
n
nLC ¼ nLC ijLC is an unknown parameter, which can be easily calculated with a given trial set of (nLC, jLC). Approximate values of nLC and jLC were obtained
by setting FP(x)¼ 1 in Eq. (3) and then this set was used as the initial trial values. After equalizing Eq. (3), the optical constants nLCand jLCare determined for any
angular frequency x.
4. Results and Discussion
Figures 4(a) and 4(b) show the measured time-domain terahertz waveforms trans-mitted through the LC cell and reference cell. It is clear that the signal passing through the LC cell is delayed with respect to that of the reference signal. Further the delay time of the e-wave signal with respect to the reference signal is larger than that of the o-wave signal. A relatively small signal, which is the reflection of the ter-ahertz wave from the window-LC interface, following the main terter-ahertz signal and separating from about 8 ps is also observed. By applying the fast Fourier transform (FFT) to the terahertz time-domain signals, we obtained the amplitude and phase spectra of the terahertz wave passing through the LC cell and reference cell. 68=[306] C.-P. Ku et al.
We calculated the optical constants of the LC by using the procedure described in the previous section.
Figure 5 shows the real part, imaginary part of the optical constants and birefringence of the LC MDA-00-3461 as a function of frequency at 25C. In the 0.3 to 1.4 THz range, this LC is not dispersive. We determine that ne¼ 1.74 and
no¼ 1.54. The birefringence of MDA-00-3461 is thus 0.20. In comparison, the
birefringence of MDA-00-3461 in the visible region is reported to be 0.26 at 589 nm and 20C, according to the Merck data sheet. The imaginary part of the refractive indices is smaller than 0.05 in the frequency range from 0.3 to 1.4 THz. There is no apparent absorption features between 0.3 to 1.4 THz. Nematic LC E7, which is widely used in terahertz devices, exhibits ne¼ 1.71, no¼ 1.57 and a
some-what smaller birefringence than those of MDA-00-3461.
Figure 5. Room temperature terahertz optical constants, n and j for e-ray and o-ray of MDA-00-3461 at 25C. The solid lines are n and j for e-ray. The dashed lines are n and j for o-ray.
Figure 4. (a) The terahertz time-domain waveforms transmitted through a reference cell and LC cell. The LC director is either parallel or perpendicular to the direction of polarization of the incident terahertz wave. (b) The expanded view of (a) from 36 to 40 ps.
5. Conclusions
We report the far infrared complex refractive indices of MDA-00-3461 at room tem-perature 25C from 0.3 to 1.4 THz by using THz-TDS system. The extraordinary and ordinary refractive indices of MDA-00-3461 are ne¼ 1.74 and no¼ 1.54 at 25C,
and it cause a birefringence of 0.20 from 0.3 to 1.4 THz. The extinction coefficient of MDA-00-3461 is relatively small. There are no absorption peaks in the frequency range investigated. MDA-00-3461 exhibits somewhat larger tetrahertz birefringence than those of E7, while the imaginary indices or absorption are comparably low. The new LC MDA-00-3461 is thus a potential useful material for tetrahertz photonic devices.
Acknowledgment
This work was partially supported by National Science Council, Republic of China, under grants 95-2218-E-007-119-MY3 and 96-2221-E-009-131-MY3.
References
[1] Ci-Ling, Pan, & Ru-Pin, Pan. (2006). Proc. SPIE, 6135 61350D, and references therein. [2] Grischkowsky, D., Keiding, S. R., van Exter, M., & Fattinger, Ch. (1990). J. Opt. Soc.
Am. B, 7, 2006.
[3] Ru-Pin, Pan, Cho-Fan, Hsieh, Ci-Lin, Pan, & Chao-Yuan, Chen. (2008). J. App. Phys., 103, 093523.
[4] Ru-Pin, Pan, Tsong-Ru, Tsai, Chao-Yuan, Chen, Chiung-Han, Wang, & Ci-Lin, Pan. (2004). Mol. Cryst. Liq. Cryst., 409, 137.
[5] Tsong-Ru, Tsai, Chao-Yuan, Chen, Ci-Lin, Pan, Ru-Pin, Pan, & Xi-Cheng, Zhang. (2003). Appl. Opt., 42, 2372.
[6] Ru-Pin, Pan, Tsong-Ru, Tsai, Chao-Yuan, Chen, & Ci-Lin, Pan. (2003). J. Biol. Phys., 29, 335.
[7] Chao-Yuan, Chen, Cho-Fan, Hsieh, Yea-Feng, Lin, Ru-Pin, Pan, & Ci-Lin, Pan. (2004). Opt. Exp., 12, 2625.
[8] Chan-Shan, Yang, Chia-Jen, Lin, Ru-Pin, Pan, Christopher, T. Que, Kohji, Yamamoto, Masahiko, Tani, & Ci-Lan, Pan. (2010). J. Opt. Soc. Am. B, 27, 1866.
[9] Chao-Yuan, Chen, Cho-Fan, Hsieh, Yea-Feng, Lin, Ru-Pin, Pan, & Ci-Ling, Pan. (2004). Opt. Express, 12, 2625.
[10] Ci-Ling, Pan, Cho-Fan, Hsieh, Ru-Pin, Pan, Masaki, Tanaka, Fumiaki, Miyamaru, Masahiko, Tani, & Masanori, Hangyo. (2005). Opt. Express, 13, 3921.
[11] Cho-Fan, Hsieh, Yu-Chien, Lai, Ru-Pin, Pan, & Ci-Ling, Pan. (2008). Opt. Lett., 33, 1174.
[12] Chao-Yuan, Chen, Cho-Fan, Hsieh, Yea-Feng, Lin, Ci-Ling, Pan, & Ru-Pin, Pan. (2006). Appl. Phys. Lett., 88, 101107.
[13] Chia-Jen, Lin, Chuan-Hsien, Lin, Yu-Tai, Li, Ru-Pin, Pan, & Ci-Ling, Pan. (2009). IEEE Photo. Tech. Lett., 21, 730.
[14] I-Chen, Ho, Ci-Ling, Pan, Cho-Fan, Hsieh, & Ru-Pin, Pan. (2008). Opt. Lett., 33, 1401. [15] Vincent, K. S. Hsiao, Zhen, Li, Zhe, Chen, Peng-Chun, Peng, & Jie, Yuan Tang. (2009).
Opt. Express, 17, 19988.
[16] Nakamura, M. (1981). J. Appl. Phys., 52, 4561.
[17] Ci-Ling, Pan, Cho-Fan, Hsieh, Ru-Pin, Pan, Masaki, Tanaka, Fumiaki, Miyamaru, Masahiko, Tani, & Masanori, Hangyo. (2005). Opt. Express, 13, 30.
[18] van Exter, M., Fattinger, Ch., & Grischkowsky, D. (1989). Opt. Lett., 14, 1128. [19] Hecht, E. (1998). Optics, 3rd ed., Chap. 4., Addison Wesley Longman: New York. [20] Pochi, Yeh. (1999). Optics of LC Displays, John Wiley, Sons, Inc.
70=[308] C.-P. Ku et al.
