Measuring electric-field-induced birefringence in polymer stabilized blue-phase liquid
crystals based on phase shift measurements
Yi-Hsin Lin, Hung-Shan Chen, Chun-Hung Wu, and Hsu-Kuan Hsu
Citation: Journal of Applied Physics 109, 104503 (2011); doi: 10.1063/1.3583572
View online: http://dx.doi.org/10.1063/1.3583572
View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/109/10?ver=pdfcov Published by the AIP Publishing
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Measuring electric-field-induced birefringence in polymer stabilized
blue-phase liquid crystals based on phase shift measurements
Yi-Hsin Lin,1,a)Hung-Shan Chen,1Chun-Hung Wu,1and Hsu-Kuan Hsu2
1
Department of Photonics, National Chiao Tung University, Hsinchu, Taiwan 30010, R. O. C.
2
Chimei-Innolux Corp., Tainan, Taiwan 74147, R. O. C.
(Received 14 January 2011; accepted 22 March 2011; published online 17 May 2011)
A simple optical method to measure the electric-field-induced birefringence and Kerr constant of polymer-stabilized blue-phase liquid crystals (PSBP-LC) is demonstrated. By measuring the phase shift of PSBP-LC and the averaged refractive index of PSBP-LC at the voltage-off state, the ordinary refractive index and extraordinary refractive index of PSBP-LC as function of applied voltage can be obtained experimentally. As a result, the electric-field-induced birefringence and Kerr constant can be determined as well. The method we proposed can help in designing PSBP-LC–based photonic devices.VC 2011 American Institute of Physics. [doi:10.1063/1.3583572]
I. INTRODUCTION
Blue-phase liquid crystals (BPLC) have attracted much attention recently since polymer-stabilized technology has widened their temperature range.1The advantages of poly-mer-stabilized BPLC (PSBP-LC) include that they are align-ment-layer-free and have a fast response time and wide viewing angle.2The photonic applications of PSBP-LC are as displays, photonic crystal lasers, and tunable focusing microlens arrays.3–6 Based on Meiboom et al.’s model, PSBP-LC is an optically isotropic medium at the voltage-off state due to the structure of the double twist cylinders and is an optically anisotropic medium under an applied voltage.7 The capability of changing from optical isotropy to anisot-ropy of PSBP-LC can be quantified by the Kerr constant and electric-field-induced birefringence, which are also impor-tant parameters for designing photonic devices. To measure the Kerr constant, the electric-field-induced birefringence of BPLC or PSBP-LC is usually measured first and then is con-verted into the Kerr constant according to the Kerr equa-tion.8–10 Moreover, many researchers proposed methods to obtain electric-field-induced birefringence of BPLC or PSBP-LC. For example, Hasebaet al. proposed a method to measure the phase retardation of BPLC and then converted the phase retardation into the electric-field-induced birefrin-gence and the Kerr constant.8However, this method requires a corrected factor of 2.7 which is a material-dependent fac-tor.8Khoshsimaet al.9proposed a conventional method for measuring electric-field-induced birefringence of the Kerr cell, but it requires a large thickness of the Kerr cell and a high electric field. As a result, the structure of PSBP-LC is not easily developed and the material is easily damaged, owing to the large thickness of the Kerr cell.9Yanet al. pro-posed a method based on a Michelson interferometer,10but some assumptions were made to obtain the induced birefrin-gence. Recently, Yan et al. proposed a direct measurement to measure the phase retardation, phase shift, and refractive index at the voltage-off state of PSBP-LC in order to obtain
the electric-field-induced birefringence and Kerr constant of PSBP-LC.11However, this method requires many individual optical setups, such as the Senarmont method, Michelson in-terferometer, and Abbe refractometer, to complete the measurement. Although many methods are proposed, the proposed methods still need to be improved. Therefore, an accurate and simple method to measure the Kerr constant and electric-field-induced birefringence of PSBP-LC is an urgent need.
In this paper, we developed a simple method to measure the electric-field-induced birefringence and Kerr constant of PSBP-LC by measuring phase shift of PSBP-LC. The princi-ples and optical setup are simple. We first measured the phase shifts of PSBP-LC as functions of applied voltage at different incident angles of polarized light and measured the averaged refractive index of PSBP-LC at the voltage-off state. According to the results of phase shifts and the averaged refractive index, the ordinary refractive index of PSBP-LC and extraordinary refractive index of PSBP-LC as a function of applied voltage were obtained. As a result, the electric-field-induced birefringence of PSBP-LC was obtained as well. The Kerr constant was then determined according to the Kerr equation. The measurement of electric-field-induced birefrin-gence and the Kerr constant of PSBP-LC we proposed can help designing and optimizing PSBP-LC-based photonic devices.
II. MECHANISM AND PRINCIPLES
The theoretical principle for measuring the electric-field-induced birefringence of PSBP-LC is described as follows. When light is incident on a PSBP-LC cell and the electric field is perpendicular to the glass substrates, the phase shift (Dd) of PSBP-LC between a high voltage (V) and no voltage can be expressed as:11
Ddðh; VÞ ¼ 2p d
k cosðhÞ ½ni neffðh; VÞ; (1) whered is cell gap, k is wavelength of the incident light, ni
is the averaged refractive index of PSBP-LC at V¼ 0, h is
a)Author to whom correspondence should be addressed. Electronic mail: [email protected].
the angle between the incident light and normal direction of PSBP-LC and neff (h, V) is effective refractive index of
PSBP-LC at h at V which can also be expressed as:12
neffðh; VÞ ¼ cos2ðhÞ n2 oðVÞ þsin 2ðhÞ n2 eðVÞ 0:5 : (2)
According to the multiple beam interference at different wavelength of incident light, niin Eq. (1) can be expressed
as:12 ni¼ m 2 d k1 k2 k1 k2 ; (3)
where k1 and k2 are the wavelengths of the light, andm is
the number of the interference cycles between k1 and k2.
From Eq.(1), at h¼ 0, Ddðh; VÞ can be simplified as: Ddðh ¼ 0; VÞ ¼2p d
k ðni noðVÞÞ: (4) That means we can obtainno(V) when we measure the phase
shift of PSBP-LC at the normal incidence. At h = 0, we can obtainne(V) according to Eq. (1), Eq. (2), and Eq. (4). In
addition, the birefringence (DnðVÞ) induced by the Kerr effect equals to (neðVÞ noðVÞ), and DnðVÞ also equals to
k K E2, where E is the external electric field and K is
Kerr constant.11 Thus, after replacing E by V/d, the Kerr constant can be expressed as:
K¼ d
2
k V2½neðVÞ noðVÞ; (5)
Therefore, we can obtain the electric-field-induced birefrin-gence by measuring the phase shift of the PSBP-LC at differ-ent angles of polarized inciddiffer-ent light at differdiffer-ent voltages and then find the Kerr constant of PSBP-LC by Eq.(5).
III. EXPERIMENTS AND DISCUSSIONS
To prepare the sample of PSBP-LC, we mixed a positive nematic LC (Dn¼ 0.142) with two UV-curable monomers EHA (2-Ethylhexyl, Fluka) and RM257 (Merck), a chiral mol-ecules CB15 (Merck), and photoinitiator DMPAP (Aldrich) at 56.9: 3.33: 3.42: 35.85: 0.5 wt. % ratios. The mixture at iso-tropic state was filled into an empty liquid crystal (LC) cell consisting of two Indium Tin Oxide (ITO) glass substrates without any alignment layers. The cell gap was 5.5 lm. We then cooled down the cell at the cooling rate of 0.1C/min, and the blue phase appeared at the temperature T < 30C. The cell was then exposed by UV light at 28.5C with intensity 3 mW/cm2for 30 min for photopolymerization. After photopoly-merization, the temperature range of PSBP-LC was between 20C and 41C. According to the results of the Kossel dia-gram, the structure of the sample is blue phase II (BPII). The morphology of PSBP-LC was then observed under reflective polarizing microscopy, as shown in Fig.1. Figure1shows the typical selective Bragg reflection and the Mozaic platelet struc-ture of PSBP-LC. The domain size is around 20–50 lm.
To measure the electric-field-induced birefringence of PSBP-LC, we measured the phase shift of the sample of
PSBP-LC. The experimental setup is depicted in Fig.2. The incident light source was an unpolarized He–Ne laser (JDSU model 1122, k¼ 633 nm). The incident light passed through a polarizer and then was split into two arms by a beam split-ter. The light of one arm, the signal arm, was incident on the sample driven by a square-wave voltage at frequency f¼ 1 kHz and then reflected by a dielectric mirror (M2). The other
arm, the reference arm, was incident on a dielectric mirror (M1) and then was combined with the signal arm by another
beam splitter. The interference fringes were magnified by a lens and recorded by a digital video camera (SONY, DCR-HC40). In Fig.2, the direction of the incident polarization is x-linearly polarized. In fact, the angles of the incident line-arly polarized lights do not affect the overall phase shift. We measured the phase shift at the different rotation angles (h) of the sample according to the position shift of the interfer-ence fringes.12We also used a white light source and spec-trometer (Shimadzu, UV-210 A) for measuring the averaged refractive index of PSBP-LC at V¼ 0 and h ¼ 0 based on the multiple beam interference. The whole system was built on a floating optical table to avoid any environment-induced fluc-tuation. In this setup, we can measure both the phase shift and averaged refractive index of PSBP-LC at the voltage-off state.
FIG. 1. (Color online) The morphology of PSBP-LC observing under a re-flective polarizing optical microscopy at 24C.
FIG. 2. (Color online) The experimental setup for measuring the phase shift of PSBP-LC and the averaged refractive index of PSBP-LC at the voltage-off state. M1is a dielectric mirror, M2is a dielectric mirror, BS is a beam splitter, and d is the cell gap of the sample. The arrow of polarizer indicates the transmissive axis of the polarizer.
The measured voltage-dependent phase shifts at differ-ent rotation angles (i.e., h in Fig.2) were shown in Fig. 3. The phase shift increases with the applied voltage because of the increase of the birefringence induced by Kerr effect. The maximum phase shift at h¼ 0 at 150 Vrmsis around 0.85 p
radians. At a fixed voltage, the phase shift decreases with the rotation angle. That is because the effective refractive index of PSBP-LC increases. From the results of the spectrum and Eq.(3), the measured averaged refractive indexniis around
1.5596. (The data are not shown here). From Eq.(4),ni, and
the measured data at 0 in Fig.3, we can obtain theno(V) as
a function of voltage, as plotted in Fig. 4 (black squares). From Eq.(1), Eq.(2), and the measured data at 5, 10, and 15in Fig.3, thene(V) as a function of voltage at 5 degree,
10 degree, and 15 degree are plotted in Fig.4as well. In Fig.
4, no(V) decreases with an applied voltage while ne(V)
increases with an applied voltage because the increase of birefringence induced by Kerr effect. At different rotation angles, we obtain the same extraordinary refractive index [ne(V)] as a function of voltage. Fromno(V) andne(V), we
also plotted niðVÞ ¼ ½2 noðVÞ þ neðVÞ=3 in Fig. 4 (gray
dots with gray line). As one can see, the ni(V) decreases
from 1.5596 to 1.5499 with voltage.
We then converted Fig.4into Fig.5which is the bire-fringence [ne(V) no(V)] of PSBP-LC as a function of the
squared electric field at different rotation angles. The maxi-mum birefringence is around 0.117, which is smaller than the host BPLC (0.142). That is because the concentration of BPLC is not 100% and some LC molecules are tangled with the polymer chains as well. In Fig. 5, the Kerr effect which follows the equation: DnðVÞ ¼ k K E2 holds only
when the electric field is small. We can calculate the Kerr constant K¼ DnðVÞ/k E2 7:93 1010m/V2
after put-ting in the experimental parameters: k is 633 nm and the slope in the small electric field is5.02 V2m2at 60 Vrms
in Fig. 5. Compared to the extended Kerr effect proposed by Yan et al.,10 Kerr constant can be expressed as: K¼ 3 ½ni noðVÞ= ðk E2Þ 10:8 1010m/V2 after
putting in the experimental parameters: ni 1.559624,
no(E)1.53232 at 60 Vrms. The Kerr constants are close to
each other by the different methods. The error mainly comes from the ratio of DnðVÞ to ½ni noðVÞ. Instead of 3, the
ra-tio of DnðVÞ to ½ni noðVÞ in our experiment is less than 3.
We averaged the ratio of DnðVÞ to ½ni noðVÞ at all
vol-tages and the ratio is around 2.42. The reason why the ratio is less than 3 might because the lattice distortion accompa-nies the local orientation of molecules.11
IV. CONCLUSION
In conclusion, we developed a simple method to mea-sure the electric-field-induced birefringence and Kerr con-stant of PSBP-LC by measuring phase shift of PSBP-LC. The optical setup is simple. The related optical principle is introduced. In our method, the ordinary refractive index of PSBP-LC and extraordinary refractive index of PSBP-LC as a function of applied voltage can be determined, and then the electric-field-induced birefringence of PSBP-LC and the Kerr constant are obtained. We also measured a sample of PSBP-LC as an example. The measured electric-field-induced birefringence at high voltage is around 0.117 and the Kerr constant is 7:93 1010m/V2. The measurement of the electric-field-induced birefringence and the Kerr constant of PSBP-LC we proposed can help in designing and opti-mized PSBP-LC-based photonic devices, such as displays, electro-optical switches, and tunable focusing lens arrays.
FIG. 3. (Color online) The measured voltage-dependent phase shifts at dif-ferent rotation angles: 0, 5, 10, and 15. The temperature was 24C.
FIG. 4. (Color online) The ordinary refractive index (squares) as a function of voltage, and extraordinary refractive index as a function of voltage at rotation angles of 5(triangles), 10(dots), and 15(diamonds). The gray dots with gray line indicate the averaged refractive index of PSBP-LC as a function of applied voltage.
FIG. 5. (Color online) The birefringence of PSBP-LC as a function of the squared electric field at rotation angles of 5(triangles), 10(dots), and 15
ACKNOWLEDGMENTS
The authors are indebted to Mr. Tsung-Han Chiang for the technical assistance. This research was supported by Chi-mei-Innolux Corp. and by the National Science Council (NSC) in Taiwan under the contract no. 98-2112-M-009-017-MY3.
1H. Kikuchi, M. Yokota, Y. Hisakado, H. Yang, and T. Kajiyama,Nature
Mater.1, 64–68 (2002). 2
K. M. Chen, S. Gauza, H. Xianyu, and S. T. Wu,J. Disp. Technol.6, 49 (2010).
3Z. Ge, S. Gauza, M. Jiao, H. Xianyu, and S. T. Wu,Appl. Phys. Lett. 94, 101104 (2009).
4Z. Ge, L. Rao, S. Gauza, and S. T. Wu,J. Disp. Technol.5, 250 (2009). 5
H. Kikuchi,Struct. Bonding (Berlin)128, 99 (2008). 6
Y. H. Lin, H. S. Chen, H. C. Lin, Y. S. Tsou, H. K. Hsu, and W. Y. Li,
Appl. Phys. Lett.96, 113505 (2010).
7S. Meiboom, J. P. Sethna, W. P. Anderson, and W. F. Brinkman,Phys.
Rev. Lett.46, 1216 (1981). 8
Y. Haseba, H. Kikuchi, T. Nagamura, and T. Kajiyama,Adv. Mater.17, 2311 (2005).
9H. Khoshsima, H. Tajalli, A Ghanadzadeh Gilani and R. Dabrowski,
J. Phys. D: Appl. Phys.39 1495 (2006). 10
J. Yan, H. C. Cheng, S. Gauza, Y. Li, M. Jiao, L. Rao, and S. T. Wu,Appl. Phys. Lett.96, 071105 (2010).
11J. Yan, M. Jiao, L. Rao, and S. T. Wu,Opt. Express18, 11450 (2010). 12E. Hecht,Optics (San Francisco, Addison Wesley, 2002).
