Investigation of the transient symmetric H state in a pi cell

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Investigation of the transient symmetric H state in a pi cell

Bo-Ru Yang, Steve J. Elston, Peter Raynes, and Han-Ping D. Shieh

Citation: Applied Physics Letters 91, 071119 (2007); doi: 10.1063/1.2772670 View online: http://dx.doi.org/10.1063/1.2772670

View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/91/7?ver=pdfcov Published by the AIP Publishing

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Investigation of the transient symmetric H state in a pi cell

Bo-Ru Yanga兲

Department of Photonics and Institute of Electro-Optical Engineering, National Chiao Tung University, Hsinchu, Taiwan 30010, Republic of China and Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, United Kingdom

Steve J. Elston and Peter Raynes

Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, United Kingdom

Han-Ping D. Shieh

Department of Photonics and Display Institute, National Chiao Tung University, Hsinchu, Taiwan 30010, Republic of China

共Received 25 June 2007; accepted 26 July 2007; published online 16 August 2007兲

The so-called symmetric H 共Hs兲 state has been reported to have submillisecond response times,

which results from the symmetric profile of the liquid crystal director; however, no direct evidence has been obtained to show the profile symmetry. The difficulty in proving this symmetric structure by direct observation results from the short lifetime of Hs state 共typically around a few tens of

milliseconds兲. In the work reported here, the authors utilize a burst driving method along with stroboscopic illumination from blue and red light emitting diodes to capture conoscopic images for the Hs director profile; these showed good agreement with their modeling. © 2007 American

Institute of Physics. 关DOI:10.1063/1.2772670兴

The use of a liquid crystal共LC兲 pi cell,1also known as the optically compensated bend共OCB兲 mode, is noted for its fast switching rate owing to its immunity from the backflow effect. Generally, it is operated in the bend state 共V state兲, which is capable of taking less than 4 ms to complete the switching process.1–5 However, because of the topological difference between the ground splay state and V state, a nucleation transition has to be completed to operate the pi cell in the V state. This transition can be initiated by applying a critical voltage in advance to prime the cell from the splay state to the V state, and the voltage should be held to sustain the device in V state. To prevent the unwanted recovery from the V state to the splay state, a number of techniques have been reported to reliably prime the pi cell.6–9

In contrast, the symmetric H共Hs兲 state is a transient state

obtained by a sudden application of voltage to the ground splay device. Owing to its topological similarity with the splay state, the operation in the Hs state needs no priming,

i.e., it is continuous with the ground state. Moreover, the Hs

state has been reported to have the merit of very fast switch-ing, on a scale of 1 ms.10

In previous work, it was suggested that under field ap-plication, the Hs state has an internal director structure in

which the director in the center of the device remains parallel to the surfaces. This “decouples” the two halves of the pi cell; thus the cell is effectively divided into two half-thickness Fréedericksz devices, from which the fast switch-ing behavior results.10–12 The switching rate enhancement, ignoring the flow effect of the pi cell, can be explained by

␶⬀ d2␥

K11␲2

, 共1兲

where␶ represents the relaxation time of the pi cell, d the cell gap,␥ the viscosity, and K11 the splay elastic constant.

Thus, the smaller the effective thickness of the switching

layer, the faster the device. Some modeling and experimental results have shown that the switching rate of the Hsstate is

faster than that of other states in a pi cell by a factor of 4, which supports the existence of the central nonswitching re-gion which decouples the LC director in the two halves of the cell.10–12 This central region and decoupled switching should lead to the Hsstate having a symmetric director

pro-file; however, no direct evidence has been presented to dem-onstrate the profile symmetry. The difficulty in proving this symmetric structure by direct observation was due to the short lifetime of Hs state 共typically around a few tens of

milliseconds, although it can be present for hundreds of mil-liseconds in certain circumstances兲. In this letter we report work where we utilized a burst driving method along with stroboscopic light emitting diode共LED兲 illumination to cap-ture the conoscopic images for symmetric LC director profile of the Hsstate.

Initially a typical pi cell 共with 2.6 um cell gap, filled with LC material E7, and using parallel rubbed polyimide as the alignment layers兲 was positioned at 45° between crossed polarizers and the transmission measured during signal ap-plication. With an impulse voltage signal of 5 Vrms, the

in-tensity variation during the state transitions from ground splay state to Hs and into the asymmetric H共Ha兲 states was

observed by a photodetector, as shown in Fig.1. The Hsstate

was observed to have a lifetime dependence on the applied voltage. As the applied voltage is increased, generally the lifetime of Hsstate共seen in the duration of the Hsplateau in

Fig.1兲 will be longer. However, at higher voltages the V state

rapidly nucleates and transition into the OCB mode occurs. To observe conoscopic images of each state, the device was driven by a burst wave form for Hsstate formation and

a continuous wave form for Hastate formation. As shown in

Fig. 2, the burst driving wave form was composed of two parts: an operating time共period A兲 and a delay time 共period B兲. The operating time was determined by the need to switch the device into the Hsstate but avoid break down into the Ha

a兲_{Electronic mail: ybr.eo93g@nctu.edu.tw}

APPLIED PHYSICS LETTERS 91, 071119共2007兲

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state共s兲共or transition into the V state兲. The delay time al-lowed recovery of the ground splay state. In this case, the operating time was set as 10 ms and the delay time as 90 ms; meanwhile, the stroboscopic LED illumination was set to delay from the start of the switching signal by 5 ms共to allow formation of the Hsstate兲, then to illuminate for 5 ms and be

off for 90 ms共to synchronize with the device switching sig-nal兲. This synchronized driving scheme ensured that only the

Hsstate was captured by the conoscope. To further check the

results, the conoscopic images were obtained using two different wavelengths of light source; using a blue LED 共␭=436–486 nm兲 and a red LED 共␭=622–654 nm兲 for illu-mination.

Based on the Frank-Oseen continuum theory,13,14 using an energy density as defined in Eq.共2兲共where the symbols have their usual meanings兲, the equilibrium director profiles in the liquid crystal device can be calculated,

F =1 2兵K11共ⵜ · n兲 2_{+ K} 22关n · 共ⵜ ⫻ n兲 − qo兴2 + K33关n ⫻ 共ⵜ ⫻ n兲兴2其 − 1 2共D · E兲. 共2兲 Using typical liquid crystal material parameters 共those for E7兲 and initializing from a ground splay state with a slight asymmetry 共to allow eventual formation of the Ha

state兲, we can obtain the director profiles of each state as shown in Fig. 3. After calculating the director profiles, an extended Jones matrix technique15can be used to determine the conoscopic images of each state for wavelengths corre-sponding to using blue and red LEDs as the light sources 共examples of which are shown in Fig.4兲.

The conoscopic measurement results within a viewing cone of around 30° show directly the symmetry of ground splay and transient Hsstates, and also the asymmetry of the

Hastate. In addition, the modeling based on the theory

out-lined above was used to determine conoscopic images within the viewing cone of around 30°共for the light field distribu-tion of the LC director profiles illustrated in Fig. 3兲. The

experimental and theoretical results are shown in Fig.4; the measured conoscopic images 共a兲–共f兲 are in good agreement with the modeling results共g兲–共l兲共at least for the restricted viewing cone of around 30°—it is difficult to obtain good agreement over very wide viewing cone angles due to the illumination system used兲. The asymmetry in the Hs state is

evident in both the experimental results关Fig. 4 images 共c兲 and共d兲兴 and the modeled images 关Figs. 4共i兲 and 4共j兲兴. The

symmetry of the ground splay state is as expected 关Fig. 4

images共a兲, 共b兲, 共g兲, and 共h兲兴. More important for this work is the symmetry evident in Fig.4 images 共e兲 and 共f兲

共experi-FIG. 1. Basic device behavior under field application共observed by a pho-todetector兲. Initially the device is in the ground splay state. When the field is applied共at around t=0 ms兲, a rapid transition into the Hsstate takes place. Later this state breaks down into the Hastate共s兲.

FIG. 2. Burst driving wave form for the device and illuminating LED. Period A represents the operating time共during which the device is switched into the Hs state兲, period B is the delay time between bursts 共allowing relaxation back to the ground splay state兲, and period C is the illumination time, during which conoscopic images are obtained.

FIG. 3. Director configurations of共a兲 splay, 共b兲 Ha, and共c兲 Hsstates deter-mined by using a simple finite-difference relaxation routine to minimize the bulk energy.

FIG. 4. Measured conoscopic images of the device:共a兲 and 共b兲 in splay state,共c兲 and 共d兲 in Hastate, and共e兲 and 共f兲 in Hsstate. Simulated results:共g兲 and共h兲 in splay state, 共i兲 and 共j兲 in Hastate, and共k兲 and 共l兲 in Hsstate. The cases of共a兲, 共c兲, 共e兲, 共g兲, 共i兲, and 共k兲 are illuminated/modeled with a blue LED, while the cases of共b兲, 共d兲, 共f兲, 共h兲, 共j兲, and 共l兲 are illuminated/modeled with a red LED. 共Each set of data has been normalized to optimize the image and exploit the image’s full dynamic range.兲

071119-2 Yang et al. Appl. Phys. Lett. 91, 071119共2007兲

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mental兲 and 共k兲 and 共l兲共theoretical兲. The good agreement between these is evident that the director profile of the Hs

state is indeed as expected, with decoupling of the director in the two halves of the cell. Moreover, according to our mod-eling, if the center point共zero tilt兲 of the director structure is off center by 5% of the thickness of the device, then the conoscopic image is off axis by 15°. Thus, we can be confi-dent that the method used here is very sensitive to asymme-try in the structure.

We have confirmed the existence of the symmetric pro-file of the liquid crystal director in the Hs state by

strobo-scopic conostrobo-scopic imaging. Along with the modeling, the transient nonswitching of the director in the center of the device and the consequent decoupling of the directors in the two halves of the device have been verified to occur. These decoupled directors divide the device into two half-thickness Fréedericksz layers which result in the fast-switching behavior.

Although the Hsstate has merits of fast switching and no

need for priming, extending the lifetime of the transient Hs

state is imperative for commercial applications. By using a repeated burst driven pi cell along with the stroboscopic LED illumination, we can observe every section of state transition by varying the position of illumination period on the time axis 共as shown in Fig. 2兲. These state transition

sections can also be modeled, which may help to come up with a method for extending the lifetime of the Hsstate.

The authors would like to express their appreciations to Liquid Crystal Institute, Kent State University for their

LC3DRAWsoftware which facilitated the visualization of

liq-uid crystal director profile.

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