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`Spatial
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`light modulator
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`technology
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`SPATIAL
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`EDITED BY
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`Hughes Research Laboratories
`Mafibu, Cafifomia
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`
`Marcel Dekker, Inc.
`
`UTD L! B RARY
`2601 N. FLOYD RD.
`RICHARDSON, TX 75083
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`UT—Dnms ‘Mfiircs
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`XLNX—1015
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`Page 3 of 102
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`Library of Congress Cataleging-in—Publication Data
`
`Spatial light modulator technology : materials, devices, and applications I edited by Uzi Efren.
`p.
`cm. -— (Optical engineering; 47)
`Includes bibliographical references and index.
`ISBN 0-8247~9108-8'
`
`1. Light modulators. 2. Light modulators—Materials. 3. Optical data processing—Equipment and
`supplies.
`I. Efren, Uzi.
`II. Series: Optical engineering (Marcel Dekker, Inc.}; v. 47.
`TA1750.S7 1994
`
`621.36—dc20
`
`94—27860
`CIP
`
`The publisher offers discounts on this book when ordered in bulk quantities. For more information,
`write to Special SalesIProfessional Marketing at the address below.
`
`This book is printed on acid-free paper.
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`Copyright c 1995 by Marcel Dekker, Inc. All Rights Reserved.
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`Neither this book nor any part may be reproduced or transmitted in any form or by any means,
`electronic or mechanical, including photocopying, microfilming, and recording, or by any infor-
`mation storage and retrieval system, without permission in writing from the publisher.
`
`Marcel Dekker, Inc.
`270 Madison Avenue, New York, New York 10016
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`Current printing (last digit):
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`PRINTED IN THE UNITED STATES-OF AMERICA
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`

`
`
`
`
`‘6
`Ferroelectric Liquid Crystal: Spatial Light
`-
`Modulators
`
`453%
`
`Garret Modd‘el
`
`Universigw of Colorado at Boulder
`Boulder, Colorado
`
`1
`
`INTRODUCTION
`
`Ferroelectric- liquid crystal (FLC) technology has only recently yielded practical light
`modulation devices. It provides a high-performance alternative to the well-established
`nematic liquid crystals in both optically and electrically addressed spatial light. modulators
`(SLMs). The desirable properties of FLCs include histability, fast response, and wide
`viewing angle.
`The purpose of this chapter is to provide an overview of the rapidly advancing field
`of FLC SLM technology. The structure and materials characteristics of FLCs which are
`most important to spatial light modulation are described in simple terms. The modeling
`and processing required to design and fabricate an FLC device are outlined. This is
`followed by a description of the three main types of FLC SLMs that are currently under
`development. The first type of SLM is optically addressed, providing direct replication
`of an image for optical processing and projection displays. These devices exhibit the
`highest Optical resolution of- the three types, limited only by the physical properties of
`the materials. The second is a matrix-addressed SLM, consisting of an array of electrically
`addressed pixels. Although this technology is important for optical processing applica-
`tions, the largest market is in flat-panel displays. The third type is the VLSI-backplane
`SLM, in which a liquid crystal cell is formed directly on an integrated circuit which drives
`it. In addition to affording high speed this approach yields a “smart” SLM which can '
`perform logic operations.
`
`2
`
`FERR'OELECTRIC LIQUID CRYSTAL STRUCTURES
`
`The physics of FLCs has been discussed in Chapter 2. Here the basic structural, electrical,
`and optical properties which are most relevant to SLMs are reviewed.
`
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`Page 5 of 102
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`238
`
`2.1 Background
`
`From the perspective of optical modulation, liquid crystals may be viewed as lying
`between electrons in solids and mechanical shutters. Liquid crystals have mechanical
`and symmetry properties which are between those of an isotropic liquid and a crystalline
`solid. They are like a liquid in that their molecules have at least some of the degrees of
`freedom of a liquid, allowing them to respond sensitively to an applied force. They are
`like a solid in having long range orientational order, with the result that the molecules,
`which are locally anisotropic, are arranged to yield macroscopic anisotrOpy. This yields
`strong electro-optic effects, which may be used to produce excellent optical modulation.
`They are much more sensitive to applied field than solids, in which electro-optic prop-
`erties depend upon electronic and nuclear motion, and exhibit much greater spatial
`resolution than mechanical shutters.
`To‘fornt a device the liquid crystal is usually sandwiched between two plates. Con-
`ducting electrodes on the inner surface of the plates provide the electrical signal which
`drives the liquid crystal. So that light may enter and exit the device at least one of the
`plates is transparent, and is typically coated with a transparent conducting oxide (TCO).
`At least one of the two surfaces which bound the liquid crystal is treated to provide a
`preferred orientation to the liquid crystal molecules. These alignment layers are impor-
`tant in determining the liquid crystal properties and are the subject of Section 3.
`The most commonly used liquid crystal has been the nematic liquid crystal described
`in Chapter 1, whose molecules exhibit orientational order but no positional order [de
`Gennes 1974]. When an electric field is applied, the dielectrically anisotrOpic molecules
`become polarized, creating dipoles which then respond to the field with a torque which
`is proportional to the square of the field. When the field is switched off, the molecules
`relax back to their initial orientations in response to elastic forces. This relaxation usually
`limits the cycling time of nematics. Because the sign of the polarization is a function of
`the sign of the field, the direction of the torque is independent of the sign of the field,
`depending only upon its rms value. Nematic liquid crystals are sensitive to the rms
`average value of the voltage and are thus switched to an on—state by ac fields in which
`the period is smaller than the response time of the liquid crystal. This is illustrated by
`the thin line in Fig. 1.
`In contrast, FLCs have an electrical polarization even in the absence of an externally
`applied electric field. Therefore the molecules respond directly to an applied electric
`
` Optical
`ReSponse
`
`Applied Voltage
`
`Figure 1 Transfer characteristics: nematic (thin line) versus ferroelectric (thick line) liquid crystals.
`
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`FLC Spatial Light Modulators
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`289
`
`field and the torque varies linearly with its magnitude. A field of one polarity drives the
`FLC into what may be defined as an on-state, and the FLC is switched off with a field
`of the opposite polarity. One of desirable features of FLCs is the fast switching which
`results from the spontaneous polarization and from the ability to drive the FLC to its
`off-state. FLCs exhibit a hysteresis, as do all ferroelectrics, illustrated by the thick line
`in Fig. 1 [Reynaerts and De Vos 1991b]. If the hysteresis is sufficiently broad and the
`slope of the transition from one state to the other is sufficiently steep, the FLC remains
`in its prior state when the applied field is switched off (to zero). This bistability is another
`of the desirable features of some FLCs.
`
`In 1975 Meyer showed that the chiral smectic C liquid crystal phase ought to be
`ferroelectric and, along with chemists from Orsay, demonstrated this [Meyer et a1. 1975].
`Smectic liquic crystals exhibit positional order in that the molecules fo'rm parallel layers.
`These layers are usually perpendicular to the bounding planes, i.e. , the layer normal is
`parallel to the planes. In the smectic C phase the average orientation of the long axis
`of the molecules, which defines the molecular director, is tilted with respect to the layer
`normal. A smectic C phase is shown in Fig. 2. In each rod—shaped molecule an electrical
`dipole is perpendicular to the long axis. A chiral smectic C phase (denoted as smectic
`(3*) consists of molecules which are chiral, i.e., which do not have mirror symmetry.
`What Meyer realized was that within each of these microscopic layers the molecular
`directors, and hence the dipole moments of neighboring molecules, would be in alignment
`with each other, with the result that each layer would be ferroelectric. Thus smectic 0“
`liquid crystals are FLCs. In a smectic 0" phase a helical structure tends to form in which
`molecular tilt angle (and hence the director) advances slightly from one layer to the
`next. Because the net polarization of each layer is different, over the distance of a helical
`pitch the net polarization is zero. Thus the ferroelectricity is not macroscopic.
`
`2.2 Surface Stabilized Ferroeleetrie Crystals
`
`In 1980 Clark and Lagerwall demonstrated that macroscopic polarization could be ob-
`tained in smectic C* liquid crystals by suppressing the helix [Clark and Lagerwall 1980].
`This is accomplished by constraining the material to fill a region between two plates
`which are separated by a distance of less than a few times the helical pitch, typically 1
`to 5 pm. These are known as surface-stabilized ferroelectric liquid crystals (SSFLCs).
`This discovery opened the way to practical application of FLCs.
`
`Smectic 0 la er
`y
`
`Stable molecular
`-
`orientations in
`Tilt cone surface stabilized
`
`
`
`Figure 2 Smectic C phase liquid crystal.
`
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`
`
`Structure and Switching
`
`In an ideal SSFLC the molecules form parallel layers which extend from one boundary
`plane to the other. This structure is referred to as the bookshelf geometry because the
`layers are next to each other like books in a bookshelf, with the shelves forming the
`boundary planes. The molecules are constrained to move about a tilt cone, shown in
`Fig. 2. For a tilt angle 9 with respect to the layer normal the molecules have two stable
`orientations, separated by 26, which lie in the plane normal to the layers (and hence
`parallel to the boundary planes). The spontaneous polarization (P) of FLC mixtures
`ranges from the order of one to hundreds of ancmz. To _switch the molecules from one
`state to the other requires a charge of 2P. Additional charge is required to produce a
`voltage across the plates which bound the FLC, as with any capacitor. Thus the total
`charge required to switch an FLC is 2P + CV, where V is the change in the applied
`voltage and C is the geometric capacitance of the cell. For a Z-um-thick cell filled with
`an FLC having a relative permittivity of 3.5, C = 1.5 nF/cmz. With the application of
`a 15—V step to a cell containing FLC with P = 30 ancm2 the spontaneous polarization
`charge is 60 nCl’cm2 and the geometric charge is 23 nCJcmz. As a voltage is applied to
`the cell, current flows nearly instantaneously to the cell, charging the geometric capac-
`itance and decaying with an RC decay time. After a delay the molecules rotate, causing
`a disPIacement current to flow. The combination of the two currents is shown in Fig. 3.
`For the values given above, 72%-of the current may be attributed to the spontaneous
`polarization. In addition to the capacitive and displacement components, current also
`flows due to ionic transport (as discussed in Section 3.5), usually on a longer time scale.
`Often this ionic component of the current may be ignored in comparison to the other
`components.
`Ideally the layers of SSFLCs are perpendicular to the boundary planes. In practice
`SSFLCs are often tilted, forming a chevron structure in which the bend where the two
`oppositely tilted sections meet is parallel to the boundary planes [Clark and Reiker
`1988], as shown in Fig. 4. The reason for the tilting is that the layers become thinner
`as the cell is cooled during formation of the smectic C* phase from the higher temperature
`smectic A“ phase (described in Section 2.4). This chevron structure complicates the
`
`15
`
`3
`
`O1
`
`
`
`Current(mA)
`
`0
`
`50
`
`100
`
`150
`
`200
`
`Time (usec)
`
`Figure 3 Switching current in response to a step voltage for a surface-stabilized ferroelectiic
`liquid crystal cell. (Courtesy R. A. Rice)
`
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`Page a of 102
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`
`FLC Spatial Light Modulators
`
`2.91
`
`
`
`Figure 4 Chevron structure in a surface-stabilized ferroelectric liquid crystal cell.
`
`dynamic and optical properties of the materials because the molecular director is no
`longer parallel to the boundary layers. The situation is more complicated than shown
`in Fig. 4 in that the molecular-director is splayed in one half of the chevron, such that
`it rotates continuously with position [Elston and Sambles 1990, Maclennan et al. 1990].
`An important consequence of chevron formation in SSFLCs is the zigzag wall defect
`formed at the interface between two areas in which the sense of the chevron bend is
`opposite [Handschy and Clark 1984, Ouchi et al. 1988a]. This and other defects reduce
`the quality of the image in SSFLC SLMs, and their elimination has been the subject of
`extensive research. In the following discussion these effects are ignored.
`Upon the application of an electric field of magnitude E the molecular reSponse
`time for switching from one state to the other is
`
`Tl
`1' — PE
`
`.
`
`(1)
`
`where 1] is the viscosity. For 1] = 150 mPa-s (equivalent to nJ—sfcm3 and cP), P = 50
`nC/cmz, and E = 105 Vfcm, r = 30 us. Usually as chiral dopant is added to a FLC
`mixture to increase P, there is a concomitant increase in 1] with the result that 1/1- does
`not increase as quickly as P. With increasing P there is also a decrease in the helical
`pitch of the material and a loss of surface stabilization if the pitch becomes significantly
`smaller than the cell thickness.
`
`The switching proceeds by the nucleation and growth of domains of the new state
`of the SSFLC within a region of the old state [Clark and Lagerwall 1980, Orihara and
`Ishibashi 1984]. These domains are separated by domain walls having a width which is
`on the order of the thickness of the cell, typically 1 to 2 p.111. The movement of these
`domain walls allows the SSFLC to switch from one state to another without having to
`go through a high-energy intermediate state, thus greatly enhancing the switching speed
`of SSFLCs.
`
`As seen from Fig. 1, in the absence of an applied field the molecules ideally remain
`in either of the bistable states indefinitely. Practically, the period over which molecules
`remain in a state is a function of the fabrication conditions for the cells, some of which
`are described in Section 3.3.
`
`Optical Properties
`
`Birefringence. SSFLCs rely on birefringence to modulate light. The refractive index
`along the optic axis parallel to the molecular director (the extraordinary axis) is signif-
`
`XLNX—1U15
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` 292 Moddei——‘_
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`icantly different from the index along an optic axis which is perpendicular to the director
`(the ordinary axis). This difference, the birefringence (An), is quite substantial for FLC
`molecules, typically ~0.14. Incident light which is linearly polarized decomposes into
`two components along these two axes such that the phase of one component is retarded
`with respect to that of the other. In a half-wave plate the thickness (d) is such that
`
`._3
`
`;
`
`iii
`
`:
`
`5
`l
`
`'
`
`And = (2m + Hg
`
`(2)
`
`where it is the wavelength of the light and m is a positive integer. For incident light
`which passes through a polarizer to become linearly polarized with an axis that is 45°
`with respect to one of the optic axes of the half-wave plate, the light is split into equal
`amplitude components along the extraordinary and ordinary axes of the half-wave plate.
`The component of the wave passing through the half-wave plate polarized along the
`extraordinary axis is delayed with respect to the component polarized along the ordinary
`axis by (2m + 1)180°. The emerging components recombine to form light that is linearly
`polarized with a plane of polarization that has been rotated by 90°. This polarization
`change may be converted into amplitude modulation by passing the beam through a
`second polarizer (the analyzer) whose axis is oriented 90° with respect to that of the first
`one.
`
`In switching an SSFLC from one state to the other the optic axis is rotated by twice
`the tilt angle 8. For an incident beam that is aligned with one of the SSFLC axes in its
`off-state, the transmitted light is extinguished upon switching the SSFLC to its other
`state if 20 equals 45°. Fortunately FLC mixtures can be synthesized for which 6 is
`approximately 225°. Thus SSFLCs can act as a switchable half-wave plates.
`Optical Transmission. Giyen any d and B for which the SSFLC is not necessarily
`a half-wave plate, the Optical transmission may be extinguished by aligning the axis of
`the polarizer to the tilt direction of the SSFLC in one state and orienting the axis of the
`analyzer perpendicular to that of the polarizer. The transmission coefficient is ideally
`zero but in practice is a function of the spatial uniformity of the SSFLC cell and the
`quality of the polarizers. Upon applying a field to switch the SSFLC to its other state
`the transmittance at normal incidence becomes
`
`T = sin2 2!! sin2
`
`
`nddn
`
`(3)
`
`where 0 (equal to 28 for SSFLCs) is the angle between the entrance polarizer and an
`optic axis of the liquid crystal. The sin2 2.0 term is a function only of the tilt angle of
`the FLC mixture. If it is not the ideal 22.5“ the transmission in the on-state is diminished,
`i.e., the insertion loss is increased. As the sinKnddant) term is an oscillatory function
`of the cell thickness (d) it would appear acceptable to have a cell in which d is greater
`than the minimum half-wave plate thickness dictated by the m = 0 case in Eq. 2. Because
`this thickness is typically 2 yum for a transmission-mode cell, one might want to make a
`thicker cell to make the fabrication easier. This is usually not desirable, however. As
`can be seen from Eq. 3, the transmission is an oscillatory function of wavelength and
`oscillates more quickly for thicker cells. Thus the performance is closest to achromatic
`for the thinnest cell meeting the half-wave plate condition. Nonoptimal values ford
`Ana's result in increased insertion loss.
`
`Optical Response Time. The optical response time is not simply the molecular
`response time defined in Eq. 1 because the optical transmission is not a linear function
`of the molecular orientation. We define two components of the optical response time:
`
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`FLC Spatial Light Modulators
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`293
`
`the delay time, which is the time between the application of the field and when T has
`reached 10% of its maximum, and the rise time, which is the time between the 10%
`and 90% of maximum transmission states. The delay time is a substantial fraction of the
`optical response time because the initial orientation of the polarization is approximately
`antiparallel to the applied field, providing only a small initial torque. The theoretically
`determined optical delay, rise, and response times are approximately 3.67, 1.87, and
`5.4a, respectively, where 1- is defined in Eq. 1 [Xue et al. 1987]. Although the experi-
`mental delay and response time values may vary significantly from these values due to
`molecular solitary wave motion and flow, they still provide an indication of the rela-
`tionship between the molecular and optical response times.
`Gray Levels. Because of the existence of two stable orientations, the terminal
`response of SSFLCs is in principle binary. A continuously variable response or gray
`levels may be obtained, however, by spatial averaging over areas in which the SSFLC
`is switched on and areas in which it is off, or by temporal averaging over periods during
`which the SSFLC is switched on and off. Both spatial and temporal averaging may be
`accomplished by the control of extrinsic driving parameters, or by taking advantage of
`the intrinsic prOperties of the SSFLC. The basic concepts of gray levels are introduced
`here, and are discussed in more detail in Section 4.3 for optically addressed SLMs, and
`in Section 5.4 for matrix addressed SLMs.
`The spatial averaging may be accomplished intrinsically by allowing domains which
`cover only a fraction of the area of interest to be switched. In intrinsic approaches the
`SSFLC is operated near its threshold. A micrograph of partially switched SSFLC is
`shown in Fig. 5. Such multidomain switching was demonstrated by applying voltage for
`a critical time so that only some domains switch [Lagerwall et a1. 1985], but this approach
`greatly constrains the electrical drive which can he used. As described in Section 5.4,
`
`100 um
`
`Figure 5 Micrograph of partially switched surface-stabilized ferroelectric liquid crystal, showing
`the multidomain structure. (From B. Landreth and G. Moddel, Proc. SPIE, 1296, 64—72 (1%90fin’:‘11:):
`age
`
`

`

`
`
`294
`
`_
`
`Moddel
`
`this approach has been applied successfully in matrth addressed SLMs. A- different
`approach to multidomain switching is to control the charge which is delivered to the
`SSFLC [Hartmann 1989a, Killinger 1991 et al.]. Because a charge of 2P is required to
`fully switch an area, an amount less than that will suffice to switch only a fraction of
`the area.
`
`.In contrast to intrinsic approaches, extrinsic approaches to obtaining gray levels
`involve operating the SSFLC in well defined states far from its threshold. An extrinsic
`approach to spatial averaging is to separate the area over which the averaging is to take
`place into several regions, each of which is addressed independently. Then each region
`which is addressed may be switched fully on, with the gray level resulting from the
`fraction of the area which is switched [Lagerwall et al. 1989]. Extrinsic approaches limit
`the spatial resolution to that of the resolution to which the regions can be patterned.
`Switching the device on and off frequently, or temporal dithering, can provide
`multiple gray levels extrinsically [Clark et al. 1985]. An intrinsic approach to temporal
`averaging is based upon the fact that the switching time is a function of the applied field
`[Landreth and Moddel 1990], as described by Eq. 1. The lower the voltage used to
`switch the device on and off, the larger the time is during which the SSFLC is in an
`intermediate state. This might appear to result from. a decreasing area fraction of switched
`liquid crystal domains, but has been shown to be due to a spatially uniform rotation of
`the optic axis [Landreth and Moddel 1992]. Thus spatially uniform switching occurs on
`the fly while domain switching dominates at longer times, after the charge to switch the
`SSFLC has been supplied and distributes itself into domains.
`
`Simulation of Switching
`
`In designing devices which incorporate SSFLCs it is important to be able to simulate
`the optical and electrical characteristics. The optical and electrical response of an SSFLC
`to an arbitrary electrical drive waveform is a function of the FLC mixture spontaneous
`polarization, viscosities, Elastic constants, tilt angle, and birefringence, and cell thickness,
`type of alignment, surface anchoring [Uchida et al. 1939], chevron characteristics, defect
`structure and temperature. Although much of the fundamental dynamics of the switching
`is understood [Xue et al. 1987, Clark and Lagerwall 1991], the experimental character-
`istics of SSFLC cells have not been modeled accurately. It is therefore necessary to
`develop a phenomenological simulation, based on experimental characteristics.
`A circuit model, shown in Fig. 6, has been developed which simulates both the
`optical and electrical characteristics [Rice and Moddel 1992b]. The response of the circuit
`is simulated using the SPICE (Simulation Program with Integrated Circuit Emphasis)
`computer program. In the input impedance circuit the input voltage (Vflc) produces a
`current which is divided among the polarization current (I901), leakage through the FLC
`resistance (Rae), and charging of the geometric capacitance (Cflc). The integrator circuit
`and clamp produce the correct general time dependence of the response to the input,
`but do not give the correct detailed response. For example, the response to a step function
`input is a linear ramp which is clamped at 1 V, but it does not produce the sigmoidal
`response a real FLC cell would. The correct response is formed using the smoothing
`circuit, whose parameters depend upon characteristic delay, rise and fall time ratios for
`the particular type of FLC cell. The optical output is represented by Vout. Finally, the
`polarization current is found from the derivative circuit. This polarization current is the
`one which is used in the input impedance circuit. The circuit values are determined from
`four parameters derived from the experimental step response of the SSFLC cell. Once
`
`
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`FL CI Spatial Light Modulators
`
`295
`
`I"
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`Input Impedance Circuit
`
`
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`lamp
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`Smoothing Circuit
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`Derivative circuit to calculate
`polarization current
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`CHMVOLIt 51V
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`19.3.99“le of the
`FLO between
`
`crossed polarizers
`
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`I
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`l P°'
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`= P
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`I 5
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`Figure 6 Circuit model which simulates the Optical and electrical characteristics of an SSFLC
`cell in response to an arbitrary driving voltage. (From R. A. Rice and G Moddel, Soc. Information
`Display Int. Symp., Digest of Technical Papers, Vol. 23, SID, 1992, pp. 224—227.)
`
`
`
`they are set, the simulation provides the optical and electrical response to an arbitrary
`input voltage waveform.
`A comparison of a measured and simulated Optical response for an SSFLC cell to
`a-ramp input drive voltage is shown in Fig. 7. Both the optical and electrical measured
`and simulated response to a step change in voltage are shown in Fig. 8.
`
`2.3 Distorted Helix Ferroelectric Crystals
`
`In contrast to the condition for forming a SSFLC described in Section 2.2, distorted
`helix ferroelectric liquid crystals (DHFLCs) are formed in the smectic C* phase when
`the thickness of the cell is greater than the helical pitch. DHFLCs have been studied
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`Relative
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`m PSpioe Model
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`Experimental Data
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`Response
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`Time (msec)
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`Figure 7 Cemparison of a measured and simulated optical response to a ramp input drive voltage.
`(Courtesy R. A. Rice)
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`for a number of years [Meyer 1977, Ostrovskii and Chjgfinov 1930, Beresnev et al.
`19883] but have become attractive for SLM applications morerecently because of the
`availability of short-pitch, high-polarization mixtures [Ffinfschiiling and Schadt 1989,
`Yoshino et al. 1986]. In DHFLC cells the electro-optic effect is linear so that gray
`scales may easin be obtained. They can also be used to display multiple colors using a
`white-light source [Abdulhalim and Moddel 19913], and Operate at lower voltages than
`SSFLCs.
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`FLCCurrent(uA)
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`C)
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`RelativeIntensity(a.u.)
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`mm PSpice Model
`SCE-3 Data
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`Time (rnsec)
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`Figure 8 Comparison of measured and simulated optical and electrical response of an FLC cell
`to a step-change in voltage. (From R. A. Rice and G. Moddel, Soc. Information Display Int.
`Symp., Digest of Technical Papers, Vol. 23, SID, pp. 224—227)
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`FLC Spatial Light Modulators
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`One Pitch
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`Figure 9 Structure of the distorted helix ferroelectric liquid crystal, showing one period of the
`helix. (From I. Abdulhalim and G. Moddel, Mol. Cryst. Liq. Cryst, 200, 79— 101 (1991))
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`Structure and Switching
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`In a DHFLC cell a bookshelf geometry is formed, as in an SSFLC cell, but the natural
`helix is not suppressed by the surfaces. This requires FLC mixtures having a very short
`pitch (e.g’., 0.35 pm), cell thicknesses much greater than the helical pitch, and weak
`anchoring at the surfaces [Ffinfschilling and Schadt 1989]. The helix is manifested in the
`advance of the molecular director from layer to layer, as shown in Fig. 9. The molecular
`director varies sinusoidally as a function of position, as shown in Fig. 10a.
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`3 Molecular
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`Figure 10 Variation of the molecular director in a distorted helix ferroelectric liquid crystal as
`function of position parallel to the boundary planes, for (a) no applied electric field; (b) a moderate
`applied field; and (c) an applied field which is greater than the critical field for unwinding.
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`As an electrical field is applied, the helix distorts such that regions in which the
`polarization is favorably oriented with the field grow,[Meyer 1977, Ostrovski and Chi-
`grinov 1980], as shown in Fig. 10b. Along with the distortion the helical pitch grows.
`As the applied field is increased the distortion grows until, at the critical field, the helix
`is. unwound. This uniform structure is depicted in Fig. 10c. In this state the structure of
`the DHFLC is similar to that of an ideal SSFLC in one of its two stable orientations
`[Beresnev et al. 19880]. A field of the opposite polarity causes a growth of regions having
`the opposite orientation of the polarization.
`As with SSFLCs, DI-l'FLCs exhibit the sort of hysteresis curve shown in Fig. 1. One
`generally drives DHFLCs with fields below the critical field to avoid the unwound state
`for several reasons: Switching from an unwound state is substantially slower than from
`an intermediate state [Fiinfschilling and Schadt 1989], and switching from one unwound
`state to the other proceeds without attaining an intermediate helicoidal state [Bawa et
`al. 1987]. Thus. the linear response available from the intermediate states is missed, and
`gray levels are not obtained. Because in DHFLCs the spontaneous polarization is not
`initially aligned with the applied field when switching between one intermediate state
`and another, the initial torque is generally larger than that in SSFLCs and hence the
`response time is shorter. (Compare to the case described in Section 2.2 under “Optical
`Response Time”)
`There are three different regions in the switching time as a function of electric field
`[Abdulhalim and Moddel 1991a]. In the low-field region, where the helix is hardly
`distorted, the net polarization is approximately zero and the switching exhibits relaxation-
`type behavior. The switching time is a function only of the elastic relaxation time and
`is independent of field. For intermediate fields a net polarization appears, and couples
`to the field in the same way as an SSFLC. The switching time in this region varies
`inversely with the field, as in Eq. 1. At high fields walls form between the areas in which
`the polarization is favorably oriented with respect to the field and shrink with a solitary
`wave behavior. In this case the response time 1- oc lix/F.
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`Optical Properties
`Because the pitch of a DHFLC is on the order of a wavelength of light it diffracts light.
`This diffraction can be used to determine if the structure is DHFLC as opposed to
`SSFLC, and to monitor the elongation and disappearance of the helix with applied field
`[Fiinfschilling and Schadt 1989].
`The main approach to modulating light using DHFLCs relies on birefringence.
`Although microscopic birefringence varies as a periodic function of position the layer
`spacing is on the order of only 20 A so that an average birefringence may be defined
`[Ostrovskii and Chigrinov 1980, Abdulhalim and Moddel 19913]. Thus Eqs. 2 and 3 .
`applr-
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`One important difference between DHFLCs and SSFLCs regards gray levels. Whereas
`SSFLCs produce gray levels only through spatial or temporal averaging, terminal states
`in DHFLCs can yield gray levels, i.e. , stable states may be obtained for which the optical
`transmission varies approximately linearly with applied field [Beresnev et al. 1988a,
`Fiinfschilling and Schadt 1989].
`The second important difference between DHFLCs and SSFLCs is evident from Fig.
`11. In it the optical ”transmission is shown as a function of the average optical axis
`orientation (Q) during the switching transient. For an SSFLC the function appears as
`the diagonal line in the figure, corresponding to a simple rotation of Q in Eq. 3. The
`data for a DHFLC clearly deviates from this line, resulting from a change in. birefringence
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`FLC Spatial Light Modulators
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