a word of gratituede

luận văn về a word of gratituede

Vloeibaar-kristaltoepassingen met in-het-vlak draaiende director Liquid Crystal Devices with In-Plane Director Rotation

Chris Desimpel

Promotor: prof dr ir K Neyts

Proefschrift ingediend tot het behalen van de graad van

Doctor in de Ingenieurswetenschappen: Elektrotechniek

Vakgroep Elektronica en Informatiesystemen

Voorzitter: prof dr ir J Van Campenhout

Faculteit Ingenieurswetenschappen

Academiejaar 2005 - 2006

Wettelijk depot: D/2006/10.500/31

The most exciting phrase to hear in science, the one that heralds new discoveries,

is not “Eureka!”, but rather “Hmm that’s funny ”

Isaac Asimov

prof dr ir Kristiaan Neyts

Faculty of Engineering

Universiteit Gent

Members of the board of examiners:

prof dr ir Dani¨el De Zutter (chairman)

prof dr ir Alex De Vos (secretary)

prof dr ir Kristiaan Neyts

prof dr ir Marc Burgelman

prof dr ir Herbert Desmet

prof dr ir Dries Van Thourhout

dr Dick K G de Boer (Philips Research, Eindhoven, the Netherlands)

dr Fatiha Bougrioua (Universit´e de Picardie - Jules Verne, Amiens,France)

Universiteit Gent

Faculty of Engineering

Department of Electronics and Information Systems

Liquid Crystals & Photonics Group

A word of Gratitude

During the past years at the university, I had the chance to meet lots ofnew and interesting people All of them helped me in a certain way.Therefore, it is impossible to thank every single one personally Never-theless, a few people deserve a personal thank you

A special thanks goes to my promotor, prof K Neyts He gave me theopportunity to join the Liquid Crystal & Photonics Group of the Uni-versiteit Gent Despite his busy agenda, he is always available for scien-tific advise or help Thanks to his continuous enthusiasm and support,our research group has become a close group of friends I also want

to acknowledge the Institute for the Promotion of Innovation by ence and Technology in Flanders (IWT-Vlaanderen) for their financialsupport

Sci-An important group which I should not forget, are my colleagues ofthe Liquid Crystal & Photonics Group (Stefaan, Goran, Artur, Jeroen,Hans, Filip S., Filip B., Julien, Reza, Matthias and Angel) and the otherresearch groups of the Physical Electronics The positive atmosphere

in the office, where everybody supports each other, is an example formany other labs

Many thanks to Goran and Stefaan for their help in my quest for ing mistakes

spell-Last but not least, I want to thank my parents and Tine who had tomiss me a lot the last months but nevertheless helped me to keep mymotivation

Chris DesimpelGent, May 11, 2006

Table of Contents

1.1 Background 1

1.2 Goal 2

2 Liquid Crystals 5 2.1 Material properties 5

2.2 Alignment 10

2.3 Electric and elastic properties 11

2.4 One-dimensional configurations 14

2.5 In-Plane switching 16

2.5.1 Director distribution 17

2.5.2 One-dimensional approximation 18

3 Optical Transmission 23 3.1 Polarization of light 24

3.2 Jones Matrix Method 26

3.2.1 Polarizer 29

3.2.2 Twisted nematic and anti-parallel rubbed 29

3.2.3 In-plane switching mode 31

3.3 Rigorous Coupled Wave Method 32

3.4 Reduced Grating Method 37

3.5 Simplified transmission model 39

3.5.1 Transmission model 39

3.5.2 Simulations 41

3.5.3 Experiments 46

4 Surface Anchoring 49 4.1 Weak and strong anchoring 49

4.2 Modeling of weak anchoring 50

4.2.1 Expressions for the anchoring energy f s 51

4.2.2 Examples 53

4.3 Weakly anchored in-plane switching mode 55

4.4 Measurement of the anchoring strength 59

4.4.1 Field-off techniques 59

4.4.2 Field-on techniques 60

4.5 Flow and memory anchoring 61

4.6 Weak anchoring experiments 62

4.6.1 Cell preparation 62

4.6.2 Microscope observations 63

a) Static microscope observation 63

b) Influence of memory alignment 66

c) Memory alignment in the 3-GPS cell 67

d) Memory alignment in the BCB cell 70

e) Switching and relaxation for FC4430 74

4.6.3 Transmission measurements 79

a) Average electro-optic measurements 79

b) Estimation of the azimuthal anchoring strength 80

5 Liquid Crystal Device with a Rotatable Director 85 5.1 Structure of the reconfigurable wave plate 86

5.2 Operating principle 87

5.3 Director simulations 90

5.3.1 Simulated director distribution 91

5.3.2 Purpose of the dielectric layer 95

a) Simplified model for the influence of the dielectric layer 96

b) Mirror plane perpendicular to the aver-age electric field 100

Table of Contents iii

5.3.3 Switching times of the device 103

5.3.4 Multistable wave plate 106

5.4 Optical simulations 107

5.4.1 General considerations 107

a) Regular rectangular mesh 107

b) Diffraction orders on a rectangular and a hexagonal lattice 109

c) Transmissive and reflective mode 111

5.4.2 Transmissive mode 112

a) Crossed polarizers 112

b) Influence of the applied voltage 117

c) Transmission as a function of time 120

5.4.3 Reflective mode 122

a) Improvement of the JMM algorithm 122

b) Reconfigurable wave plate 125

5.5 Experiments 127

5.5.1 Production process of the reconfigurable wave plate127 a) Device design 128

b) Device processing 129

5.5.2 Measurements 132

a) Distinguishing the three different driv-ing configurations 133

b) Control of the average director alignment 135 c) Influence of the applied potential 137

d) 360◦in-plane rotation of the director 140

e) Improvements to the device 141

5.6 Applications for the new liquid crystal device 143

5.6.1 Hexagonal device with rubbed alignment layers 144 5.6.2 Electric field driven alignment direction 144

5.6.3 Intermediate director alignment 144

6 Conclusion 147 6.1 Achievements 147

6.2 Outlook 148

Nederlandse Samenvatting

Vloeibaar-kristaltoepassingen met

in-het-vlak draaiende director

Vloeibare kristallen zijn, door een aantal unieke eigenschappen, eenveel gebruikt materiaal in tal van optische toepassingen Vloeibare kris-tallen zijn optisch dubbelbrekend en laten dus toe om de polarisatievan het invallende licht te veranderen De elektrische anisotropie vanvloeibare kristallen heeft tot gevolg dat de uniaxiale as die de polari-satiewijziging controleert op eenvoudige wijze kan gestuurd wordendoor een extern aangelegd elektrisch veld Daarom worden vloeibarekristallen vaak gebruikt als elektrisch controleerbare dubbelbrekendelagen

Waarschijnlijk de meest bekende toepassing waarin de elektrische

en optische anisotropie van vloeibare kristallen ten volle benut wordt,

is het zogenaamde vloeibaar-kristalbeeldscherm of Liquid Crystal play (LCD) Vloeibaar-kristalbeeldschermen hebben doorheen de jareneen belangrijk deel van de beeldschermmarkt ingenomen Dankzij huntalrijke voordelen zoals beperkte gewicht en afmetingen, de eenvoud

Dis-in productie en het lage energieverbruik hebben ze een aantal sterketroeven ten opzichte van andere beeldschermtechnologie¨en

Het onderzoek naar vloeibare kristallen is nog steeds volop aan degang, maar stilaan ligt het zwaartepunt van vloeibaar-kristalonderzoekminder bij beeldschermen Sommige nieuwe toepassingen zoals Spa-tial Light Modulators zijn nauw verwant aan beeldschermen, terwijlandere zoals diffractieroosters, dubbelbrekende lagen en solitonen vaneen totaal andere aard zijn Een gemeenschappelijk aspect van veelnieuwe onderzoeksonderwerpen is het gebruik van microscopisch klei-

ne variaties Microscopisch kleine veranderingen in een optisch aal brengen speciale effecten met zich mee zoals diffractie en verstrooi-

materi-ing die een meer nauwkeurige studie vragen.

Mijn onderzoek begon als een studie van de optische pen van vloeibaar-kristalbeeldschermen Het belangrijkste aandachts-punt was hierbij de in-het-vlak draaiende of in-plane switching (ips)mode In de in-het-vlak draaiende mode wordt de gemiddelde rich-ting van de moleculen in het vloeibaar kristal (de director) gedraaid ineen vlak parallel met de substraten Tijdens mijn onderzoek ben ik incontact gekomen met vele aspecten van vloeibare kristallen zoals mo-dellering, optica, verankering aan het oppervlak, technologie, Ge-bruik makend van de in-het-vlak draaiende mode heb ik uiteindelijkeen nieuw vloeibaar-kristalcomponent ontwikkeld met een aantal op-vallende eigenschappen

eigenschap-Het doctoraatswerk start met een beknopte inleiding tot

vloeiba-re kristallen In de inleiding worden de terminologie, de belangrijksteeigenschappen en het modelleren van vloeibare kristallen besproken.Speciale aandacht gaat hierbij naar de in-het-vlak draaiende mode dieverder gebruikt wordt in de andere hoofdstukken

Optische transmissie doorheen vloeibare kristallen

Vloeibaar-kristaltoepassingen hebben bijna steeds een optisch aspect

Om de resultaten van de optische experimenten te kunnen vergelijkenmet berekeningen is daarom een optisch algoritme nodig dat toelaat

de optische transmissie doorheen de inhomogene anisotrope lagen teberekenen Tijdens mijn onderzoek heb ik gebruik gemaakt van ver-schillende optische algoritmes Voor eendimensionale lagen volstaat

de Jones-matrix Methode Dit is een eenvoudig 2 × 2 matrix algoritmedat toelaat op snelle wijze de transmissie doorheen het vloeibaar kristal

te berekenen Voor twee- en driedimensionale lagen, is een der optisch algoritme vereist Daarom worden eveneens de RigorousCoupled Wave Method en de Reduced Grating Method gebruikt Tweebestaande methoden die nauwkeurig de optische transmissie doorheenperiodieke anisotrope media berekenen

uitgebrei-Nadeel van de Rigorous Coupled Wave Method en de ReducedGrating Method is echter dat deze tijdrovend zijn en een grote hoe-veelheid computergeheugen vereisen Daarom is een bijkomend ver-eenvoudigd optisch algoritme opgesteld, gebaseerd op de Jones-matrixMethode Dit laat toe om een snelle berekening te maken van de opti-sche transmissie doorheen twee- en driedimensionale dubbelbrekendelagen De nauwkeurigheid van het vereenvoudigd algoritme wordt na-

Nederlandstalige Samenvatting vii

gegaan door vergelijking met de resultaten van de andere algoritmes

Oppervlakteverankering van vloeibare kristallen

Een tweede aspect van vloeibare kristallen waar uitgebreid aandachtaan wordt besteed is de verankering van de vloeibaar-kristalmoleculenaan het oppervlak Voor toepassingen is een defectvrij vloeibaar-kris-talvolume van belang Daarom worden vloeibare kristallen gewoon-lijk gebruikt in dunne lagen tussen twee glassubstraten Controle van

de director aan het oppervlak laat toe om een controleerbare en produceerbare verdeling van de director in het volume te bekomen.Gedurende vele jaren werd verankering gezien als een nevenaspectvan vloeibaar-kristaltechnologie Maar door het toenemend belang vanzachte verankering in allerhande toepassingen treedt het de laatste ja-ren steeds meer op de voorgrond

re-In klassieke toepassingen van vloeibare kristallen zoals bv schermen, wordt een vaste verankering aan het oppervlak gebruikt Ditbetekent dat de director van het vloeibaar kristal aan het oppervlak ineen vaste richting wijst In het hoofdstuk over verankering wordt die-per ingegaan op zachte verankering Zachte verankering is een algeme-

beeld-ne term voor alle situaties waarin de oppervlaktedirector van het baar kristal kan gewijzigd worden door een extern aangelegd elektrischveld of een elastische kracht Dergelijke oppervlakken vertonen ´e´en ofmeerdere stabiele richtingen voor de oppervlaktedirector, maar elek-trische of mechanische krachten kunnen de oppervlaktedirector wijzi-gen Toepassingen van zachte verankering situeren zich in het domeinvan multistabiele vloeibaar-kristalconfiguraties, elektrisch controleer-bare verankering en reductie van de drempelspanning en energiever-bruik bij toepassingen Het gedrag van de oppervlaktedirector wordtbepaald door de gebruikte materialen, de behandeling van het opper-vlak en de oppervlaktetopologie

vloei-Verschillende materialen worden in dit hoofdstuk vergeleken ophet vlak van oppervlakteverankering, met als ultiem doel een mate-riaal te vinden waarbij de sterkte van de azimutale verankering van dedirector aan het oppervlak zo laag mogelijk is Om de verschillendematerialen te kunnen vergelijken werd een meetprocedure ontwikkeldwaarmee de sterkte van de oppervlakteverankering experimenteel kangemeten worden Uiteindelijk werd de surfactant FC4430 aangeduidals materiaal met een zeer zwakke azimutale verankering van de direc-tor

Ontwikkeling van een nieuw vloeibaar-kristalcomponent

De kennis die verzameld werd over de diverse aspecten van vloeibarekristallen heeft uiteindelijk geleid tot de ontwikkeling van een nieuwtype vloeibaar-kristalcomponent met de unieke eigenschap dat de di-rector 360◦ kan draaien in het vlak parallel met het substraatopper-vlak Het schakelen van de director wordt veroorzaakt door horizon-tale velden tussen zeshoekige elektroden in een honingraatmotief aan

de onderzijde van een di¨elektrische laag met bovenop een kristallaag De nieuw ontwikkelde component kan onder andere ge-bruikt worden als herconfigureerbare dubbelbrekende laag in optischeexperimenten

vloeibaar-Vooreerst wordt het werkingsprincipe van de component ken aan de hand van driedimensionale berekeningen van de director-verdeling De mogelijkheid om de director 360◦ te draaien in het vlakparallel met het substraatoppervlak wordt gedemonstreerd en aan dehand van uitgebreide optische simulaties wordt aangetoond dat de op-tische component zich voor de gemiddelde transmissie gedraagt alseen homogene dubbelbrekende laag

bespro-Uiteindelijk werd een testcomponent gebouwd in samenwerkingmet de Chalmers University of Technology in G ¨oteborg (Zweden) en

de vakgroep Intec van de Universiteit Gent Door middel van menten kon worden aangetoond dat de director zoals vooropgesteld in

experi-3 verschillende richtingen kan gealigneerd worden Het ultieme doel,het draaien van de director over 360◦, bleek niet volledig gerealiseerd

te zijn Op het eind van het hoofdstuk worden een aantal suggestiesgegeven om de component te verbeteren en het draaien van de directorover 360◦mogelijk te maken

De resultaten van dit werk heeft geresulteerd in een tiental artikelsdie gepresenteerd werden op internationale conferenties of gepubli-ceerd werden in internationale tijdschriften

English Summary

Liquid crystal devices with

in-plane director rotation

Liquid crystals are a widely used material in all kinds of optical tions The growing importance of liquid crystals as a versatile material

applica-in optical setups rises from their unique features Optically, nematicliquid crystals are uniaxially birefringent and thus modify the polar-ization state of the light wave propagating through the material Theelectrical anisotropy allows to reorient the uniaxial axis, also known

as the director, by application of an externally applied electric field.Therefore, liquid crystals serve as an electrically controllable birefrin-gent layer

The most familiar application of liquid crystals exploiting the cal and electrical anisotropy, is the liquid crystal display (LCD) Liquidcrystal displays acquired an important position on the display marketbecause they are lightweight, easy to produce and use a limited amount

opti-of power

The research on liquid crystals is still very active, but the focus ismoving gradually away from pure display research The unique fea-tures of liquid crystals are now exploited in totally different domains.Some of the new applications like Spatial Light Modulators are closelyrelated to displays, while others such as phase gratings, wave platesand solitary waves are of a totally different nature A common aspect

of many new research topics is miniaturization Also in new liquidcrystal devices, the involved electrodes and surface topologies have mi-crometer scale features This leads to microscopic variations inside theliquid crystal material Microscopic changes in an optical material in-duce special effects such as diffraction and scattering of the transmittedlight which require further study

My research started as a study of the optical characteristics of uid crystal displays, focused on the in-plane switching mode of liquidcrystals During my research, I came in contact with many differentaspects of liquid crystals: modeling, optics, anchoring, technology, Using the principle of in-plane switching, I worked toward a new type

liq-of liquid crystal device with remarkable features The common aspect

of the different topics treated in my phd thesis is liquid crystal deviceswith microscopic lateral variations

The text starts with a brief introduction to the field of liquid tals, explaining the main features of liquid crystals and how to modeland use them Special attention goes to the in-plane switching mode ofliquid crystals, which is further used for different purposes in the otherchapters

crys-Optical transmission through liquid crystals

Applications of liquid crystals involve almost always optics For a parison of the optical experiments with simulational results, a goodtool is required for the calculation of the optical transmission through

com-a liquid crystcom-al lcom-ayer Therefore, three different existing opticcom-al com-rithms are used to model the light propagation through the inhomoge-neous liquid crystal layers For one-dimensional liquid crystal layers,the Jones Matrix Method is used A simple 2 matrix formalism whichgive fast and accurate results For two and three-dimensional liquidcrystal layers the Rigorous Coupled Wave Method and the ReducedGrating Method have been used Two existing methods, which cal-culate accurately the optical transmission through periodic anisotropicmedia

algo-A drawback of the Rigorous Coupled Wave Method and the duced Grating Method is that they require a large amount of com-puter memory and calculation time Therefore, an additional simplifiedtransmission model was developed based on the Jones Matrix Method,which allows a fast and easy calculation of the transmission throughthin three-dimensional liquid crystal layers The usefulness and cor-rectness of the simplified algorithm was demonstrated by comparisonwith the accurate optical algorithms

Re-Weak surface anchoring of liquid crystals

A second aspect of liquid crystals which is studied in more detail isthe anchoring of the liquid crystal molecules at the surface For appli-

English Summary xi

cations it is important to obtain a region free of defects with a knowndirector distribution Therefore, liquid crystals are usually handled inthin layers between two substrates Control of the director at the sur-faces allows a reproducible director distribution in the liquid crystalvolume Therefore it is an important aspect when designing liquid crys-tal devices

Anchoring was longtime considered a side topic of liquid crystals,but with the increasing importance of weak anchoring it entered in thespotlights in the past years Nowadays, many of the mechanisms arebeing studied and it is a main challenge for chemists to develop newmaterials with specific anchoring properties In classic liquid crystaldevices such as displays strong anchoring is used, which implies thatthe surface director is fixed In the chapter on anchoring, the phenom-ena related to weak anchoring of liquid crystals are studied Weak an-choring is a generic term for all situations where the surface directorcan be altered by an externally applied field or elastic torque Such sur-faces exhibit one or more stable orientations of the surface director, butelectric or mechanical torques can change the orientation of the surfacedirector The applications of weak anchoring are situated in the field

of multistable nematic liquid crystal devices, electrically controllableanchoring and reduction of the threshold voltage and power consump-tion of liquid crystal devices The behavior of the surface anchoring isdetermined by the surface material, treatment or structure

Different alignment materials have been compared on their ing properties with as ultimate goal finding a surface material in whichthe azimuthal anchoring, the anchoring strength related to changes ofthe director twist angle at the surface, is reduced to a minimum As

anchor-a tool for companchor-aring the manchor-aterianchor-als, anchor-a meanchor-asurement method wanchor-as oped to accurately estimate the weak azimuthal anchoring strength atthe surface As a result, the surfactant FC4430 was indicated as a mate-rial with a weak azimuthal anchoring strength

devel-Development of a new liquid crystal reconfigurable wave plate

The knowledge gathered about the different aspects of liquid crystalswas finally combined in the last chapter to develop a new type of liq-uid crystal device with the unique ability to rotate the liquid crystaldirector 360◦ in the plane parallel to the glass substrates Switching ofthe liquid crystal director is possible to three different directions Theswitching is induced by horizontal fields between hexagonal electrodes

in a honeycomb arrangement on the underside of a stack comprising adielectric layer and a liquid crystal layer Both switching and switchingback are driven by an electric field The presented device can serve as

a reconfigurable wave plate in optical setups or as a pixel in displayapplications

First, the principle operation of the device is studied by mensional director simulations The feasibility of a 360◦in-plane direc-tor rotation was demonstrated and by means of extensive optical simu-lations, the working as a reconfigurable wave plate was shown Finally,

three-di-a first prototype hthree-di-as been built in collthree-di-aborthree-di-ation with Chthree-di-almers sity of Technology in G ¨oteborg (Sweden) and Intec department at theUniversiteit Gent By microscope observation has been proved that thedirector could be aligned in three different directions as expected, butthe ultimate 360◦rotation did not succeed At the end, a number of sug-gestions were given to improve the device and realize the 360◦directorrotation

Univer-The results of the work has been published in two papers in SCIJournals and was presented at several scientific meetings and interna-tional conferences

List of Tables

2.1 Temperature range of the nematic phase of the used uid crystals 92.2 Electrical parameters of the used liquid crystals 143.1 The ordinary and extra-ordinary refractive index of theliquid crystals used in this work, with the temperatureand wavelength at which they were determined 244.1 Ranges for weak, medium and strong anchoring for theazimuthal and polar anchoring energy 545.1 Time constant of the exponential decay of the averagetwist φd with 5 and 10 V applied Column 1 gives thetime constant for the proposed device (default): thick-

liq-ness of the liquid crystal layer d = 2.1 µm, thickliq-ness

d o = 1.3 µm and dielectric constant εd = 3.5 of the electric layer, dimensions and spacing of the hexagons

di-a = 3 µm di-and b = 5 µm Column 2 shows the effect of

re-ducing the thickness of the dielectric layer and column 3

of increasing its dielectric constant Column 4 shows theeffect of a change in the dimensions of the hexagonalelectrodes and their spacing 1055.2 Time constant of the exponential decay of the averagetwistφdfor different thicknesses of the liquid crystal lay-

er and applied voltages of 5 and 10 V 1055.3 Time constant of the exponential decay of the averagetwistφdfor different liquid crystals and applied voltages

of 5 and 10 V 106

different values of the field h and an alignment direction

φ0= 85◦ 212.13 Midplane twist angleφ(1/2) as a function of the normal-

ized applied field h for different values of the alignment

directionφ0 21

3.1 The polarization ellipse described in the xy-plane by the

oscillating electric field vector of a plane wave

propagat-ing in the z-direction . 253.2 Representation of the polarization state of light on thePoincar´e sphere 263.3 Electro-optic characteristic of an anti-parallel rubbed and

a twisted nematic liquid crystal cell, calculated with thedirector distribution obtained in Figure 2.8 for a wave-lengthλ of 600 nm 303.4 Bright state and dark state of a twisted nematic liquidcrystal display 313.5 Electro-optic characteristic of a liquid crystal cell in thein-plane switching mode, calculated for different direc-tions of the alignment 323.6 Schematical representation of the diffraction modes inthe isotropic regions above and below the periodic layer.The modes are grouped in incident (i), reflected (r), trans-mitted (t) and backward incident (b) waves depending

on their propagation direction 363.7 Definition of the inclination angleϑ0and the azimuthalangleϕ0of the wave vector k0of an incident plane wave 393.8 Basic principle of the simplified algorithm based on theExtended Jones Matrix Method for the optical transmis-sion model through thin liquid crystal layers A planewave in air, represented by a number of parallel rays,

is obliquely incident with inclination angleθ0 on a uid crystal medium of which the director distribution isgiven on a rectangular regular mesh 403.9 Simulated transmission at the top surface of the liquidcrystal layer in the in-plane switching mode after pass-ing the analyzer for an unpolarized, obliquely incidentplane wave, between the center of two neighboring elec-trodes as a function of the lateral position for differentapplied voltages 423.10 Intensity of the diffraction orders in the Fraunhofer dif-fraction pattern of an unpolarized plane wave, obliquelyincident in the in-plane switching mode 43

liq-List of Figures xvii

3.11 Variation of the phase of the electric field componentsδx

andδy, the phase differenceδdi f and the absolute phase

δabs before propagation through the analyzer at the topsurface of the liquid crystal layer of the calculation inFigure 3.9 for an applied voltage of (a) 5 V and (b) 25

V 443.12 Variation of the effective refractive index of the extra-ordinary wave for the director in the midplane of the liq-

uid crystal layer and propagation direction k used in the

calculations of Figures 3.9 and 3.11 453.13 Measured intensity of the transmitted diffraction ordersafter propagation through the analyzer together with thesimulated intensity for different values of the refractiveindex of the ITO electrodes 463.14 Measured and simulated polarization states of the dif-fraction orders before propagation through the analyzer,represented on the Poincar´e sphere 47

4.1 The twist angle φ in the weakly anchored sional approximation of the in-plane switching mode as

one-dimen-a function of the relone-dimen-ative heightζ, for different equallyspaced values of the electric field 564.2 The midplane twistφ(1/2) and the surface twist φ(0) forweak and strong anchoring as a function of the appliedfield 574.3 Twist φ as a function of the height z with indication of

the extrapolation length ξa , for h = 1.0 and h = 1.2 in

caseφ0= 85◦ andρ = 0.25 584.4 Electro-optic characteristic for different values of the an-choring strength in the in-plane switching mode 594.5 Observation of the Schlieren texture of the liquid crystalcells between crossed polarizers for the four tested align-ment materials 644.6 Director distribution in the different types of singularpoints which can appear in the director distribution ofSchlieren textures 654.7 Line defects in the liquid crystal cells after applying ahigh voltages to the electrodes for 3-GPS and BCB 66

4.8 Director distribution inside the surface inversion wall cated above the center of the in-plane switching elec-trodes in the 3-GPS cell and its appearance as two closelyspaced dark lines when observed through a microscopewith crossed polarizers along the axes A and P 674.9 Variation of the twistφ as a function of the lateral posi-

lo-tion x in a surface inversion wall for different values of the azimuthal anchoring strength W a 694.10 Variation of the transmission through a surface inversionwall between crossed polarizers as a function of the lat-

eral position x for different values of the azimuthal choring strength W a 694.11 Width of the inversion wall Λ as a function of the anchor-

an-ing strength W a 704.12 Transmission images of the in-plane switching BCB cellwith defects between crossed polarizers 714.13 Origin of the defect line in area 3 of Figure 4.12, by ob-serving the effect of an externally applied electric field

E on the director distribution in the plane parallel to the

substrate 734.14 Transmission image of the FC4430 cell between crossedpolarizers Between each picture 100 V has been appliedover the electrodes for 1 min, followed by 3 min of shortcircuit 754.15 Transmission image between crossed polarizers (parallelwith the edges of the pictures) with a voltage of 100 Vapplied 764.16 Schematic director distribution in an in-plane switchingliquid crystal cell with the director weakly anchored atthe surface, while a high voltage applied Above, thetransmitted intensity profile is shown, measured with

a CCD-camera for the electrodes parallel or at an angle

with the polarizers (electrode width w = 24 µm) . 774.17 Transmission image for crossed polarizers (parallel totthe edges of the pictures) after switching off the appliedvoltage of 100 V of the observation in Figure 4.15(b) 784.18 Measured average electro-optic characteristic of the non-rubbed in-plane switching liquid crystal cells betweencrossed polarizers, with the polarizer axes parallel andperpendicular to the electrodes 79

List of Figures xix

4.19 Electro-optic characteristic in a uniform region betweenneighboring electrodes of the BCB cell, measured (fulllines) and calculated (dashed lines) 814.20 Electro-optic characteristic in a uniform region betweenneighboring electrodes of the FC4430 cell, measured (fulllines) and calculated (dashed lines) 82

5.1 Setup of the reconfigurable wave plate with indication

of the used coordinate axes The area used in the dimensional director simulations is indicated with thedashed rectangle and contains the hexagonal electrodes

three-(situated in the xy-plane) with on top a dielectric layer, a

liquid crystal layer and the top substrate 875.2 The hexagonal electrode pattern situated in the xy-plane.

The four groups of electrodes are marked with differentgray scales, with indication of a rectangular and a hexag-onal building block 885.3 Three possibilities for driving the electrode sets two by

two The electrodes are situated in the xy-plane and the

gray levels indicate different voltage levels In each ing configuration, the direction of the average horizontal

driv-electric field E av is indicated 885.4 Indication of the approximate direction of the horizontalcomponent of the local electric field between neighbor-ing electrodes (represented by small arrows) and the av-

erage horizontal electric field E av for driving

configura-tion C1 The mirror planes xz and yz are drawn as dotted

lines 895.5 Illustration of the three directions along which the direc-tor can be aligned and the principle of a 360◦director ro-tation by successive application of the three driving con-figurations 905.6 Simulation of a 180◦director rotation by application of 4consecutive driving configurations 925.7 The director and potential distribution in different hori-

zontal planes in the device at t1 = 500 ms while driving

configuration C2is applied 94

5.8 Distribution of the director and the potential in the plane (y = 0 in Figure 5.2) at t1 = 500 ms when driv-

xz-ing configuration C2is applied (a) without the dielectriclayer (the liquid crystal layer is positioned directly abovethe electrodes, plotted area: 20.4 × 2.1 µm), (b) the device

as described above with a dielectric layer of 1.3 µm serted between the electrodes and the liquid crystal layer(plotted area: 20.4 × 3.4 µm) 955.9 Simplified two-dimensional configuration which allows

in-an in-analytic approximation of the field for the in-plin-aneswitching mode Electrode stripes in a dielectric layer

with thickness 2d obetween liquid crystal media 96

5.10 Potential variation along the x-axis in Figure 5.9 if the

po-tential between neighboring electrodes is approximated

by a linear function 97

5.11 Analytic approximation of the electric field lines and quipotential lines in the in-plane switching configurationfor isotropic media 98

e-5.12 The angleθe with the x-axis (top) and the magnitude |E| (bottom) of the electric field E(x, d o+) just above the in-terface between the dielectric and the liquid crystal layerfor the three cases of Figure 5.11 100

5.13 The angleθe with the x-axis (top) and the magnitude |E| (bottom) of the electric field E(x, d o+) just above the in-terface between the dielectric and the liquid crystal layerfor different thicknesses of the dielectric layer, εd = 3.5andεlc=εk= 19.6 101

5.14 The angleθe with the x-axis (top) and the magnitude |E| (bottom) of the electric field E(x, d o+) just above the in-terface between the dielectric and the liquid crystal layer

for different widths of the gap g between the electrodes,

keeping the distance between the center of neighboring

electrodes w + g constant (d o = 1.3 µm, εd = 3.5 and

εlc=εk= 19.6) 102

List of Figures xxi

5.15 Distribution of the potential and the director in the

equi-potential mirror plane (xz of Figure 5.2), at t0 = 250 ms

with driving configuration C1 applied (a) without electric layer (plotted area: 20.4 × 2.1 µm), (b) with a di-

di-electric layer (d0 = 1.3 µm, plotted area: 20.4 × 3.4 µm),(c) with the same dielectric layer but larger electrode di-mensions (plotted area: 23.3 × 3.4 µm), (d) with a dielec-tric layer with higher dielectric constant (plotted area:20.4 × 3.4 µm) 1035.16 Variation of the average twistφdversus time for differentvoltages when applying a sequence of driving configura-tions 1045.17 Evolution of the maximum, minimum and average twist

as a function of time after removing the applied voltages 1075.18 Relation between the rectangular and hexagonal build-ing block of Figure 5.2 The location of the hexagonalbuilding block is indicated with a white background inthe rectangular period, the other matching areas are in-dicated with the same gray level 1085.19 Construction of two non-orthogonal bases inside eachtetrahedron of the irregularly meshed hexagonal build-ing block 1085.20 Wave vectors of the diffraction orders used in the opticalcalculations of the Rigorous Coupled Wave Method (allcircles) and the diffraction orders of the hexagonal lattice

(only the filled circles), represented in the xy-plane 110

5.21 Different layers in the optical simulations of the urable wave plate (a) transmissive mode, (b) reflectivemode 1115.22 Definition of the different azimuthal angles φd, φav, φp

reconfig-andφaused during the optical simulations 1115.23 Transmission through the reconfigurable wave plate be-tween crossed polarizers, as a function of the polarizerorientationφp 1135.24 The zero order transmission through the reconfigurablewave plate positioned between crossed polarizers, as afunction of the polarizer orientationφp in the three dif-ferent driving configurations 115

5.25 Transmission through the reconfigurable wave plate sitioned between crossed polarizers as a function of thepolarizer orientationφp for driving configuration C2and

po-an applied voltage of 5 V 1165.26 Transmission through the reconfigurable wave plate po-sitioned between crossed polarizers as a function of thepolarizer orientationφp for driving configuration C2and

an applied voltage of 10 V 1175.27 The zero order transmission through the reconfigurablewave plate positioned between crossed polarizers, cal-culated with the Rigorous Coupled Wave Method as afunction of the polarizer orientationφp for driving con-

figuration C2with applied voltages of 5, 10, 15 and 20 V 1185.28 The polarization state of the zero order transmission as

a function of the polarizer orientationφprepresented onthe Poincar´e sphere, calculated with the Rigorous Cou-

pled Wave Method with driving configuration C2for theideal case (solid) and the applied voltages 5, 10, 15 and

20 V (dashed) 1195.29 Effective retardation of the reconfigurable wave plate as

a function of the applied voltage, normalized in lengths forλ = 632 nm 1205.30 The zero order transmission as a function of time for 5and 10 V when applying the sequence of driving config-

wave-urations C1− C2− C3− C1− C2− C3− C1 1215.31 Reflection at an ideal wave plate (homogeneous liquidcrystal layer) as a function of the polarizer orientationφp for driving configuration C2withφd= 30◦ 1235.32 The zero order reflection at the reconfigurable wave as afunction of the polarizer orientationφp in the three dif-ferent driving configurations 1255.33 Reflection at the reconfigurable wave as a function ofthe polarizer orientationφp for driving configuration C2with an applied voltage of 5 V 1265.34 Reflection at the reconfigurable wave as a function ofthe polarizer orientationφp for driving configuration C2with an applied voltage of 10 V 128

List of Figures xxiii

5.35 Scheme of the device design (a) The whole design on a

3 × 3 inch substrate with 25 individual cells, (b) One 12 ×

12 mm cell of the design with 5 contact pads at the sideand a square are in the center containing the hexagonalelectrodes, (c) a 31 × 31 µm detail of the square area withindication of the interconnection level (light gray), the

vias (black) and the hexagonal electrodes with a = 3 µm and b = 5 µm (dark gray) 129

5.36 Picture of the substrate produced by Intec (a) the whole

3 × 3 inch substrate with 25 cells, (b) a detailed scope picture of the hexagonal electrodes (image size 73×

micro-68 µm), the interconnection electrodes and the vias in a

cell with a = 3 µm and b = 5 µm 131

5.37 Picture of a finished hexagon cell A 1 inch glass strate is used as counter substrate and four wires are sol-dered to the contact pads 1325.38 Simplified outline of a polarizing microscope used in re-flective mode 1335.39 Pictures of the three driving configurations applied tothe reconfigurable wave plate, with crossed polarizersparallel to the picture edges The applied voltage is a

sub-10 V/120 Hz square wave and the white arrow indicatesthe direction of the average electric field in the respectivedriving configurations Image dimension 45 µm × 50 µm 1345.40 Origin of the colored line observed through a microscopeabove the hexagonal electrodes for driving configuration

C1with the average electric field along the y-axis (a) the

horizontal electric fields in the liquid crystal layer above

a hexagonal electrode, (b) the fields parallel to yz-plane

in the liquid crystal layer 1355.41 Observation of the reflection through a microscope fordifferent orientations of the reconfigurable wave plate -

60◦, 0◦ and +60◦ (from top to bottom) In the three

col-umns, the driving configurations C1, C2 and C3 are spectively applied with a 10 V/120 Hz square wave Pic-ture taken in reflection with polarizer and analyzer alongthe horizontal and vertical edges of the pictures Imagedimension 190 µm × 225 µm 136

re-5.42 Observation of the Schlieren texture in the able wave plate through the microscope when no voltage

reconfigur-is applied, with indication of the director dreconfigur-istribution 1375.43 Observation of the reflection through a microscope forapplied voltages of 0, 2.5, , 10 V (from top to bot-tom) In the three columns, the driving configurations

C1, C2and C3 are respectively applied Measurement inreflection with polarizer and analyzer along the horizon-tal and vertical edges of the pictures 1385.44 The waveforms applied to the four sets of interconnectedhexagons in order to obtain a 360◦ in-plane rotation ofthe director 1405.45 Observation of the reflection through a microscope ofthe three driving configuration applied sequentially with

10 V amplitude and 2 s per driving configuration surement in reflection with polarizer and analyzer alongthe horizontal and vertical edges of the pictures 142

Mea-List of Symbols and

Abbreviations

Abbreviations3-GPS (3-glycidoxypropyl)trimethoxysilane

EJMM Extended Jones Matrix Method

FC4430 Novec surfactant (3M)

LCD Liquid Crystal Display

OLED Organic Light Emitting Diode

PDA Personal Digital Assistant

Electrical symbols

µ0 Magnetic permeability of vacuum (µ0= 4π 10−7H/m)

1x Unit vector along the x-direction

1y Unit vector along the y-direction

1z Unit vector along the z-direction

ε Dielectric tensor

ρ Dimensionless reduced surface-coupling parameter

ε0 Dielectric permittivity of vacuum (ε0 = 8.85 10−12F/m)

εd Dielectric constant of a dielectric layer

εlc Dielectric constant of a liquid crystal layer in the isotropic

approximation

f d Oseen-Frank distortion energy

f e Macroscopic electrostatic energy

f s Surfce anchoring energy

h Normalized electric field

V th Threshold voltage

W a Azimuthal anchoring parameter

W p Polar anchoring parameter

Liquid crystal parameters

∆n Birefringence or optical anisotropy: ne− no

∆ Width of a surface inversion wall

∆ε Dielectric anisotropy:εk− ε⊥

γ1 Rotational viscosity

 Easy direction of the surface director

E av The average horizontal electric field

n Liquid crystal director

φ Azimuthal angle of the liquid crystal director

φ0 Azimuthal angle of the alignment

φav Azimuthal angle of the average horizontal electric field

φa Azimuthal angle of the analyzer transmission axis

φd Average of the twist angle in all nodes of the mesh

List of Symbols and Abbreviations xxvii

φp Azimuthal angle of the polarizer transmission axis

θ Tilt angle of the liquid crystal director

θ0 Pretilt of the liquid crystal director at the surface

θe Angle of the electric field E with the xy-plane

εk Dielectric constant parallel to the uniaxial axis

ε⊥ Dielectric constant perpendicular to the uniaxial axis

ξa Extrapolation length for the azimuthal anchoring

a Side length of a hexagonal electrode

b Distance between two neighboring hexagonal electrodes

C1 Driving configuration of the reconfigurable wave plate

C2 Driving configuration of the reconfigurable wave plate

C3 Driving configuration of the reconfigurable wave plate

d Thickness of a liquid crystal layer

d o Thickness of the dielectric layer between the liquid crystal

layer and the electrodes

g Distance between the electrodes in the ips mode

k11 Splay elastic constant

k22 Twist elastic constant

k33 Bend elastic constant

nd Refractive index of a dielectric layer

neff Effective refractive index of the extra-ordinary mode

ne Extra-ordinary refractive index, parallel to the uniaxial axis

no Ordinary refractive index, perpendicular to the uniaxial axis

s Strength of a singular point

w Width of the electrodes in the ips mode

Optical symbols

χ Ellipticity angle of the polarization ellipse

∆x Period in the x-direction

δx Phase of the x-component of the Jones vector

∆y Period in the y-direction

δy Phase of the y-component of the Jones vector

λ Wavelength in vacuum

ψ Rotation of the longest principle axis of the polarization

el-lipse

ϕ0 Azimuthal angle of the wave vector of a plane wave in air

ϑ Inclination angle of the wave vector of a plane wave

ϑ0 Inclination angle of the wave vector of a plane wave in air

c Speed of light in vacuum (c = 299 792 458 m/s)

Chapter 1 Introduction

Technology has experienced a tremendous evolution in the past years.People got used to the recently developed consumer applications andbenefit without thinking from the numerous advantages A vital part ofmany new devices is the user interface Whereas 20 years ago, devicesused to have a few LED’s (light emitting diodes) to indicate their status,many small applications nowadays have an extensive menu on a colordisplay

Liquid crystal displays (LCD’s) acquired an important position onthis quickly growing market Liquid crystal devices began their evo-lution as simple black-and-white displays with only a few pixels (theacronym for “picture element”) in digital watches and calculators Atthis time, they evolved toward full color displays with hundreds ofthousands of pixels and are used in a wide variety of applications:desktop monitors, televisions, projectors, notebooks, car navigationsystems, PDA’s (personal digital assistant), digital cameras, audio-video equipment, mobile phones, head-up projection displays, Important competitors in the field of displays are the classic cath-ode ray tube (CRT), organic light emitting diodes (OLED) and plasmadisplays The heavy competition between different display technolo-gies forces industry to continue improving their products But LCD’sbenefit from some major advantages to fulfill the growing demands.They are small and lightweight, easy to produce, require low drivingvoltages and use a limited amount of power

A large effort has been made over the past decade to produce LCD’s

at lower cost, with improved properties The viewing angle dency is reduced (color and intensity change when looking obliquely

depen-at the display), the colors have better sdepen-aturdepen-ation and the contrast rdepen-atiohas increased (the ratio between the luminances of a white and a blackscreen)

The research on liquid crystals is still very active, but the focus ismoving gradually away from pure display research The unique fea-tures of liquid crystals are now exploited in totally different domains.Some of the new applications like Spatial Light Modulators are closelyrelated to displays, while others such as phase gratings, wave platesand solitary waves are of a totally different nature A common aspect

of many new research topics is the exploitation of microscopic devicefeatures inside liquid crystals Liquid crystals are typically used as aversatile material in optical setups Microscopic variations in an opticalmaterial involve special effects such as diffraction and scattering of thetransmitted light which require further study

My work started as a study of the optical characteristics of liquid crystaldisplays, focused on the in-plane switching mode of liquid crystals.During my research, I came in contact with many different aspects ofliquid crystals: modeling, optics, anchoring, technology, Using theprinciple of in-plane switching, I worked toward a new type of liquidcrystal device with remarkable features

In the second chapter, a brief introduction in the field of liquid tals is given, explaining the main features of liquid crystals and how tomodel and use them Special attention goes to the in-plane switchingmode, which is further used in the other chapters

crys-Applications of liquid crystals involve almost always optics Forcomparing optical experiments with simulational results, a good tool isrequired for calculating the optical transmission through a liquid crys-tal layer Therefore, chapter 3 deals with the optical algorithms usedduring my work to model light propagation through inhomogeneousliquid crystal layers At the end of the chapter a simplified transmis-sion model is presented which allows fast and easy calculation of thetransmission

1.2 Goal 3

Chapter 4 investigates in more detail the anchoring of liquid tals at surfaces, an important aspect of liquid crystal technology An-choring was longtime considered a side topic of liquid crystals, butwith the increasing importance of weak anchoring it entered in thespotlights in the past years Nowadays, many of the mechanisms arebeing studied and it is a main challenge for chemists to develop newmaterials with specific anchoring properties Through a number of ex-periments different alignment materials are compared and a method isdeveloped which allows to measure the anchoring strength at the sur-faces

crys-Finally in chapter 5, a new type of liquid crystal device is duced The device is based on hexagonal electrodes in a honeycombarrangement on one of the two parallel substrates The simulations inthe chapter focus mainly on its applications as a rotatable wave plate inoptical setups, but other applications such as displays are also possible

intro-I have studied the principle of operation of this device by numericalsimulations and optimized the dimensions A first prototype has beenrealized in collaboration with Chalmers University of Technology in

G ¨oteborg (Sweden) and Intec department at the Universiteit Gent Thefeasibility of the device is demonstrated throughout the experimentsand some suggestions for future improvements are being made