Liquid crystal tunable filters for sensing applications

Transcription

1 Hui Tian Promotoren: prof. dr. ir. Kristiaan Neyts, Jeroen Beeckman Begeleider: Robert Zmijan Masterproef ingediend tot het behalen van de academische graad van Erasmus Mundus Master of Science in Photonics Vakgroep Elektronica en informatiesystemen Voorzitter: prof. dr. ir. Jan Van Campenhout Faculteit Ingenieurswetenschappen Academiejaar 27-28

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3 Hui Tian Promotoren: prof. dr. ir. Kristiaan Neyts, Jeroen Beeckman Begeleider: Robert Zmijan Masterproef ingediend tot het behalen van de academische graad van Erasmus Mundus Master of Science in Photonics Vakgroep Elektronica en informatiesystemen Voorzitter: prof. dr. ir. Jan Van Campenhout Faculteit Ingenieurswetenschappen Academiejaar 27-28

4 Acknowledgements I would like to thank all those who gave me the help to complete this thesis. I want to thank the ELIS (the Electronics and Information Systems) and INTEC (Information Technology) departments of Gent University and the Erasmus Mundus committee for giving me the permission to commence this thesis, to perform experiments in the department and to do any necessary research work. All my colleagues in these two departments are very kind. They gave me great support in my research work. I want to thank them for all their help, interest and valuable hints. I also would like to thank Prof. Patrick De Visschere, his lecture Display Technology gave me a good understanding of the liquid crystals, which is of great help for my thesis. I also want to thank all the members in this Erasmus Mundus program, especially for the coordinator Prof. Roel Baets, the secretary Dave Steyaert and all the classmates of mine. All their encouragement are very helpful for me to complete the thesis. I would like to express my deep gratitude to my promoter Prof. Kristiaan Neyts from the ELIS department of Gent University for the discussions on this topic. He has given me a large number of excellent suggestions during the research for this thesis. I also would like to thank to my promoter Jeroen Beeckman. He spent a lot of time to help me in the research for and writing of this thesis. He gave me very important simulation suggestions and very patient explanations and suggestions for many difficulties I met during my work. He also offered me a lot of help and corrections to improve this thesis in English style and grammar. My supervisor, Robert Zmijan, was also of great help in all the time of my research for this thesis. He explained very clearly how to use all the devices I needed to do the experiment and helped me to find the solutions when I was in difficult times. His suggestions during my work gave me a lot of help how I can improve my thesis. Especially, I would like to give my special thanks to my parents and husband. Although they are not in Belgium, their support and love encouraged me to complete this thesis.

5 De toelating tot bruikleen "De auteur (s) geeft (geven) de toelating deze masterproef voor consultatie beschikbaar te stellen en delen van de masterproef te kopiëren voor persoonlijk gebruik. Elk ander gebruik valt onder de beperkingen van het auteursrecht, in het bijzonder met betrekking tot de verplichting de bron uitdrukkelijk te vermelden bij het aanhalen van resultaten uit deze masterproef." Tian Hui

6 Overview Erasmus Mundus Master of Science in Photonics Masterproef ingediend tot het behalen van de academische graad van Liquid crystal tunable filters for sensing applications Hui Tian Promotoren: prof. dr. ir. Kristiaan Neyts, Jeroen Beeckman Begeleider: Robert Zmijan Masterproef ingediend tot het behalen van de academische graad van Erasmus Mundus Master of Science in Photonics Vakgroep Elektronica en informatiesystemen Voorzitter: prof. dr. ir. Jan Van Campenhout Faculteit Ingenieurswetenschappen Academiejaar Summary Liquid crystals have played an important role in the scientific research. Due to their unique properties, a lot of applications have been developed by extensive research in this field. As one example, in this thesis, a four stage Lyot-Öhman type liquid crystal tunable filter (LCTF) is fabricated by using one E7 liquid crystal cell (4μm) and three High Δn liquid crystal cells (4μm, 8μm, 18μm). The electrical and optical properties of each component of this LCTF have been examined separately. By analysis of the spectra of each stage, both Δn and the thickness of each cell have been calculated. A simulation for the transmission of the E7 cell with the application of different voltages is carried out. The required retardation for each stage should be 2π, 4π, 8π, 16π and they can be achieved by applying a certain voltage on each cell. This LCTF has a narrow transmission band of 11nm to 26nm (FWHM) and is tunable nearly over the whole visible range (4nm-68nm). An extra liquid crystal cell in front of the filter acts as a variable retarder for polarization selection. Good experimental results for the whole setup are obtained for both wavelength and polarization sensing. This LCTF have many applications in different fields and some interesting ones are introduced in this thesis. Keywords: Liquid crystals, Lyot-Öhman filter, wavelength tunable filter.

7 Liquid Crystal Tunable Filters for Sensing Applications Tian Hui Promotor(s): Prof. dr. ir. Kristiaan Neyts, Jeroen Beeckman Supervisor: Robert Zmijan Abstract This article explains the design and fabrication of a liquid crystal tunable filter (LCTF) and how it realizes both polarization and wavelength sensing. Keywords Liquid crystals, Lyot-Öhman filter, wavelength tunable filter. I. INTRODUCTION Liquid crystals were discovered in 1988 and became popular among scientists from late 2th century. Due to their unique properties, a lot of applications have been developed by extensive research in this field, such as liquid crystal displays, hollow liquid crystal fibers, liquid crystal solar cells, liquid crystal thermometers, etc. Another example is what we explored in this article, the liquid crystal tunable filter (LCTF). Digital video cameras have seen a tremendous improvement in resolution and sensitivity in recent years. In consumer applications, the color cameras use broad-band red, green and blue color filters to discriminate colors. In professional applications one is often interested in the intensity in a small spectral range. The LCTF designed in this article is such a narrowband filter which has many applications. In some production lines for apples, we can use this LCTF to test whether the apples are ripe or not by taking pictures for different wavelengths. Another application is in astronomy, we can use this LCTF to observe the space objects (planets, stars). Lots of information for polarization and spectrum can be obtained by taking images of the objects through this filter [1]. II. LIQUID CRYSTAL TUNABLE FILTER A. Lyot-Öhman filter The Lyot-Öhman filter is a multistage filter [2-7]. Each stage consists of an initial linear polarizer, followed by a birefringent plate of fixed retardation such as quartz, and a final polarizer oriented parallel to the initial polarizer. The fast and slow axes of the quartz are oriented at 45 with respect to the polarizers. Each plate is twice as thick as the preceding one, so the retardation of the k th plate Г k is k Γ k = Γ k = Γ 1. And the entire transmission of the whole filter is 4 2 T = T cos πγk k = 1 ( ) H. Tian is with the ELIS Department, Ghent University (UGent), Gent, Belgium. Hui.Tian@UGent.be., where T represents energy losses due to the absorption and reflection. B. LCTF in Lyot-Öhman type In this article, we fabricate a four stage Lyot-Öhman type LCTF (figure 1). For each stage, instead of a quartz plate, a liquid crystal cell is used between two parallel foil polarizers. The cells are oriented with rubbing direction at 45 with respect to the axes of the polarizers. All the cells use nematic liquid crystals with anti-parallel rubbing alignment and the size is 4 by 4 cm. The thicknesses of the liquid crystal layers in the four cells are around 4μm, 4μm, 8μm, 18μm. The liquid crystal we used for the first cell is E7 which is a commercial material (from Merck Ltd.), while for the rest cells we use a special High Δn material developed by Prof. Dabrowski (Military University of. Technology, Poland). Different voltages will be applied on the four cells in order to obtain the required retardation for each cell as shown in figure 1. Retardation: 2π 4π 8π 16π Figure 1. The configuration of the LCTF. The estimated thicknesses of cells are (from left to right): E7 4μm, High Δn cells 4μm, 8μm, 18μm. The required retardation for each cell is shown in the figure. III. MEASUREMENT OF A SINGLE CELL A. Transmission spectrum of a single liquid crystal cell The transmission spectrum of a single cell is measured between parallel polarizers. Figure 2 shows the transmission spectra for the 4 cells used in the filter at zero voltage and figure 3 shows the transmission spectra of one High Δn cell (8μm) with the application of different voltages. From these graphs it is easy to see that for thinner cells, there are fewer extrema (maximum and minimum) and when the applied voltage increases, the spectrum shifts to the left. Each maximum in the spectrum corresponds to a retardation of a multiple of 2π. B. Δn and thickness For High Δn cells, we have obtained some data of Δn from the manufacturer. For each extremum in the spectrum, substitute the Δn into the retardation equation Г=2πΔnd/λ, we can obtain the corresponding thickness d. The average value

8 for all these thicknesses is a very accurate value for the real thickness of the cell. By substituting the average thickness into the retardation equation, we can obtain the new accurate value for Δn for different wavelengths. It is given by λ Δ n( λ ) = λ For E7 cells, the accurate value of Δn has already been discussed in a paper [8]. Transmission (%) E7 4μm High Δn 4μm High Δn 8μm High Δn 18μm Figure 2. Transmission spectra for the 4 cells Transmission (%) V 1.V 1.5V Figure 3. Transmission spectra of one High Δn cell (8μm) with the application of different voltages. C. Simulation of the transmission When we apply a voltage on the cell, the molecules in the cell will rotate towards the electric field. Δn now depends on the distribution of the tilt angle of the molecules. The distribution can be simulated with freely available software [9]. The cell can be seen as a stack of very thin layers of liquid crystals. If we only consider one wavelength, for each layer, Δn can be seen as a constant. The average value of Δn for the whole cell is given by 1 d Δ navg = n( ) d Δ z dz. The transmission with different voltage can be simulated by using this Δn avg and figure 4 shows one simulation result. It proves that now we can use the simulation result to design any device. It is easy to change the parameters in the simulation and only good design will be performed in practice. Transmission (%) μm 1. V Measurement Simulation Figure 4. Transmission simulation for an E7 cell. IV. WAVELENGTH AND POLARIZATION SENSING OF THE LCTF Due to a lot of absorption and reflection, the amplitude of passband of the whole filter will be very low. In order to detect the passband easier, we use a neutral density filter (1% transmission) to measure the reference spectrum for the following experiments. A. Wavelength sensing Ideally, the transmission of this LCTF is the multiplication of the transmission of each stage. Figure 5 shows the multiplication result and the real measured spectrum for the whole filter. We can see they have a good correspondence and for other passband, we can obtain similar results, which mean the LCTF can realize the wavelength sensing. The FWHM of the peaks ranges from 11nm to 26nm and the tuning range is nearly the whole visible spectrum (4nm-68nm). Transmission (%) Measurement result Multiplication of four transmission spectra Figure 5. Multiplication of four transmission spectra and the measurement result for the whole filter at the passband of 5nm. B. Polarization sensing In order to realize polarization sensing, an extra liquid crystal cell which acts as a variable retarder should be added in front of the LCTF. The polarization of the output light for this retarder depends on the retardation of this cell. By changing the voltage applied on this cell, we can change the retardation and light with selected polarization can pass through the whole device. V. CONCLUSION A four stage Lyot-Öhman type LCTF filter is fabricated. The thicknesses and Δn of E7 and High Δn cells were calculated and good transmission simulation result for E7 cell was obtained. At last, we proved this filter can realize both polarization sensing and wavelength sensing. ACKNOWLEDGEMENTS I would like to thank my promoters and supervisor for their patient instruction and I also thank all the others in liquid crystal group for their kind help. REFERENCES [1] R. W. Slawson, Z. Nikkov, E. P. Horch, Publications of the Astronomical Society of the Pacific 111, 621 (1999). [2] B. Lyot, Acad. Sci. (Paris) 197, 1593 (1933) [3] B. Lyot, Ann. Astrophys. 7, 32 (1944). [4] Y. Ohman, Nature 41, 157, 291 (1938). [5] Y. Ohman, Ark. Astron. 2, 165 (1958). [6] J. M. Beckers, L. Dickson, R. S. Joyce, Appl. Opt. 14, 261 (1975). [7] G. Shabtay, E. Eidinger, Opt.Express 1, 1534 (22) [8] J. Li, S. T. Wu, S. Brugioni, R. Meucci, S. Faetti, J. Appl. Phys. 97, 7351 (25). [9]

9 Contents Table of symbols 1 Table of Abbreviations....2 Chapter 1 Introduction Liquid crystals What are liquid crystals? Liquid phases Nematic phase Smectic phases Other phases Molecular orientation in the nematic phase Electrical properties Electric field Surface interaction Freedericksz Transition Optical properties Birefringence in Liquid Crystals Jones matrix Optical transmission Liquid crystal tunable filter Previous type Observation in astronomy...2 Chapter 2 Fabrication of the Lyot-Ohman type filter Lyot-Ohman type filter Measurement of a single liquid crystal cell Fabrication of liquid crystal cells Transmission spectrum of a single liquid crystal cell Analysis and explanation...31

10 3. Difference of refractive indices (Δn) High Δn cells E7 cell Thickness Simulation of the transmission Tilt angle distribution Spectrum simulation Absorption of foil...44 Chapter 3 Measurement of the filter Experiment setup Measurement of the filter for wavelength sensing What voltage should be applied on the filter? Wavelength sensing Measurement of the filter for polarization sensing Variable retarder with liquid crystals Polarization sensing Problems and discussion Degradation of High Δn cells Inhomogeneity of the thickness Switching speed Low amplitude of total transmission Applications...65 Chapter 4 Conclusion...66 References...68

11 Table of symbols L F K 11, K 22, K 33 φ θ D E ε ε // Δε n n // n o n e Δn λ T d Г I u A e, B e, C e, A o, B o, C o director Frank free energy density splay, twist and bend elastic constants twist angle tilt angle electric displacement vector electric field vector dielectric constant (perpendicular to the director) dielectric constant (parallel to the director) dielectric anisotropy refractive index (perpendicular to the director) refractive index (parallel to the director) refractive index for ordinary wave refractive index for extraordinary wave the difference between ordinary and extraordinary refractive indices wavelength transmission thickness of the cell retardation Oseen-Frank free energy potential Cauchy coefficients Tian Hui

12 Table of Abbreviations LCD ITO LCTF CCD FWHM liquid crystal display Indium Tin Oxide Liquid crystal tunable filter charge-coupled device Full width at half maximum Tian Hui

13 Chapter 1 Introduction Liquid crystals were discovered in 1988, when Friedrich Reinitzer, an Austrian botanist, observed that a material known as cholesteryl benzoate did not melt like other compounds, but had two distinct melting points. By that time, he had discovered some important features of this new phase of matter, such as the reflection of circularly polarized light and the rotation of polarization of light. Together with another physicist, Otto Lehmann, who continued Reinitzer s research, Reinitzer is often credited as the father of liquid crystals. Liquid crystals became popular among scientists from late 2 th century. Due to their unique properties, a lot of applications have been developed by extensive research in this field. For example, early in 1991, liquid crystal displays (LCD) were already well established in our everyday life. As more and more devices based on liquid crystals are invented, liquid crystals will play an important role in modern technology. Apart from LCD, there are also some other fascinating applications such as hollow liquid crystal fibers, liquid crystal solar cells, liquid crystal thermometers, etc. Another example is the liquid crystal tunable filter, which was first used to obtain simultaneous, low-resolution spectrophotometry of multiple stars within a moderately crowded field. However, in my thesis, I will explore on a new application of this filter. Digital video cameras have seen a tremendous improvement in resolution and sensitivity in recent years. In consumer applications, the color cameras use broad-band red, green and blue color filters to discriminate colors. In professional applications one is often interested in the intensity in a small spectral range. When faced with the problem of generating all-optical birefringent narrowband filters, one solution is provided by liquid crystal tunable filter. Tian Hui

14 1. Liquid crystals 1.1 What are liquid crystals? Most materials in nature can exist in different phases, depending on the degree of order of the molecules. Three common state of matter are the solid (crystalline), the liquid and the gaseous phase. In the solid state, the molecules have fixed position and orientation with respect to each other. In the liquid state, the average distance between molecules is more or less the same as in the solid state, but now they are able to move around. The liquid phase does not have any order in position or orientation. Like the liquid state, the gas state does not show any order, but the distance between molecules is much larger, so it is much easier to compress gas compared with solid and liquid. [1,2] Apart from the conventional phases, there are a large number of intermediate phases. One group of these intermediate phases show partial order, and are called mesogenic phases (or meso-phases). In meso-phases, molecules are not as ordered as in the solid phase but more ordered than in liquid. Meso-phases include disordered crystal phases and ordered liquid phases, and what we call liquid crystals belong to the latter. Liquid crystals exhibit some features from both liquid and solid. They can flow, but the molecules are arranged and oriented in a crystal-like way which will be visible in their properties. Figure 1 illustrates the alignment of molecules for solid, liquid and liquid crystal state. [1] Fig.1. The alignment of molecules for solid, liquid and liquid crystal state Commonly ordinary liquid are isotropic in nature due to the disordering, which means the optical, magnetic, electric properties, etc. will be the same in any direction. Typically, the liquid crystals are composed of organic molecules with moderate size and elongated shape, and the partial ordering of this kind of molecules leads to their anisotropic properties. Figure 2 Tian Hui

15 shows the typical shape of a liquid crystal molecule. Fig.2. Typical shape of a liquid crystal molecule There are two types of liquid crystals. The well-known one is thermotropic liquid crystals. As the temperature increases, the thermotropic liquid crystals transit into one or several liquid crystal phases until they reach the isotropic liquid phase. The other type is lyotropic liquid crystals, where the transition depends on the concentration of the solution. 1.2 Liquid crystal phases There are various kinds of liquid crystal phases characterized by the type of ordering. One can distinguish them by thinking of the positional order and orientational order. In my thesis, I will only discuss thermotropic liquid crystals. Most thermotropic liquid crystals have no ordering at high temperature. During heating, they might inhabit one or more phases with anisotropic orientation ordering Nematic phase One of the most common phases is the nematic phase. In nematic phase there is some degree of orientation order, which means all the molecules tend to align parallel to each other. We can indicate the average direction of orientation of the neighbors of each point with a unit vector L, known as a director. However, the positional order here is absent, which is similar as in isotropic liquid crystal phase, and that explains some liquid properties. [1] Smectic phases Isotropic Nematic Smectic Fig.3. The alignment of molecules for liquid and nematic and smectic liquid crystal state Tian Hui

16 The smectic phases normally are obtained at lower temperature than nematic. Besides the orientation order as in nematic, they have also one dimensional positional ordering. The molecules are positioned and can only move in layers. Due to the different orientation of the molecules with respect to each layer, they can be divided into two smectic phases. In smectic A phase, the molecules are perpendicular to the layers; while in semectic C phase, they are oblique from the layer. Figure 3 shows the alignment of molecules for liquid and nematic and smectic liquid crystal state. [1] Other phases Apart from the previous phases, there are many other types of liquid crystals with more complicated structures. The left figure below shows the chiral nematic phase (cholesteric phase). This phase is typically composed of chiral molecules (molecules without mirror symmetry) and exhibits chirality. The structure in this phase can be visualized as a stack of thin nematic layers and the director in each layer tends to twist a bit with respect to the previous one. The long axis of each molecule is more or less parallel with the director. Another example is the discotic phase, in which the molecules are disc-like shape and aligned parallel with the short axes. As shown in the right figure below, in this case, the molecules are stacked in columns, so we call it discotic columnar phase. [2] Fig. 4. Chiral nematic liquid crystal phase (left) and discotic columnar phase (right). In all the phases shown above, the nematic phase is the most important phase for different application. From now on, I will only discuss the different properties of nematic phase. 1.3 Molecular orientation in the nematic phase As we said before, for each point in the nematic liquid crystal, the average orientation can be indicated by a vector. Now if we consider the whole liquid crystal, the orientation of all the Tian Hui

17 molecules can be described by a vector-field (director field) L() r. External forces can cause changes in the orientation of the molecules, which will be visualized in the macroscopic properties of the liquid crystal system. The basic deformations are splay, twist and bend, which are illustrated in figure 5. The Frank free energy density of the director field is described by the distortion energies of these three deformations F = K11( divl) + K22( L rotl + q) + K33 L rotl 2 In Cartesian coordinates, every component of L can be determined by the twist angle φ and tile angle θ, as in figure 6. [1] L = cosϕ cosθ L L x y z = sinϕ cosθ = sinθ SPLAY TWIST BEND Fig.5. Basic deformations of the molecules in nematic liquid crystals. [1] Fig.6. The director orientation in Cartesian coordinate. [1] For most applications such as displays, a thin liquid crystal layer sits between two close parallel glass plates. In this case, the problem is simplified to one dimension, and the φ and θ can be seen as only a function of z, which is the direction perpendicular with the glass plates. Tian Hui

18 Nematic liquid crystals are uniaxial media. Due to the anisotropy of the medium, the electrical and optical parameters are different if measured parallel with or perpendicular to director. The orientation of molecules has a profound influence on the way light and electric fields behave in the material. In the following subchapters, the fascinating electrical and optical properties of nematic liquid crystals will be discussed. 1.4 Electrical properties One method to change the orientation of the molecules is to apply an external electric field. This is also the most useful way to switch the medium. For most optical devices, a conductive transparent layer made from Indium Tin Oxide (ITO) is deposited on the inner face of the glass plates. For liquid crystal with positive dielectric constant, if the electric field is big enough, the molecule will rotate and tend to align along the electric field Electric field When nematic liquid crystals are situated in the electric field, as I said above, due to the dielectric anisotropy of the medium, the electric displacement vector D and electric field vector E are usually not parallel to each other. This anisotropy can be expressed by a reciprocal ellipsoid (figure 7) with the following expression D D x y Dz + + = 1 ε ε ε x y z Because of the uniaxiality of nematic liquid crystals, two of above three dielectric constants are equal, ε x ε y ε while the other dielectric constant is different = = (perpendicular to the director) ε x = ε (parallel to the director) and the ellipsoid becomes an ellipsoid of revolution. [1] Tian Hui

19 Fig.7. Reciprocal ellipsoid for a uniaxial material [1] For most of the liquid crystal materials, ε is larger than ε, which is called positive anisotropy, otherwise, called negative anisotropy. For positive anisotropy, as long as the director is not parallel to the electric field, the induced dipole moment is not parallel to the electric field. The dipole molecules tend to orient themselves along the direction of the field. Figure 8 shows for positive anisotropy material, how the molecule orients in electric field. Originally the molecule is oriented almost horizontally. When a vertical electric field is applied on the liquid crystals, a torque is exerted on the molecule and the molecules start to rotate towards the electric field until they reach to an equilibrium state. If the external electric field is strong enough, the molecules will orient along its direction. Original orientation Situation in electric field Result for medium electric field Result for strong electric field Fig.8. The molecule orientation in electric field for positive anisotropy liquid crystals Tian Hui

20 1.4.2 Surface interaction If there is no external electric field, the liquid crystal molecules in bulk will be free to orient to any direction. In applications, thin layers of liquid crystals are usually used, so the interface interaction plays an important role in determining the molecule orientation. Most of the time in order to control the orientation of the directors, it is useful to introduce some outside agents to the medium. Several alignment cases are illustrated in figure 9. [2] Planar alignment: most liquid crystals prefer to orient their director parallel to the surface and the molecules can orient in any direction parallel to the substrate. Homeotropic alignment: some liquid crystals with special chemical properties prefer to orient their director perpendicular to surface. Alignment by rubbing: Another widely used alignment method is by rubbing. Polymer layers are deposited on the surface and rubbed with a soft cloth with appropriate pressure. The liquid crystals on this surface will prefer to orient parallel to the direction of rubbing. Normally this alignment is combined with a small deformation in the vertical direction, which is called pretilt. Pretilt depends on the strength of the rubbing. This can be used to make sure the molecules will rotate in the same direction. Figure 1 illustrates the how the molecules orient by this alignment in two view direction. Planar alignment Homeotropic alignment Alignment by rubbing Fig. 9. Different alignment cases. Fig. 1. Alignment by polymer rubbing: azimuthal alignment along the rubbing direction (left); pretilt with the plane of substrate (right). [2] Tian Hui

21 1.4.3 Freedericksz Transition In most cases, the electric field effects in liquid crystals are influenced by the surface anchoring (alignment). For example, as in figure 11(a), the liquid crystal material is situated between two close parallel plates with planar alignment. When an external electric is applied perpendicularly to the plane of plates, due to the surface anchoring, the molecules will not rotate immediately. Slowly increase the applied electric field and at a certain threshold voltage, the electric field effect is stronger than the surface anchoring, as a result, molecules in the centre start to rotate towards the electric field and deformation occurs (figure 11(b)). That is because molecules in this region receive the least surface interaction force. With the increase of electric field, the deformation will spread from the centre to both sides until at a very high voltage, all the molecules will orient along the direction of the electric field. The changes of the tilt angle in the middle of the cell (mid-tilt) can be used to describe this process (figure 11(c)). The occurrence of such a deformation in the centre is called a Freedericksz Transition. Other types of Freedericksz Transition will be observed for different boundary conditions or different liquid crystal configurations. (a) (b) (c) Fig. 11. Liquid crystals with planar alignment between two parallel plates with (a) a small voltage; (b) a medium voltage; [2] (c) Mid-tilt of the liquid crystal layer as a function of the applied voltage. Tian Hui

22 1.5 Optical properties Liquid crystals suggest a good way to fabricate optical devices. Due to their anisotropy, besides the dielectric constants, the refractive index in the direction perpendicular with respect to the director is also different from the one parallel to director. Birefringence can be found in such materials, which is very important for many applications Birefringence in Liquid Crystals Birefrigence is the decomposition of a ray of light into two rays when it passes through certain materials. The decomposed rays are the ordinary wave and the extraordinary wave, with different polarization. For uniaxial material, as I discussed before, ε is different fromε. The ordinary wave is always perpendicular to the director, so the refractive index (n ) for this wave is equal to n = ε The extraordinary refractive index (n e ) lies in the plane formed by the director and the wave vector and its value depends on the propagation direction of the light. The reciprocal ellipsoid can be used to calculate the n e. As in figure 12, the light which propagates in z direction can be decomposed into two polarized waves. The polarization of ordinary wave is perpendicular to the director and the polarization of extraordinary wave makes an angle of θ with the director. The polarization plane of the incident light cuts the ellipsoid along an ellipse. The lengths of the long and short axes correspond to the magnitudes of the refractive indices. From the geometry we can see that n e satisfies n e nn n = = n sin θ + n cos θ n n 1 co n 2 s θ If the difference between the two indices is small enough, then it can be approximated as 2 ne n n n θ. [1] ( )cos. Tian Hui

23 Fig. 12. Reciprocal elliposoid for a uniaxial material. The light propagates along z direction, and k is the wave vector. [1] Due to the two different indices, the two decomposed waves will propagate in the liquid crystal with different speed, as illustrated in figure 13. Only polarized light in one of these two directions will not change polarization along the medium. Any other polarized light can be decomposed into these two polarized modes; however, the polarization of incident light will change along its way because of different speed of the two decomposed modes. At the output of the device, the phase difference between these two modes determines the polarization of the output light. Fig. 13. Light propagation in a birefringent medium Jones matrix One of the powerful techniques to calculate the optical transmission for optical systems is Jones calculus, which was developed in 1941 by R.C.Jones. [2] Tian Hui

24 Fig. 14. Optical system S with a light ray incident from the left and exit at the right. [2] Polarized light is represented by a Jones vector, and linear optical systems are represented by Jones matrices. The Jones vector is defined by Ex E, where E x and E y are two complex y numbers which denote the x and y components of the electric field of light. Normally the components of the Jones vector are normalized. Figure 14 shows the typical optical system. Light incidents from the left side, and then passes through some optical devices, finally, exits from the right side. If we use Jones vectors to express the incident light and output, the relation between them can be described by a matrix formula form, E J J E E x x x J E = y J E 21 J i = i 22 y Ey Here, J is called Jones matrix of the optical system. The following cases are some useful examples for this thesis: (1) Light propagates through an isotropic layer with thickness d and refractive index n. The phase retardation is the same, 2πnd/λ, for both components. If we make the assumption that there is no reflection of light from either surface of the system, the input and output can related by 2π dn i E λ x e Ex E = 2π dn i y i E y λ e. (2) In a uniaxial material such as nematic liquid crystals, the retardation is different for the two components because refractive indices for extraordinary and ordinary wave are different and then the speeds for the two components are different. If the director is in the xz-plane, the relation becomes 2π dne i E λ x e Ex E = 2π dno i y i E. y λ e Tian Hui

25 The phase retardation Г between the two modes is 2π Γ= ( ne n ) d. λ The output polarization is determined by Г. One of the important properties for liquid crystals is this Г can be tuned by applying different voltages. That is because the orientation of the director can be controlled by an electric field and the value of n e depends on the angle between the director and the propagation direction (figure 12). This variable retardation property for liquid crystal will be discussed more detailed with the experiments in the next chapter. (3) If the optic axis lies in the xy-plane and makes an angle φ with the x-axis (figure 15), then extra rotation matrixes are needed in the transformation. Both the incident light and the output light have to be transferred to the modes with respect to the extraordinary and ordinary axes of the medium. The transformation now becomes 2π dne i E λ x cosϕ sinϕ e cosϕ sinϕ Ex E = 2π dn sin cos o y ϕ ϕ i i i sinϕ cosϕ i E. y λ e Fig. 15. The index ellipsoid of a positive uniaxial material, The angle φ between the extraordinary axis and x-axis is the azimuth angle. [2] Optical transmission In real applications, one-dimensional liquid crystal devices are mostly used. Then we only focus on the optical transmission in the perpendicular direction. By using the Jones matrix technique introduced in the subchapter above, it can be easily calculated. [2] Tian Hui

26 For nematic liquid crystal, due to the uniaxiality, the incident light can be decomposed into the ordinary and extraordinary waves. The refractive indices for them have been calculated before n n e o cos = + n = n θ sin θ n 2 2 where θ is the angle between the director and the x -axis (tilt angle), which is shown in figure 12., The entire layer can be considered as a stack of thin layers. First consider such an elementary thin layer of the liquid crystal. The twist and refractive indices can be seen as constants in this thin layer. The transformation for such a layer is given by 2π neδz i Ex ( z z) λ +Δ cosϕ sinϕ e cosϕ sinϕ Ex( z) E ( ) 2 n sin cos o z y z z = π Δ ϕ ϕ i i i sinϕ cosϕ i +Δ Ey ( z). λ e Then the transformation for the whole layer is just the multiplication of a series of similar Jones matrixes, each with its own refractive indices and twist angle. If the liquid crystal layer is a twist-less (φ constant), the relation between input and output light can be simplified as 2π neavg, d i Ex( z d) λ + cosϕ sinϕ e cosϕ sinϕ Ex( z) E ( ) 2 n sin cos oavg, d y z d = π ϕ ϕ i i i sinϕ cosϕ i + Ey ( z), λ e where n o,avg and n e,avg are the average refractive indices of the layer and are given by 1 d neo ( ), avg= n eo ( )( ) d z dz. If we use crossed polarizers, with one parallel with the x-axis and the other parallel with the y-axis (figure 14), the transmission is given by 2 2πn 2 eavg, d 2πnoavg, d i i λ λ T = cosϕsinϕ e e 2 π ( neavg, noavg, ) d = sin 2ϕ sin λ 2 Γ = sin 2ϕ sin, where Г is the phase retardation between two decomposed waves. Tian Hui

27 Similarly, if we use parallel polarizers with their axes in the direction of x or y axis, the transmission is obtained in the same way 2πn 2 eavg, d 2πnoavg, d i i 2 λ 2 λ T = cos ϕ e + sin ϕ e Tian Hui

28 2. Liquid crystal tunable filter (LCTF) Liquid crystals have many applications, in which the most familiar one is liquid crystal display. However, their fascinating properties discussed in the previous section can be used in many other devices. Moreover, many scientists have investigated exotic and new properties and applications of liquid crystals. In recent years, scientists have become interested in liquid crystal devices for narrow-bandwidth filters. While wavelength selection devices are very common in the microwave region, in the optical and infrared region such kind of devices is usually cumbersome, expensive, and difficult to use. The LCTF suggests one possible solution for this problem. In fact, the accessible wavelength range and the excellent image quality through the filter have led to many applications. For example, airborne hyperspectral imaging, crop stress analysis, machine vision quality control, astronomy, and semiconductor process control, etc. In this thesis, I will explore a LCTF which can select the light with certain polarization and wavelength. 2.1 Previous type A LCTF is typically a multistage Lyot-Ohman type filter, where each stage can be controlled by an electric field in order to get variable retardation. [3-8] Figure 16 shows a 4-stage Lyot-Ohman filter. Each stage consists of an initial linear polarizer, followed by a birefringent plate of fixed retardation such as quartz, and a final polarizer oriented parallel to the initial polarizer. The fast and slow axes of the quartz are oriented at 45 with respect to the polarizers. Each plate is twice as thick as the preceding one, so the retardation of the k th plate Г k is Γ = 2 Γ = 2 k Γ. And the entire transmission of the whole filter is k 4 1 k cos ( k ), T = T πγ k = 1 where T represents energy losses due to the absorption and reflection. Tian Hui

29 Fig stage Lyot-Ohman filter [8] Most of the incident light suffers destructive effect stage by stage and only the selected narrow band can pass through the filter. The ideal transmittance of each stage is illustrated in figure 17 and the pass band shown by the black line is the multiplication of the transmittance of each stage. Obviously, the pass band width is mostly determined by the last stage, so additional stages will narrow the bandwidth and also reduce the transmittance outside the pass band. The stages with smaller retardation are necessary to eliminate the side bands. 1 8 Transmission (%) first stage second stage third stage fourth stage product of 4 stages Fig. 17. Ideal transmittance of a 4-stage Lyot-Ohman filter. The black line is the transmittance trough all 4 stages, which is the product of the transmittances through the individual stage. The transmission of individual stage is shown by the line with different color. Tian Hui

30 Fig. 18. A single LCTF stage. [9] The device described above is a traditional Lyot-Ohman filter. For the LCTF, there is an additional liquid crystal waveplate in each stage, following the fixed retarder (figure 18). The molecules of liquid crystals are initially aligned with the director nearly perpendicular to the light path and parallel to the optic axis of the fixed retarder. Due to the variable retardance of the liquid crystal cell by application of different voltages, the retardance of each stage can be tuned now; therefore, the filter pass band is also electronically tunable over a certain range. 2.2 Observation in astronomy The filter introduced in this thesis can be used to observe some space objects in astronomy. Similar work has been done in 1999 by R.W.Slawson et al with the LCTF discussed in the previous section. This LCTF was used to obtain simultaneous, low-resolution spectrophotometry of multiple stars within a moderately crowded field. [9] Fig. 19. Schematic view of the extraction of continuum scans from a hyperspectral stack of cluster images. [9] Tian Hui

31 Figure 19 simply illustrates the process of observation. A series of images are obtained through a LCTF with a wavelength step of 5 nm. A standard star with a known spectral type is used as a reference. By comparing the collected spectral data at different wavelengths for the reference star with its known spectrum, some corrections for the stack of images can be carried out. Then by collecting together the observed fluxes at the various wavelengths for a selected star in the images, a continuum spectrum of that star can be constructed. Tian Hui

32 Chapter 2 Fabrication of the Lyot-Ohman type filter In the previous chapter, the basic properties of liquid crystals have been introduced, especially the optical and electrical properties, which is indispensable to understand the principle of the liquid crystal tunable filter studied in this thesis. Before the fabrication of the whole LCTF, each component of this filter will be examined in this chapter. The thickness of each liquid crystal plate and refractive indices of the liquid crystal used in the experiments will be calculated. Some simulation work based on the theory before is carried out to compare with the experimental results. Tian Hui

33 1. Lyot-Ohman type filter The LCTF we introduced in this thesis is also a Lyot-Ohman type filter. Figure 2 shows the layout of this filter. It consists of four stages and for each stage, instead of a combination of a quartz plate and a liquid crystal plate, only a liquid crystal plate is used between two parallel polarizers. In order to fix the liquid crystals, we put them between two close parallel glass plates, which is called a liquid crystal cell. All the cells use nematic and the size of them is 4 by 4 cm. The thicknesses of the liquid crystal layers in the four cells are 4μm, 4μm, 8μm, 18μm. The liquid crystal we used for the first cell is E7 which is a commercial nematic liquid crystal (from Merck Ltd.), while for the rest of the cells we use a special High Δn material developed by Prof. Dabrowski (Military University of. Technology, Poland). Five parallel foil polarizers are used at the both sides of each cell, with their axes at 45 with respect to the ordinary and extraordinary axes of each liquid crystal plate. Table 1. Some parameters (approx) for E7 and High Δn liquid crystal materials. E7 High Δn n e n o Δn K 11 12e e-12 K e e-12 ε ε // Δε Fig. 2. The configuration of Lyot-Ohman type LCTF used in the experiment Tian Hui

34 The retardation of each cell for zero voltage is given by 2π Γ = Δn d, λ where Δ n= n n Δ n= n n e o e, avg o, avg., d is the thickness of each cell, while for nonzero voltage, In order to obtain a thin pass band, as we explained before, the retardation of each cell should be twice as big as the preceding one. It means for a certain wavelength, the product (Δn d) of each cell should also be twice as big as the preceding one. Because it is difficult to make very thin cells, we use E7 liquid crystal to make the first cell, for which the Δn is not as high as the other three cells, and then the thickness can be a bit larger and the cell is easier to make. For this filter, the retardations of each cell we used are 2π, 4π, 8π, 16π, respectively. By application of different voltage on the cells, Δn will change its value, which means this filter can be tuned in a wide wavelength range. Tian Hui

35 2. Measurement of a single liquid crystal cell In order to fabricate such a filter, it is very important to know the properties of each component of this device. The optical spectrum is a good way to analyze the properties of each component. In this section, we will measure the transmission spectrum of each cell with the application of different voltages. 2.1 Fabrication of liquid crystal cells The basic unit for most applications is a simple liquid crystal cell, which is a thin liquid crystal layer sandwiched between two parallel glass substrates. Typically the distance between two substrates ranges from 1µm to 1µm, depending on the application. Figure 21 shows the cross-section of a liquid crystal cell. The two glass plates are kept at a distance by spacers (cylindrical or spherical). The spacers are mixed in the glue which keeps the two substrates together. In order to control the orientation of liquid crystal molecules electrically, the inner faces of both glass plates are coated with a transparent electrode (ITO) which can be connected to the voltage source. Also alignment layers are deposited on both electrodes and control the orientation of molecules by rubbing. [2] lead Fig. 21. Cross-section of a liquid crystal cell [2] Figure 22 shows three rubbing methods for nematic cells. In the left picture, both alignment layers are rubbed in the same direction, this is called a splay-cell and the director does not twist. If the alignment layers are rubbed in the opposite direction, as shown in the middle picture, then the directors are parallel with each other. In the last picture, the top alignment layer is rubbed at 9 with respect to the bottom alignment layer, so the directors will rotate along the vertical axis and the cell is called a twisted nematic cell. In our experiments, we use anti-parallel cells, which are also illustrated in figure 21. For any analysis and calculation later on, we do not need to take into account the twist angle. Tian Hui

36 Splay-cell Anti-parallel rubbed Twisted nematic Fig. 22. Different rubbing methods. Figure 23 shows the image of one real cell illuminated between parallel polarizers and crossed polarizers. The thickness of this cell is around 18μm. However, due to the inhomogeneous thickness, we can see different color areas in the cell. The rubbing direction is shown in the pictures by the horizontal arrows. The other arrow points the place of gate, which is used to fill the liquid crystal into the cell. By connecting the wires (blue lines) to the inner faces of the substrates, the voltage can be easily applied. P P P, A gate gate A rubbing direction rubbing direction Fig. 23. Images of one cell (18μm) between parallel (left) and crossed polarizers (right). The arrows show the directions of the polarizer (P) and the analyzer (A). 2.2 Transmission spectrum of a single liquid crystal cell The experimental setup to measure the spectrum of a single liquid crystal cell is shown in figure 24. The separate device on top is a wave generator, which is used to apply voltage on the cell. The spectrometer is connected to a computer and controlled by a Labview program. The figure below, from left side to right side, shows the measurement devices: Light source (Xenon lamp), Tian Hui

37 Attenuator, Diaphragm (due to inhomogeneous thickness, as small as possible), Polarizer (axis at 45 with respect to the horizontal direction), Liquid crystal cell (vertical or horizontal rubbing direction), Polarizer (parallel with the previous polarizer), Collimator (lens), Spectrometer. Fig. 24. Experiment setup for optical spectrum measurement The intensity of the Xenon lamp is not uniform for the whole wavelength range. So before the measurement of the real spectrum, the reference spectrum has to be measured first. The reference spectrum is measured by using the same setup but the cell is removed. In this way, the effects such as the absorption and reflection caused by polarizers can be eliminated. By comparing this measurement result with the theoretical result, we can have a better idea how the cell works. However, when we consider the real application for the whole filter, only real transmission is useful. Then everything has to be taken into account, so does the influence of the polarizers. The final data recorded by the computer are the normalized intensities of light at different wavelength, in other words, this spectrum which is not influenced by the light source and polarizers is given by Normalized Transmission with cell inside transmission = Reference transmission When all the parameters are set, the measurement process is automatically controlled by the Tian Hui

38 computer. We apply to the cell an AC voltage with frequency 2Hz. That is because there are ions in liquid crystals. If we apply a DC voltage, the ions with different charges will move towards the substrates with the opposite direction and an electric field opposite to the applied electric field will be built. With the increase of the ions on both substrates, the applied electric field will be eliminated by this built-in field. The computer records the spectrum at a serious of voltages with a certain step. Normally the step is chosen as.1 Volt and the voltages range from Volt to 3 Volt. Figure 25 shows the transmission spectra of the 4 cells we used in this LCTF without application of voltage. The thicknesses shown here for the 4 cells are estimated thicknesses. From these graphs it is easy to see for thinner cells, there are fewer extrema (maximum and minimum) and the thickest cell (18μm) has the most extrema. However, E7 has fewer extrema than the High Δn cell when their thicknesses are the same. That is because the Δn of E7 cell is less than the High Δn material. In the next section, we will explain this in detail. Until now the reason of one interesting phenomena is clear. Usually the colors of thinner cells are much more vivid than the thicker ones, because for thicker cells, more extrema means more transmitted wavelengths are mixed together, in other words, the color is a mix of several colors. (a) 1 E7 cell 4μm (b) 1 Hign Δn cell 4μm 8 8 Transmission (%) Transmission (%) Tian Hui

39 (c) 1 High Δn cell 8μm (d) 1 High Δn cell 18μm 8 8 Transmission (%) Transmission (%) Wavlength (nm) Fig. 25. Transmission spectra of the 4 cells used in the LCTF Figure 26 shows the transmission spectra of E7 cell and High Δn cell (8μm) with the application of different voltages. We can see from the graphs when the applied voltage increases, both the spectra of E7 cell and High Δn cell shift to left. For higher voltage, there will be fewer extremums in the fixed wavelength range (4-8nm). (a) 1 Transmission (%) E7 cell 4μm V 1.V 1.5V 2.V 2.5V 2.9V Tian Hui

40 (b) 1 Transmission (%) High Δn cell 8μm V 1.V 1.5V (c) 1 Transmission (%) High Δn cell 8μm 2.V 2.5V 2.9V Fig. 26. Transmission spectra of the E7 cell and High Δn cell (8μm) with the application of different voltages Tian Hui

41 2.3 Analysis and explanation As we explained in the first chapter, when the cell is situated between parallel polarizers with their axes in the direction of x or y axis, the transmission is given by 2πn 2 eavg, d 2πnoavg, d i i 2 λ 2 λ T = cos ϕ e + sin ϕ e, where φ is the angle between the director (rubbing direction) and the x axis. In this experiment, both axes of polarizers are fixed at 45 with respect to the rubbing direction. Hence, T = cos ϕ = sin ϕ = πn 2 eavg, d 2πnoavg, d i i λ λ e + e 2 π ( ne, avg no, avg ) d = cos λ 2 = cos 2 Γ 2 where the retardation Г is given by 2 π ( n n ) d 2πΔnd λ λ e, avg o, avg Γ= =, Δ n= ne, avg no, avg When the retardation is a multiple of 2π (, 2π, 4π, 6π ), T=1, which corresponds to the maximum in the spectrum; when the retardation is an odd multiples of π (π, 3π, 5π, 7π ), T=, which corresponds to a minimum in the spectrum. For the same cell, large retardation corresponds to small wavelength, so the extrema at the left side corresponds to larger retardation. Typically the refractive indices ( n and n ) of liquid crystal are the functions of wavelength. So the ordinary and extraordinary refractive indices are rewritten as n ( λ) n ( λ) n ( λ) no = n ( λ), ne = = n ( λ)sin θ + n ( λ)cos θ n ( λ) n ( λ) 2 1 cos θ 2 n ( λ) As illustrated in figure 27, if no voltage is applied on the cell, the orientation of the director only depends on the alignment layers and the material. For anti-parallel rubbing alignment, θ is a constant for the whole cell. It means n o and n e only depends on the wavelength of the light, so does Δn (n o n o,evg, n e n e,evg ). The number of maxima in the wavelength range 4-8 nm is equal to the number of integers in the range from Δnd/8 toδnd/4, or we can say Tian Hui [1]

42 Δn(4 nm) Δn(8 nm) The number of maximum= i d 4 8, where [] means to choose the maximum integer which is smaller than the real number inside the []. Obviously, when the thickness d is larger, there will be more maxima in the spectrum from 4nm to 8nm. On the other hand, if d is the same as the other cell, but both Δn at 4nm and 8nm are smaller, such as the E7 cell compared with High Δn cells, then the whole equation will be also smaller and that is why the E7 cell has fewer extrema in the spectrum. When the applied voltage is larger than the threshold voltage (Freedericksz Transition), the molecules in the centre start to rotate towards the direction of the electric field and the deformation spreads to both sides with the increase of the voltage. θ is the function of both voltage V and z, where z is the vertical axis and parallel with the electric field. As a result, n e depends on λ, V and z, n e,avg can be calculated from n e and the normalized z-axis (z/d, where d is the thickness of the cell). n e,avg is the function of λ and V, so is Δn. As the applied voltage increases, from the above equation, we can see that n e decreases with the increase of θ, so does Δn. In order to obtain the same retardation for the same cell, λ should be smaller than before. That is why all the extrema shift to the smaller wavelength part with the application of higher voltage. Finally if the voltage is high enough, all the molecules will be along the electric field, θ=2/π and Δn=, there will be no birefringent phenomenon and all the light will pass through the cell. This maximum corresponds to retardation. Fig. 27. The orientation of directors in the liquid crystal cell when the applied voltage: V= (left); V>V tn (right). [2] Tian Hui

43 3. Difference of refractive indices (Δn) In this section, only the situation without application of voltage is considered. From the equation of retardation, in order to calculate the accurate thickness of the cells, it is very important to know the dependence of the Δn with the wavelength. 3.1 High Δn cells For High Δn cells, we have obtained some data for Δn from the manufacturer, but they are not accurate enough. However, we can use them as an initial guess to get more accurate data. Figure 28 shows these inaccurate data by black dots and the red line is the fitting curve for these data. We cannot obtain a good fitting result if we use the model for Δn introduced in previous papers, so we tried the other fitting methods. The fitting equation is given by Δ ( λ) = λ λ 6 2 n. Now we can know the Δn at any wavelength by using this equation Δ n' Fig. 27. The value of Δn from the manufacture company and the fitting curve The maximal points of transmission in all the graphs we have shown before do not reach to 1%, that is mainly due to the absorption of ITO. So we rewrite the transmission equation as Tian Hui

44 cos 2 Γ T = T 2 2π dδn Γ= λ where T part takes into account the absorption and is less than 1. By slowly increasing the applied voltage from volt to 4 volt, all the extrema shift to the left until the last maximum ( retadation) comes out. Then by comparing this series of figures, the corresponding retardations for all the exterma can be easily found in the spectrum at volt (for example, figure 28). 1 8 Transmission (%) π 5π 4π Fig. 28. One example spectrum at Volt. By using the equation of retardation and fitting equation of Δn, for every extremum, we can obtain a thickness. Then calculate the average value d avg for all these thicknesses. d avg is more close to real thickness but still not accurate enough. We only use it to estimate Δn more accurately. The more accurate thickness we finally used to the analysis and simulation is calculated by using the new estimated value of Δn, which can be obtained in the following way. Substitute d avg into the equation of retardation and we will get a new series value of Δn at different wavelength. Figure 29 is the picture of one inhomogeneous cell we used to calculate Δn. The thickness of different point shown in the picture is calculated as d avg. Figure 3 shows the new series of Δn obtained at different point (with different d avg ) on this cell and also the original data of Δn (Δn ) from the manufacture. Tian Hui

45 Fig. 29. Thickness of different point on one cell illuminated between parallel polarizers. LC6: μm; μm; μm; μm.6 Δ n LC6-1 LC6-2 LC6-3 LC6-4 Δ n' Fig. 3. New series of Δn obtained at different point on LC6 and the original data of Δn (Δn, pink line) By fitting all the curves of the new series of Δn at different point, we obtain the new equation λ Δ n( λ) = ( λ: nm ) 2 2 λ And from now on, the thickness will be calculated by using this new Δn λγ d = 2πΔn. The calculation of the thickness of the different points on the cell is one way to analyze the quality of the cell. For bad cells such as in figure 29, the thickness can help us to find the problem of the cell and give us some hints how the hole in the cell was formed. Tian Hui

46 3.2 E7 cell The formula of Δn for E7 cells have already been introduced in the article by Jun Li et al. [1] They derived the extended Cauchy model, which is better for mixtures of different pure materials. If we use this model to fitting the curve of Δn for the High Δn material, the fitting result is a bit worst than the previous one. n n e o Be Ce Ae λ λ. Bo Co Ao λ λ The Cauchy coefficients (A e, B e, C e, A o, B o, C o ) were obtained by fitting the experimental results. They are independent on wavelength but dependent on temperature. Table 2 shows the fitting parameters for the extended Cauchy model at different temperatures. Δn= n e -n o, which can be easily obtained by using this table. Table 2. Fitting parameters for the extended Cauchy model at different temeperatures. [1] Tian Hui

47 4. Thickness Even when we only have the spectrum at Volt and we do not know the corresponding retardation for each peak, the thickness can still be calculated. By using the formula of Δn, the thickness for both High delta n cell and E7 cell will be obtained in the same way. Choose any maximum at wavelength λ 1 in the spectrum which is measured without voltage applied on the cell. The corresponding retardation satisfies 2 π dδn( λ ) 1 Γ 1 = = k 2π. (k is integer) λ1 Its neighbor maximum on the right side satisfies 2 π dδn( λ ) From the two equations above, we can obtain ( k 1) 2π 2 Γ 2 = = λ2 Δn( λ1) Δn( λ2) d = 1 λ1 λ2 1 d = Δ n( λ1) Δ n( λ2) λ λ 1 2 Substitute the equation of d into either equation of Г, k is given by k Δn( λ1 ) λ 1 ( λ ) ( λ ) ( λ ) λ1 1 λ λ λ Δn( λ ) 1 = = Δn 1 Δn 2 Δn So both the thickness and the value of k can be calculated by the same method, where k corresponds to the retardation of the two cells by the equations above. We made a matlab program which follows this method. Instead of randomly choosing of any maximum, the program will calculate the thickness by using all the maxima (minima) and their neighbors. The final thickness is the average value of all the thicknesses obtained. Figure 31 shows the results of such a program for two High Δn cells (4.44μm, 18.2μm) and one E7 cell (3.6μm). The blue lines are the measured spectrum and the green lines are the simulated spectrum by using the calculated thickness. Here we did not take into account the absorption of ITO or any other influences such as reflection. From all these figures, we can see the simulated spectra have a good correspondence with the real spectra. 1 Tian Hui

48 (a) 1 9 High delta n cell 4.44um Transmission (%) (b) 1 9 High delta n cell 18.2um Transmission (%) Tian Hui

49 (c) 1 9 E7 cell 3.6um Transmission (%) Fig. 31. Measured spectrum (blue line) and simulated spectrum (green line) by using the calculated thickness Tian Hui

50 5. Simulation of the transmission In the previous section, all the simulations were done under the condition that no voltage was applied on the cell. Now we consider a more complex situation, that is, the transmission spectrum with the application of different voltages on the cell. Due to the lack of parameters of High Δn cells, the simulation work was only done on the E7 cell. However, one can follow the same method for High Δn cells. 5.1 Tilt angle distribution The program I used to calculate the tilt distribution was made by Richard.James who is working now in University College London. This program is freely available from the website: For simplicity, the main idea is explained by using one elastic constant formulation: 2 1 dθ 1 I= K Δ 2 dz ε εe sin ( θ) There is no twist, K is the elastic constant, Δε is the dielectric anisotropy, θ(z) is the tilt angle and E is the electric field. In order to reach to the equilibrium state, the free energy should be minimized by θ(z). Take the first order variations of the above equation, we get d θ K dz ε 2 Δ εe sin( θ)cos( θ) = By using θ ( z) θ1 and θ ' ( z) θ2, the second order differential equation is converted into two first order equations θ = θ ' 1 2 dz Kθ + ε Δ εe sin( θ )cos( θ ) = ' The reorientation of directors will change the dielectric constants and influence the electric field. where u ε u =, E = u is the potential. For one dimension problem, Solving these two equations, we obtain d du ε zz dz = dz, ε ε ε 2 zz = +Δ sin θ, Tian Hui

51 2 dθ du 2 d u 2Δ εsin( θ)cos( θ) + ε εsin ( θ) 2 dz dz +Δ = dz This equation can be converted into two first order equations in the same way by using uz ( ) u 1 ' and u ( z) u, 2 { θ, θ, u, u } u = u ' ' 2Δ εsin( θ1)cos( θ1) θ2u2 + ε +Δεsin ( θ1) u2 = can be solved from the four first order equations above. If we consider two elastic constants which correspond to splay and bend deformations, the problem is more complex. Now the derivation is much more difficult and it is better to solve it with the aid of software like Maple. Figure 32 shows the tilt distributions of the cell at five different voltages. 9 Tilt angle (degree) 6 3 E7 cell 3.6μm pretilt 2 degree 1.V 1.5V 2.V 2.5V 2.9V z (normalized with the thickness) Fig. 32. Tilt distributions at different voltage in an E7 cell 5.2 Spectrum simulation As explained in the previous sections, the transmission is given by Tian Hui

52 T 2 Γ = cos, 2 where 2πΔn d Γ=, Δ n= ne no, λ n = n ( λ), n = o e n ( λ), θ is the tilt n ( λ) n ( λ) 2 1 cos θ n ( λ) angle. When we apply voltage to the cell, the distribution of θ can be calculated. Now n e is no longer a constant for a single wavelength but depends on the value of θ. We can look at this cell as a stack of very thin layers of liquid crystals. If we only consider one wavelength, for each layer, Δn can be seen as a constant because the changes of θ is very small. In this way, the average value of Δn can be calculated along the whole cell. Then substitute the Δn in the transmission equation by this average value and the transmission for one wavelength is obtained. For another wavelength, the same steps are followed and finally, we obtain the whole spectrum in the range of 4-8nm. The parameters for n ( λ) and n ( λ) can be found in table 2. We selected the values for a temperature of 2 C. Figure 33 shows the measured spectra and the simulated spectra with the application of different voltages on an E7 cell. (a) 1 (b) Transmission (%) E7 cell 3.6μm 1.V Transmission (%) E7 cell 3.6μm 1.5V Tian Hui

53 (c) 1 (d) 1 Transmission (%) E7 cell 3.6μm 2.V Transmission (%) E7 cell 3.6μm 2.5V (e) 1 Transmission (%) E7 cell 3.6μm 2.9V Fig. 33. Measured spectra (black line) and simulated spectra (red line) with the application of different voltages on E7 cell Tian Hui

54 6. Absorption of foil The polarizer we used to measure the spectrum of a single cell is not a foil polarizer but a more expensive one with better properties. The foil polarizer is much cheaper and is the one we used to fabricate the LCTF, so it is necessary to examine the properties of these two types of polarizers. Figure 34 shows the transmission spectra of the two polarizers. In both cases, unpolarized white light was used as reference light. Ideally, 5 percent of the light will pass through the polarizer. However, due to the absorption and reflection of the polarizer, more light loss is unavoidable. In graph (a), we can see the light loss for the foil polarizer is larger than the expensive polarizer we used. Only around 22 percent of the incident light passes though the foil, while for the other one it is around 35 percent. So the losses for unpolarized light for them are around 78 percent and 65 percent, respectively. The absorption of foil in the small wavelength region is larger than in the large wavelength region. In graph (b), the foil polarizer was situated in turn cross and parallel with respect to the expensive polarizer and the green curve is the transmission spectrum for the expensive polarizer. We can see from the figure that the spectrum is nearly at zero level in crossed orientation; in the parallel orientation, by using the transmission of black line divided by the transmission of green line, we obtained that after the first expensive polarizer, 52 percent of the polarized light pass through the foil polarizer. Then the loss of foil for polarized light is more or less 48 percent. The accurate value of this loss for foil may be smaller than this because in our experiment it is very difficult to keep the axis of the foil polarizer exactly parallel with the axis of the expensive polarizer. (a) 1 8 Foil Polarizer Polarizer Transmission (%) Ideal polarizer 5% transmission Tian Hui

55 (b) 1 Transmission (%) Parallel(polarizer-foil) Cross(polarizer-foil) Polarizer Fig. 34. Transmission spectra of two typies of polarizers. In both cases, white light was used as reference light. Tian Hui

56 Chapter 3 Measurement of the filter In the previous chapter, the electrical and optical properties of the components of this LCTF have been examined separately. In this chapter, the whole filter will be fabricated and examined. By analysis of the recorded data, we can find the working points for this LCTF (i.e. the voltages that are needed to select a certain wavelength). The aim of this LCTF is to realize the sensing of both wavelength and polarization of light. However, the four cell Lyot-Ohman type filter can only filter out the selected wavelength with a polarization parallel to the first polarizer. An additional liquid crystal cell will be put in front of the filter which acts as a polarization selection device. Good experimental results are obtained for both wavelength and polarization sensing. This proves the possibility of real applications of such a device. Since liquid crystals are not very stable materials, there are still some problems we found during the experiments. When we design such a filter for real application, it is important to take into account all these problems. In the final part of this chapter, the problems will be discussed and some potential applications will be introduced. Tian Hui

57 1. Experimental setup In order to measure the transmission spectrum of this LCTF, many preparation works have to be done beforehand. The first job is to glue the four cells and five foil polarizers together to fabricate the whole filter. The order and the orientation of cells and polarizers are shown in figure 35. The cells are oriented with vertical rubbing direction and the axes of all the polarizers are parallel and at 45 with respect to the rubbing direction. The thickness of each cell we used in our filter can be calculated by using the program introduced in last chapter. Retardation: 2π 4π 8π 16π Fig. 35. The configuration of the LCTF. The thicknesses of cells are (from left to right): E7 3.6μm, High Δn cells 3.84μm, 7.87μm, 17.8μm. Secondly, different voltages have to be applied on the four cells in order to obtain the required retardation for each cell as shown in figure 35. So we need a wave generator which can drive the four cells together at the same time. The used wave generator is shown in figure 37(b). A Labview program is made to realize such a function. Then the voltage applied on each cell can be controlled by a computer. Figure 36 shows the working panel of this program. The voltages applied on the four cells are controlled by four output channels of the wave generator (CH1_ampl (V) CH4_ampl (V)). The required voltage to obtain the right retardation for each cell is calculated and shown on the panel (CH1 (V) CH4 (V)). By applying these voltages to the corresponding output channels, the four cells of this filter can be driven simultaneously and achieve the required retardations. Tian Hui

58 Fig. 36. The working panel of the Labview program which is used to control voltages on the four cells. Due to a lot of absorption and reflection, the amplitude of passband of the whole filter will be very low. In order to detect the passband easier, we use a neutral density filter (1% transmission) to measure the reference spectrum (figure 37(a)). When the real spectrum of the LCTF is measured, the neutral density filter is removed. In this way, the final recorded data for transmission is ten times as large as the real one. Since there is no polarizer in the setup when we measure the reference spectrum, the recorded spectrum takes into account all the effects of reflection and absorption of polarizers and liquid crystal cells. The whole setup to measure the spectrum of the LCTF for wavelength and polarization sensing is shown in figure 37(d), with the cells connected to two wave generators (figure 37(b,c)) by the leads with different colors. The polarizer and liquid crystal cell in the red box shown in the figure is the polarization switch part, which we will discuss in section 3.3. The polarizer is only used for testing which polarization of light can pass through the setup and in real application, this polarizer will be removed. If this LCTF is only used for wavelength sensing, both the polarizer and the cell in the red box will be removed and the rest setup is what we used in next section. Tian Hui

59 (a) (b) (c) (d) Fig. 37. The experiment setup. (a) the setup to measure the reference spectrum; (b) the wave generator used to apply voltage on the cells; (c) the wave generator used to apply voltage to the first addition cell which is used to select polarization; (d) the setup to measure the spectrum of the light through the filter. Tian Hui

60 2. Measurement of the filter for wavelength sensing 2.1 What voltage should be applied on the filter? The voltages applied on each cell to get the required retardation can be obtained by using the spectra we measured for each cell before. As we explained in the last chapter, the peaks in the spectra will shift to left with the increase of the applied voltage. By comparing the spectra at different voltages, it is straightforward to find the corresponding retardations for each maxima and minima in the spectra. For example, figure 38(a) shows a spectrum for one high Δn cell (8μm) at 1.5 volt. The retardation for each extremum is shown in the figure. The required retardation for the 8μm high Δn cell in the whole filter is 8π and the corresponding wavelength for this peak is 53nm at 1.5 volt. With the application of another voltage, this peak will shift and the corresponding wavelength will change. By recording all the corresponding wavelengths for 8π at different voltages, we can draw the green curve in figure 38(b). In this way, all the corresponding wavelengths for the required retardations for the four cells in the voltage range from volt to 2 volt can be collected. This is shown by the curves with different color in figure 38(b). From this graph, we can see the peak of 4π retardation for High Δn cell (4μm) cannot reach to 7nm, so the good tunable range for this filter is from 4nm to 68nm. If we select a certain wavelength as a passband, the voltage that should be applied on each cell can be found in this graph. For example, as shown in the graph by the Dash-Dot lines, when 5nm is selected as the passband of the whole filter, the voltages applied on each cells should be 1.47 V, 1.56 V, 1.54 V and 1.78 V, respectively. Tian Hui

61 (a) 1 8 High Δ n cell 8μm at 1.5V Transmission (%) π 7π 6π 5π (b) Retardation 2pi_E7 cell 4μm 4pi_High Δn cell 4μm 8pi_High Δn cell 8μm 16pi_High Δn cell 18μm Voltage (V) Fig. 38. (a) Transmission spectrum for high Δn cell (8μm) at 1.5 volt. (b) The relation between wavelength and applied voltage with required retardation for each cell Tian Hui

62 2.2 Wavelength sensing Ideally, the transmission of this LCTF is the multiplication of the transmission of each stage. Figure 39(a) shows the transmission of each stage with the applied voltage obtained from figure 38(b) for 5nm. The multiplication of those four transmission curves is shown in figure 39(b) by the red curve. The measurement result for the complete filter (with the application of the same voltage on the stage) is shown by the black curve. Comparing these two curves, we can see the bandwidths are more or less the same. The measurement result has a good correspondence with the ideal multiplication case. The difference in transmission is because we used different reference lights to record the transmissions of a single cell and the complete filter. Previously, we use two parallel polarizers to measure the reference light for the transmission of a single cell. But when we measure the reference spectrum of the complete filter (all the cells and polarizers are glued together), only an extra neutral density filter is used and both the polarizers are removed. As we explained before, the recorded data will be ten times as large as the real transmission. Compared with the spectrum of a single cell, it also consists of the effects such as the absorption and reflection caused by the foil polarizers and more cells. The small side peaks are probably due to two reasons. One is that the voltages applied on each cell are not accurate enough, so the wavelength corresponding to the peaks for 2π, 4π, 8π and 16π retardations are not exactly the same; the other is that the axes of each polarizer are not exactly parallel and also probably they are not accurately at 45 with respect to the directors of the cells. If the selected passband is changed, the desired voltages to be applied on each cell can be easily found in figure 38(b). The transmission spectra for other selected passband are shown in figure 4(a). Because the absorption of the foil is larger for shorter wavelengths, the amplitude of the passband in this range is smaller. Figure 4(b) shows the FWHM (Full width at half maximum) of the transmission spectra. This bandwidth decreases with the decrease of the selected wavelength as passband, and ranges from 11nm to 26nm. In this way, we have proved that this LCTF can be used for wavelength sensing applications. Tian Hui

63 (a) 1 Transmission (%) max: 5nm 2pi_1.47V 4pi_1.52V 8pi_1.59V 16pi_1.76V (b) 1 8 Measurement result Multiplication of four transmission spectra Transmission (%) Fig. 39. (a) Transmission spectra for each stage at the voltage obtained from figure 37 at 5 nm. (b) Multiplication of four transmission spectra in (a) and the measurement result for the whole filter at the passband of 5nm. Tian Hui

64 (a) 1 8 Transmission (%) nm 55nm 587nm (b) FWHM (nm) Fig. 4. (a) Transmission spectra for different selected passband. (b) FWHM (Full width at half maximum) for different passband. Tian Hui

65 3 Measurement of the filter for polarization sensing 3.1 Variable retarder with liquid crystals Theoretically, there are several ways to realize polarization sensing for this filter. The first one is to use the Mauguin-regime for a twist nematic cell. [1] In this regime, the ordinary and the extraordinary waves will follow the rotation of the optical axis of the cell and the polarization of light will also rotate with this rotation. However, if we apply a high voltage on the cell, then all the molecules tend to align along the electric field and as we explained before, all the light will pass through the cell and there is no difference between ordinary and extraordinary waves. For cells with a total twist angle of π/2, the condition for Mauguin-regime is Δnd 1. λ 2 The cell is oriented in front of the filter with its axis at the output part parallel to the axis of polarizers in the filter. Without application of the voltage, light with the polarization perpendicular to the polarizers in the filter will pass through while at a high voltage, light with the polarization parallel to the polarizers will be selected. But in my lab, we do not have this type of cells. The second method is to use a planar nematic cell as a variable retarder. [2] This method is similar as what we used in this thesis, but the only difference is if we want to select the light with the polarization parallel to the polarizers in the filter, instead of applying a certain voltage V 1 (shown in figure 42(a), we will explain in next part), we apply a very high voltage on this cell. Similar as in the first method, at very high voltage all the light will pass through the cell, so only the light with the polarization parallel to the polarizers in the filter can pass through the whole device. However in the experiment we found this is an ideal case and the transmission of this cell at a high voltage is not high enough. So it means not all the molecules orient along the electric field, there is still a birefringent effect in this cell. Finally we choose the following method in this thesis. An extra liquid crystal cell is situated in front of the LCTF (figure 41). This cell acts as a variable retarder, which means with the application of different voltage, the retardation for this cell will change its value since the orientation of molecules depends on the applied voltage. The polarization of the output light for this cell depends on the retardation, so it can be controlled by the voltage applied on the cell. LC LCTF Variable retarder Fig. 41. LCTF with an extra liquid crystal cell as a variable retarder for polarization sensing. Tian Hui

66 Figure 42(a) shows the transmission curves for this retarder for a single wavelength (585nm). The black curve is measured between parallel polarizers and the red curve is measured between corssed polarizers, as shown in the black box and red box at the right side of figure 42(a), respectively. We can see in this figure, every maximum of the black curve corresponds to a minimum of the red curve, and vice versa. For example, if the applied voltage is V 2 (shown in the graph), the transmission for red curve is maximum, which means light now can pass through the setup with crossed polarizers. Then if we rotate the first polarizer to a crossed orientation, as shown by the black curve, the transmission becomes minimal with same voltage V 2 and light is blocked by the parallel polarizers. If this wavelength (585nm) is selected as the passband of this LCTF, for the whole device as shown in figure 42(b,c), we can obtain the polarization status after the retarder by applying V 1 and V 2 on the retarder as shown in the graph 42(a). In figure 42(b), if we apply V 1 to the retarder, the incident light with the polarization perpendicular to the polarizers in the filter will keep perpendicular to the polarizers after passing through the retarder. So the light with this polarization can not pass trough the whole filter at V 1. However, if we apply V 2 to the retarder, after the retarder, the polarization of the light rotate to an orientation parallel to the polarizers. Now the incident light with the polarization perpendicular to the polarizers in the filter can pass through the whole filter. For figure 42(c), the situation is opposite. The light with the polarization parallel to the polarizers in the filter will pass through the whole filter when we apply V 1 on the retarder while it will be totally blocked with V 2 applied on the retarder. In this way, with application of different voltage, we can select which polarization of light can pass through the LCTF. (a) 12 1 Transmission (%) V 2 V 1 crossed polarizers parallel polarizers Voltage (V) Tian Hui

67 (b) (c) Fig. 42. (a) Transmissions at different voltage for a single wavelength (585nm) when the variable retarder between crossed polarizers (red curve) and parallel polarizers (black curve). (b) and (c) Status of the polarization of the light after the retarder when V 1 and V 2 are applied on the retarder. 3.2 Polarization sensing In order to test our device, first we measure the transmission when the light with the polarization parallel to the polarizers in the filter can pass through the setup with the application of certain voltages. Then we rotate the first polarizer 9 but keep the same applied voltage on the retarder. The polarization of light now is perpendicular to the polarizers in the filter. As we explained before, it should be blocked and we record the transmission spectra again. The spectra for these two cases for different passbands are shown in the different graphs in figure 43(a). The graphs in figure 43(b) are the opposite situations for these Tian Hui

68 passbands. The contrast ratio is calculated by integrating the visible parts of the two curves in the same graph. We calculate it in this way because in the application we use a CCD camera to detect the output light and it can only detect the integration of the intensity of light with different wavelength. (a) Contrast Contrast 5. 7 Transmission (%) Transmission (%) Transmission (%) Contrast 6.3 Transmission (%) Contrast Tian Hui

69 (b) Contrast Contrast 6. 7 Transmission (%) Transmission (%) Transmission (%) Contrast 4.85 Transmission (%) Contrast Fig. 43. (a) Transmissions measured when the polarization parallel to the polarizers in the filter can pass through the setup with the application of certain voltage (black curves) and when the light is blocked by rotating the first polarizer over 9 (red curves); (b) Transmissions measured when the light with the polarization perpandicular to the polarizers in the filter can pass through the setup with the application of certain voltage (red curves) and when the light is blocked by rotating the first polarizer over 9 (black curves) The above graphs prove that the whole setup can be used for both polarization sensing and wavelength sensing. However, we can see for shorter wavelength part, the contrast ratio is lower. That is because the absorption of foil in this range is larger, as we explained in last chapter. In general, we can say that the contrast is mainly limited by the appearance of unwanted side bands. When we define the contrast ratio as the relation between the maximum transmissions in unblocked and blocked states, it is much larger. Tian Hui

70 4. Problems and discussion We have proved this device can realize both polarization and wavelength sensing. However, some problems for this filter were found during the experiments. When we design such a filter for real application, these problems must be taken into account. 4.1 Degradation of High Δn cells During the measurements we found that the transmission spectra for High Δn cells change after a period of time. As shown in figure 44(a) for one High Δn cell (8μm), with the application of 2 V, the red curve was measured in Dec. 27 and the black curve was measured two months later. All the peaks in the spectrum shift to the left after two months. However, without application of voltage, the measurement results at these two dates are same (figure 44(b)), which means the thickness of the cell does not change. But the orientation of molecules in the cell with the application of voltage is not as same as before, which causes the spectrum shift. The High Δn cells are degraded after a period of time, so we have to measure the High Δn cells again to obtain accurate data when we want to fabricate the whole filter. As we said in the second chapter, High Δn liquid crystal material is a lab material made by a university. It is not very stable and can be influenced by some factors. One reason for this shift may be the increase of temperature. However we did not find such phenomenon in E7 cells. Because E7 liquid crystal material is a commercial material and much more stable, it is unlikely that a change in temperature would cause this effect. Tian Hui

71 (a) 1 8 Transmission (%) Voltgae 2.V Measured in Feb. 28 Measured in Dec (b) 1 8 Transmission (%) Voltage V Measured in Feb. 28 Measured in Dec Fig. 44. (a) Transmission spectra for a High Δn cell (8μm) measured on different dates with the application of voltage (2. V). (b) Transmission spectra for the same cell measured at different dates without the application of voltage. Tian Hui

72 4.2 Inhomogeneity of the thickness Due to some reasons in practical technique and the material we used to make all the cells, it is very difficult to obtain very homogeneous cells (I obtained these cells from my supervisor.). When we measure the transmission of the whole device, we may measure at a different place on each cell rather than the place we measured for the transmission of a single cell. Due to the inhomogeneity, the thickness of these two places measured in different experiments on the same cell will be not exactly the same and the transmission will be a bit different for these different thicknesses. The voltages applied on each cell to achieve the right retardation for the whole filter are obtained from the transmission spectrum of a single cell, so when we measure the whole filter, for the places with a bit different thickness, these voltages are not so accurate. As a result, the final voltages applied on each cells to obtain good passband for the whole device have to be tuned around the voltages we obtained form the experiments before. That is why for the measurement of the whole device, in the Labview program used to control the voltage on each cell (figure 26), CH1 (V) CH4 (V) give us the reference voltage (obtained from the experiment of a single cell) for each cell at different passband and the real voltages applied on each cell can be controlled by changing the value in CH1_ampl (V) CH4_ampl (V). If very homogeneous cells can be made, then we can directly use the voltages obtained from the measurements of a single cell. 4.3 Switching speed The fourth cell in this device is very thick and the light cannot propagate very fast in the liquid crystals, so the switching speed for this filter is not so fast. One way to improve the switching speed is to change the fourth cell to a combination of a quartz plate and a liquid crystal cell, which is similar as the previous type of the LCTF we introduced in the first chapter (figure 18). Light can pass through much faster in the quartz than in liquid crystals. The retardation for the quartz plate is not variable when the thickness is fixed, but the retardation for the liquid crystal cell can change with the application of different voltage. The retardation for this combination of quartz and liquid crystal cell will decrease with the increase of the applied voltage on the cell due to the variable retardation of the cell. So the transmission spectrum will shift to the left when the voltage applied on the cell increase and at very high voltage, the retardation for the cell is zero and the retardation for this stage is only the retardation of the quartz plate. Figure 45 schematically shows the transmission of the fourth stage which consists of a quartz plate and a liquid cell at low and high voltage. Because the retardation of quartz is not variable, in order to obtain the same tuning range as before for a single cell stage (the whole visible part), the thicknesses of the cell and the quartz have to satisfy certain conditions. Assuming the Δn for the quartz is Δn q (Δn q <<.2) and the Δn for the cell is Δn c (for High Δn liquid crystal, Δn c.4, which depends on the wavelength and we have obtained the equation for Δn in chapter 2), from the figure we can see in order to realize the tuning range, for very high voltage, Tian Hui

73 and for zero voltage, 2πΔnd q q Γ ( λ = 4 nm ) 16π 16π 4 2πΔnd q q 2 πδnc(7 nm) dc Γ ( λ = 7 nm ) 16π + 16π, 7 7 where d q is the thickness of the quartz plate, d c is the thickness of the liquid crystal cell and n c satisfies λ Δ nc ( λ) = ( λ: nm, chapter 2) 2 2 λ From the three equations above we can obtain the condition, d q 32 ( nm ) Δ n 56 Δnd q q dc ( nm), Δnc(7 nm) =.357. Δn (7 nm) c However the quartz is more expensive, so the cost of the device with this change will be higher than before. q 1 16π low voltage high voltage 16π Transmission (%) Fig. 45. Schematic of the transmission of the fourth stage which consists of a quartz plate and a liquid cell at low and high voltage. Tian Hui

74 4.4 Low amplitude of the total transmission Form all the transmission spectra of the complete device we can see that the total transmission is very low. That is due to a lot of absorptions and reflections in the filter. Using a neutral density filter to measure the reference spectrum in my thesis is one method to improve the recorded transmission. High quality foil polarizers can be used to reduce the absorption while they are more expensive. Another method is to put some liquid like material between the glass substrate and the foil. Its refractive index is close to the glass and the reflection can be reduced in this way. Tian Hui

75 5. Applications There are many applications for this LCTF we designed in this thesis. An interesting one of them is shown in figure 45. In some production lines for apples, we can use this LCTF to test whether the apples are ripe or not. The red light is selected as the passband of the LCTF. Then the red light reflected by the ripe apple can pass through the filter and detect by the CCD camera. But the green light reflected by the unripe apple will be blocked by the LCTF and cannot detect by the CCD camera. Another application is in Astronomy, instead the previous type introduced in chapter one, we can use this LCTF to observe the space objects (planets, stars). Because this filter can realize both polarization sensing and wavelength sensing, so besides the information of spectrum, the polarization information of the reflected light will be also obtained when we use it to observe for example a planet. By analysis of the spectrum and polarization of the reflected light, a lot of information about the planet (the shape, the atmosphere content, etc.) can be obtained. Fig. 45. The LCTF is used to detect whether the apple is ripe or not. Tian Hui