Liquid Crystal Displays Irma Alejandra Nicholls College of Optical Sciences University of Arizona, Tucson, Arizona U.S.A. 85721 iramirez@email.arizona.edu Abstract This document is a brief discussion of the optics concepts found in the work of Dr. Boris Zeldovich. He is working to develop new technologies that improve the quality of liquid crystal displays (LCD). He proposed the creation of a nematic liquid crystal cell with a periodic structure to enhance the contrast ratio. His research predicts 100% diffraction of the light incident on the cell. Some of the physical optics concepts include polarization, half-wave plates, birefringence, nematic liquid crystals (NLC), and diffraction. Biographical Information Dr. Boris Zeldovich is a Professor of Physics at the University of Central Florida [1]. He received his Doctor of Physical and Mathematical Sciences degree from the Lebedev Physics Institute in Moscow, Russia. He is known for the discovery of the nonlinearity of liquid crystals and his current research is based on nonlinear optics, physical optics, and the propagation of light through waveguides and inhomogeneous media. His awards include the USSR State Prize in 1983 and the OSA Max Born award in Physical Optics in 1997. Dr. Zeldovich is a member of the USSR Academy of Sciences, and a fellow of the Optical Society of America. Introduction Pixels are the dots that make up the image in a liquid crystal display. One type of pixels operates by diffracting the incident light when the pixel is OFF and this diffracted light is covered by an aperture [2] as shown in figure 5. However, if the diffraction produced by the LCD is not complete a certain amount of light passes through the pixel in its OFF state. This decreases the quality of the image in liquid crystal displays. Past research indicates that the diffraction efficiency of an LC grating can be controlled by the cell thickness and the difference in the refractive indices of the ordinary and extraordinary axis [3-4]. Studies also show that when a voltage is applied to a LC cell it is possible to control the diffraction properties that separate the polarization of light 1
of a specific wavelength into its components [5]. In order to understand nematic liquid crystal cells one must have a basic understanding of the structure and optical properties of liquid crystals. Once basic optical theories and terms are defined, a discourse of the nematic liquid crystal cell and its application to projection systems can begin. Liquid Crystals A liquid crystal is a substance that behaves optically like a crystal, but flows like a liquid. Overall, the molecules of a liquid crystal have the same orientation. A unit vector called the director [6], illustrated in figure 1, is used to designate the preferred orientation of the molecules in a liquid crystal. By convention this vector is symbolized by the letter n. An important property of the director is that n and n are equivalent vectors [7]. Nematic liquid crystals are the most important type of liquid crystals in the design of LC displays [6]. The nematic phase is the closest to the liquid state of matter. The molecules move in a constant direction essentially parallel to each other. Figure 1 shows the array of the molecules in a nematic liquid crystal [7]. The majority of the long molecules tend to point in the direction of the director. n Figure 1. Molecular structure of a nematic liquid crystal. Birefringence One of the optical properties of a nematic liquid crystal is birefringence. Birefringence is observed when light travels at different speeds, depending on its direction and polarization (defined below) as it passes through a material [8]. A birefringent material produces two images when placed in front of an object due to two different indices of refraction. Figure 2 represents the effect of birefringence on a crystal. One image appears directly above the object and is said to be produced by ordinary rays. This direction of propagation has a refractive index called n o. The second image, observed next to or above the ordinary image, is said to be produced by extraordinary 2
rays. The index of refraction in this direction is designated as n e. The birefringence of a nematic liquid crystal depends on its temperature [6]. The amount of birefringence n of a material is quantified by the difference in refractive indices [8]. n = (n e n o ) (1) Polarization Birefringent crystal Ordinary image This is a birefringent crystal This is a birefringent crystal Figure 2. Birefringence of a crystal Extraordinary image Another property of liquid crystal materials to consider is polarization [8]. Polarization refers to the oscillation of the electric field vector components in electromagnetic waves. Light can be unpolarized, linearly polarized, circularly polarized, or elliptically polarized. Only circular polarization is relevant for the understanding of this essay. Circular polarization occurs when the components of the electric field vector rotate uniformly in the xy-plane [9]. The magnitudes of the x and y components are equal. The sense of rotation can be right-handed or left handed. Circular polarization is illustrated in figure 3. A half-wave plate is a birefringent optical element that changes the polarization of light by introducing a phase shift of π radians between the electric field components [8]. This phase shift produces a change in the sense of rotation of circularly polarized light. The optical thickness of a half-wave plate should be one half the wavelength of the incident light as indicated by equation 2, λ t ( n) = 2 (2) where t is the thickness of the plate, λ is the wavelength of light, and n e and n o are the indices of refraction of the extraordinary and ordinary rays respectively. Figure 3 shows that right circularly polarized light becomes left circularly polarized after passing through a half wave plate and vice versa. 3
x x y z y z Left Circularly Polarized Light Half-Wave Plate Right Circularly Polarized Light Figure 3. Circularly polarized light passing through a half-wave plate. Diffraction Liquid crystals also diffract light. Diffraction occurs when light passes through a narrow aperture and it spreads in discrete directions (figure 4). Each direction is designated as a diffraction order m, with m = 0 being the direct transmission of the beam through the slit. Orders m = ± 1 are the rays by the sides of the 0 th order. A diffraction grating is an optical element that has a collection of very fine slits used to produce diffraction patterns. The diffraction orders produced by a grating are separated by an angle θ m called angle of diffraction [8]. This angle can be found using the grating equation sinθ m = mλ Λ (3) where θ m is the angle that the light is deviated from the direction of direct transmission, m is the diffraction order, λ is the wavelength of the incident light, and Λ is the period of the grating. m = +2 m = +1 m = 0 m = -1 m = -2 Figure 4. Diffraction of light as it passes through a narrow slit. Scientific Description 4
Dr. Zeldovich proposed the development of a nematic liquid crystal cell of periodic structure that diffracts 100% of the incident light into the ± 1 st orders when the pixel is OFF. All the light goes through the cell when the pixel is ON. This increases the contrast ratio. The contrast ratio is the ratio of the intensity of the brightest color to the darkest color that a display can produce [9]. If the horizontal component of the director rotates in a repetitive way, and the cell fulfills the conditions to act as a half-wave plate, the light that is normally incident on the cell will be diffracted completely into the 1 st and -1 st orders of diffraction [2]. The light then can be covered by an aperture. This constitutes the OFF state of a pixel (Figure 5a). The pixel lights up when a voltage breaks the original periodic structure, the molecules take the orientation of the electric field and diffraction is no longer produced (Figure 5b). Applied Voltage NLC Cell 1 st diffraction order Lens V Lens Incident light (a) -1 st diffraction order Aperture Incident light NLC Cell Non-diffracted light going through the lens Figure 5. (a) Represents the nematic LC cell in OFF state of the pixel. (b) Shows the ON state after a voltage V is applied. [10] (b) Aperture In order for the cell to constitute a half wave plate its thickness must be determined by equation (2). When right circularly polarized light, passes through this material, its polarization will change to left circularly polarized and at the same time it will be diffracted to the 1 st diffraction order. And left circularly polarized light would be transmitted in to the -1 st diffraction order as right circularly polarized light. The angle of diffraction θ [2] in this case is found using the equation 5
2λ t sinθ = = 4( n)( ) (4) Λ Λ Equation (4) is equation (3) above when m is equal to one and only one half of the period of the nematic cell is taken into account because of the property of the director where n is equivalent to n. To maintain stability, each LC material has a definite ratio of thickness to period t/λ of the NLC cell [2]. Figure 6 shows different LC materials and the voltage required to distort their periodic structure as a function of the thickness to period ratio. Figure 7 represents their maximum diffraction angle vs. thickness to period ratio. Voltage vs. Thickness to Period Ratio for Different LC Materials 3 2.5 PCH-5 (T=38.5 C) 2 1.5 ZLI-1646 1 0.5 PCH-5 (T=30.3 C) K15(5CB) PCH-5 (T=46.7 C) E7 M15 (50CB) K21(7CB) 0 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4 0.41 0.42 0.43 0.44 0.45 Thickness t o Perio d R at io ( t / Λ) Figure 6. Voltage Required for NLC cells of different LC materials as a function of the Thickness to Period ratio. Data taken from [10]. 6
Maximum Diffraction Angle vs. Thickness Ratio for Different LC Materials 25 20 E7 19.6 MBBA 20.1 M15 (50CB) 17.5 15 K15(5CB) 14.7 K21(7CB) 15.6 Maximum Diffraction Angle θ (in degrees) 10 PCH-5 (T=30.3 C) PCH-5 (T=38.5 C) 8.9 8.3 PCH-5 (T=46.7 C) 8 5 ZLI-1646 6.4 Figure 7. Maximum diffraction angle vs. thickness to period ratio compared for different LC Numerical materials. Example Data taken from [10]. Numerical Example The liquid crystal MBBA [9-10], at 22 C, has values of n e = 1.769 λ= 589nm n o = 1.549 Λ= 3432.3nm Using equation (1) the birefringence or refractive index difference is n= 1.769 1.549= 0.22 0 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4 0.41 0.42 0.43 0.44 0.45 Thickness to Period Ratio (t/λ) The thickness t of the material to satisfy the conditions for complete diffraction is given by equation (2) t = λ 589nm = = 1338. nm 2 n 2( 0.22) 6 And the angle of diffraction, as indicated by equation (4) is 2λ 2[ 589nm] sin θ = = = 0.3432 θ = 20. 1 Λ 3432.3nm Conclusion The nematic liquid crystal cell, proposed by Dr. Zeldovich, makes it possible to achieve 100% diffraction of light entering a pixel in the OFF state. This increases the quality of the image in a LCD by increasing the contrast ratio of the pixel. 7
The nematic liquid crystal cell by itself can be used as a beam splitter that separates light into its right and left circular polarizations [2]. It can also be used as a beam combiner when a beam of right circularly polarized light and another one of left circularly polarized light are incident on the cell, a single beam may be produced. 8
References 1. My Details. College of Optics and Photonics at the University of Central Florida. 26 Nov 2006, 23:36 UTC. <http://www.optics.ucf.edu/people/details.aspx?peopleid= 317>. 2. Sarkissian, H., et al. "Periodically Aligned Liquid Crystal: Potential Application for Projection Displays." Molecular Crystals and Liquid Crystals 451.1 (2006): 1-19. 3. C. -J. Yu, J. -H. Park, J. Kim, M. -S. Jung, and S. -D. Lee, "Design of Binary Diffraction Gratings of Liquid Crystals in a Linearly Graded Phase Model," Appl. Opt. 43, 1783-1788 (2004) <http://www.opticsinfobase.org/abstract.cfm?uri=ao-43-9-1783> 4. M. L. Jepsen and H. J. Gerritsen, "Liquid-crystal-filled gratings with high diffraction efficiency," Opt. Lett. 21, 1081- (1996) <http://www.opticsinfobase.org/ abstract.cfm?uri=ol-21-14-1081> 5. C. J. Yu, J. H. Park, J. Kim, S. Y. Chung, and S. D. Lee, Concept of a Liquid Crystal Polarization Beamsplitter Based on Binary Phase Gratings, Appl. Phys. Lett. 83, 1918-1920 (2003) 6. Singh, Shri. Liquid Crystals Fundamentals. Singapore: World Scientific Publishing Co. Pte. Ltd., 2002. 7. Oswald, Patrick, and Pawel Pieranski. Nematic and Cholesteric Liquid Crystals. Trans. Doru Constantin. Ed. G. W. Gray, J. W. Goodby, and A. Fukuda. United States of America: CRC Press Taylor and Francis Group, 2005. 8. Hecht, Eugene. Optics. Ed. 4. United States of America: Addison Wesley, 2001. 9. Gu, Claire, and Yeh, Pochi. Optics of Liquid Crystal Dysplays. United States of America: John Wiley and Sons Inc, 1999. 10. Sarkissian, H., N. Tabirian and B. Zeldovich. "Periodically Aligned Liquid Crystal Cell for Projection Displays." Liquid Crystals IX, Jul 31-Aug 2 2005. 9