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Liquid Crystal Optics and Electro-Optics Chang-Kui Duan 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT Introduction Most studied & applied properties: light-scattering ability externally applied field control or realign the anisotropic liquid crystal axis, thereby controlling the effective refractive index and phase shift form the basis for various optical transmission, reflection, switching, and modulation applications. LCs are noted for their large birefringence and easy susceptibility to external field perturbation. basic principles and seek only some general understanding by dealing with analytically or conceptually solvable cases. 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT LCD pixel Schematic of a typical liquid crystal display pixel consisting of electronic driving circuit, polarizers, liquid crystal cell, color filter, and phase plate 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT Content 0. Introduction 1. Electro-Optics of Anisotropic and Birefringent Crystals 2. Electro-Optics of Nematic Liquid Crystals 3. Nematic Liquid Crystal Switches and Displays 4. Electro-Optical Effects in Other Phases of Liquid Crystals 5. Nondisplay Applications of Liquid Crystals 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT 1. Electro-Optics of Anisotropic and Birefringent Crystals ① ② ③ ④ Anisotropic, Uniaxial, and Biaxial Optical Crystals Index Ellipsoid in the Presence of an Electric Field: Linear Electro-Optics Effect Polarizers and Retardation Plate Basic Electro-Optics Modulation 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT Permittivity tensor (介电张量) The polarization and dielectric displacement are now given by Pi 0 ij E j Di Pi 0 Ei 0 ( ij ij )E j (i , j x , y , z ) The elements of the permittivity tensor depend on the choice of coordinate system 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT Principal axes A coordinate system can be found such that the tensor is diagonal i.e. 2 D n x x D 0 0 y D 0 z 0 n 2y 0 Ex Ey nz2 E z 0 0 • This coordinate system define the principal axes and principal planes associated to the crystal. • The corresponding refractive indexes are known as principal indexes. 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT Biaxial, Uniaxial & isotropic crystal Crystals with three different principal refractive indexes are referred to as biaxial crystals Crystal with two different principal refractive indexes are referred to as uniaxial crystals For uniaxial crystals, the refractive indexes are nx=ny=no, and nz=ne where “o” stands for ordinary axis and “e” for extraordinary axis. If no>ne the crystal is said to be a positive uniaxial crystal 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT Uniaxial crystal such as nematic liquid crystal n1 = n2 = no, ordinary ray; n3 = ne extraordinary ray index ellipsoid x2 y2 z2 2 2 1 2 n x n y nz The ellipsoid in (x, y, z) intersect the axis at x = ±nx; y = ±ny; z = ±nz 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT For light propagate along direction k The direction of D is in the plan perpendicular to k. Ordinary wave: Do perpendicular to the z-k plane no() n0 Extraordinary wave: De in the z-k plane but perpendicular to k cos sin 1 2 2 ne ( ) n0 ne2 2 2017/4/30 2 Chang-Kui Duan, Institute of Modern Physics, CUPT k Uniaxial crystals (cont’) 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT Presence of an Electric Field: Linear Electro-Optics Effect In the presence of an applied field, the index ellipsoid becomes: (1/n2)i are dependent on the applied field E. 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT Linear optical effect 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT Examples For a widely used electro-optics crystal such as lithium niobate (LiNbO3), r33 = 30.8 (in units of 10-12 m/V), r13 = 8.6,r22 = 3.4, and r42 = 28, with ne = 2.29 and no = 2.20 (at 550 nm). For these values of electro-optics coefficients (10-11 m/V), an applied dc voltage of 10,000 V is needed to create a phase shift of in a crystal of centimeter length. liquid crystal electro-optics devices, the typical ac voltage needed is around 1 V and the liquid crystal thickness is on the order of a few microns 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT Polarizers and Retardation Plate Typical electro-optic modulation scheme with polarizer– analyzer sandwiching an electro-optics crystals and a retardation plate. 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT Linear and circular polarizers Linear polarizers are usually made of anisotropic absorbing materials in which the absorption along a crystalline axis is much stronger than the orthogonal axis Circular polarizers are usually made by putting in tandem(串连) a linear polarizer and a birefringent retardation (相位延迟) plate, with the polarization vector bisecting the so-called fast and slow axes of the retardation plate 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT Polarization of output light Various states of polarization resulting from the addition of two orthogonal components of a polarized light with a relative phase shift. 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT Basic Electro-Optics Modulation For A is oriented at 45° with respect to the crystalline axes At the exit plane of the crystal of length l crystal x y 2 2017/4/30 (n y nx )l 0 Chang-Kui Duan, Institute of Modern Physics, CUPT Basic Electro-Optics Modulation = crystal + phase shift by retardation plate. E x (l ) A exp( t k x l ) E y (l ) A exp( t k x l crystal ) By summing the components of Ex and Ey on the transmission axis of the output polarizer (along y) 2 I E y (d ) E x i E y j . j Ai sin 2 2 2017/4/30 2 Chang-Kui Duan, Institute of Modern Physics, CUPT 2 2. Electro-optics of Nematic Liquid Crystals In general, the distortions on the electronic wave function of liquid crystal molecules caused by an applied field do not cause appreciable change to its contribution to the refractive indices However, the orientation of the molecules can be dramatically altered by the applied field principal mechanism used in liquid-crystal-based electro-optical devices. 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT Dual-Frequency Liquid Crystals transparent conductor ITO to allow the application of an electric field across the cell AC instead of DC: Avoid current flow, degration 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT ne no along E ne no away E Mixing and doping 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT Dual-frequency liquid crystal Since the dielectric anisotropy is frequency dependent (cf. Fig. 3.5), one could create a mixture of liquid crystals with different dielectric dispersions such that the resulting so-called dualfrequency liquid crystal (DFLC) possesses an effective positive anisotropy at one frequency of the applied ac electric field, but possesses a negative anisotropy at another ac frequency. 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT Freedericksz Transition Revisited Geometry for observing (a) the S (splay) deformation, (b) the B (bend) deformation, and (c) the T (twist) deformation. 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT Case 1: One-elastic-constant approximation. Standard variation method: d 2 E2 K 2 sin cos 0 dz 4 1/ 2 2 d E c cos(2 ) dz 8 K d E c cos(2 ) 0 2 8 K E2 c cos(2 m ) 8 K m 2017/4/30 2 作业: Reminder: (2/d)=m d/dz | z=2/d =0! 1/ 2 d Chang-Kui Duan, Institute of Modern Physics, CUPT Solution For relatively small reorientation angles only if E > EF 4 K VF EF d 1/ 2 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT Case 2: Freedericksz transition voltage including elastic anisotropies. 4 K11 VF EF d 1/ 2 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT Case 3: Freedericksz transition voltage including elastic conductivity. The maximum reorientation angle m is described by 4 K11 VF , = K 33 K11 K11 1/ 2 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT Field-Induced Refractive Index Change and Phase Shift Director axis reorientation profile in the cell at various applied voltage above the Freedericksz transition. 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT Phase shift for light passing through Approximation: Twisted configuration with maximum angle 900 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT current liquid crystal display devices: twisted configuration. Tilting and unwinding of the director axis of a 90° twisted nematic liquid crystal cell under the action of an applied field. 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT 3. NEMATIC LIQUID CRYSTAL SWITCHES AND DISPLAYS To obtain higher resolution, faster response, wider field of view, larger display area, and more functions in each display pixel. Two types: transmissive and reflective make use of the polarizing and birefringent properties conjunction with polarizers and phase (retardation) plates broadband (from near UV to far infrared) birefringence, and transparency 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT A twisted nematic liquid-crystal switch. (a) When the electric field is absent, the LC cell acts as a polarization rotator; the light is transmitted. (b) When the electric field is present, the cell’s rotatory power is suspended and the light is blocked. 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT Liquid Crystal Switch: On-Axis Consideration for Twist, Planar, and Homeotropic Aligned Cells normally black (NB) mode: two parallel polarizers normally white (NW) mode: two orthogonal polarizers 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT Off-Axis Transmission, Viewing Angle, and Birefringence Compensation Has to be considered for display application transmission function T is now a function of many variables Example: NB mode For on-axis light, the initial transmission is 0. When the voltage is on, the transmission is at a maximum for the on-axis light for the off-axis light, the e and o waves will pick up an extra phase shift because of the extra optical path length 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT Birefringent compensation film to place a birefringent film (of opposite anisotropy to that of the liquid crystal) adjacent to the LC film limiting case of = 0 compensation film should have birefringence of opposite sign to that of the liquid crystal 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT Sophisticated treatment For arbitrary angle or director axis angular and spatial distributions, and more complicated cell structure, the phase shift, and therefore the transmission of light through the cell and other accompanying polarization selective elements, is not amenable to simple analytical treatment. More sophisticated Jones matrix methods or numerical technique such as the finite difference time domain (FDTD) numerical methods discussed in the next chapter are needed to solve such a complex propaga- tion problem. 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT Liquid Crystal Display Electronics 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT Optical modulation of LCD 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT 4. Electro-optical Effects in Other Phases of Liquid Crystals nematics are the most extensively used other phases (smectic, cholesteric, etc.) and ‘‘mixed systems’’ capable of field-induced reorientation have also been employed for electrooptical studies and applications ferroelectric liquid crystals, generally switch faster than nematic cells 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT Surface Stabilized FLC Ferroelectric liquid crystal under an applied field, Typical values: 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT Approximation Under the assumption that e is appreciable, the first term can be neglected: solution 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT An practical case : tilt angle phase retardation : = 2dn/ 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT Soft-Mode FLCs • SMFLCs use changes in the tilt while remains constant. capable of continuous intensity change • SMFLCs employ smectic-A* phase • experimental setup 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT 5. NONDISPLAY APPLICATIONS OF LIQUID CRYSTALS extremely broad spectral range (from near UV to far infrared and into the microwave regime). fluid nature and compatibility with most optoelectronic materials a whole host of tunable lens, filters, switches, and beam/image processing devices have emerged. good candidates for biochemical sensing applications due to organic nature light emitting diodes and electroluminescence devices 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT LC Spatial Light Modulator A typical optically addressed liquid crystal spatial light modulator (OALCSLM) operating in the reflective mode 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT Tunable Photonic Crystals with LC Infiltrated Nanostructures Photonic crystals in 1-, 2- and 3D forms made of various optoelectronic materials photonic crystals can function as tunable filters, switches, and lasing devices optical holography offers a quick one-step process for the fabrication of photonic crystals (limited) 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT Tunable Frequency Selective Planar Structures Transmission Unit cell of an all-dielectric polarization independent FSS for operation in the visible region as a stopband filter. 2017/4/30 reflection Chang-Kui Duan, Institute of Modern Physics, CUPT Covered with LC 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT Liquid Crystals for Molecular Sensing and Detection 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT Beam Steering, Routing, and Optical Switching and Laser Hardened Optics Although most optical elements involve low level light, liquid crystals are actually excellent laserhardened materials capable of handling very intense pulsed lasers or high power continuous wave cw lasers. Intensity 1010 W/cm2 liquid crystals also do not suffer any structural/chemical damages. 2017/4/30 Chang-Kui Duan, Institute of Modern Physics, CUPT