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Monte carlo simulations for tuning optical properties in a two-stage liquid crystal retarder system via Mueller matrix method
Abstract
This study employs the Mueller matrix method to analyse the optical properties of a two-stage liquid crystal (LC) retarder system. The system is constructed using planar-aligned nematic LC cell retarders and linear polarisers. The orientation of the LC molecules (LCMs) in the cells are determined through Monte Carlo (MC) simulations by using a lattice Hamiltonian model that includes the Lebwohl-Lasher energy, external field interaction and the Rapini-Papoular term. The analysis focuses on the tunable wavelength range of 400–800 nm. The external field and the thicknesses of both LC cells are used as key parameters for tuning the optical transmission characteristics. The results demonstrate that the interplay between the thickness of the retarders and the applied external field significantly affects the transmission spectra, enabling precise control over wavelength selectivity and broadband transmission. Thinner configurations exhibit sharper wavelength selectivity and higher sensitivity to external fields, while thicker configurations provide broader, more uniform transmission across a wider wavelength range.
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We revisited the nematic-isotropic (NI) transition of the Lebwohl–Lasher lattice model with a detailed investigation of samples containing 200 × 200 × 200 particles. The large-scale Monte Carlo (MC) simulations involved were carried out following the standard Metropolis, as well as the cluster MC Wolff algorithms. A notable free-energy barrier was observed between the isotropic and nematic phase, leading to long-lived metastable states and hysteresis. We provide an improved estimate of the nematic-isotropic transition temperature T NI , of the supercooling and superheating temperatures, of the temperature of divergence of pretransitional effects T C ∗ as well as an analysis of the size distribution of the ordered domains above T NI , contributing to a better understanding of this transition of key importance for liquid crystals.
This article is part of the theme issue ‘Topics in mathematical design of complex materials’.
The Mueller Matrix (MM) elements of the planar liquid crystal cell which is illuminated with a broad band light source was investigated and six MM elements were experimentally measured as functions of wavelength in the range of 500--800 nm at different cell alignment angles. Analysis of the MM curves were used to explain how the state of the linearly polarized light changes at the output of the LC cell. The trends of the MM curves were found to be in agreement with the recent studies on Mueller Stokes characterization of the LC based electro-optical devices. The values at different wavelengths correspond to different phase retardation values, hence it is parallel to changing the cell thickness. It is also found that the state of the polarization ellipse of the travelling light is an important factor that affects the amount of light depolarization.
This pedagogical overview of liquid crystals is based on lectures for postgraduate students given at the International Max Planck Research School "Modeling of Soft Matter". I am delighted to dedicate it to my scientific advisor, Prof. Yuriy Reznikov, thus acknowledging his valuable contribution to my life.
We report Monte Carlo simulations based on the Lebwohl-Lasher model for characterizing the molecular director configuration in a nematic liquid crystal cell presenting periodical boundary anchoring conditions. We demonstrate the molecular orientation and spatial behaviour, while profiling the local order parameter distribution for the proposed confining geometry, as well as the boundary and interface interaction fields propagation through the namatic bulk for various temperatures in the proximity of the nematic-isotropic transition. Simulations were also performed concerning with the light passing through the planar and homeotropic periodical regions of the nematic cell and a mapping of the transmitted intensity was obtained for several ambient temperatures. The boundary constraints and the selected periodical geometry of the simulated system play an extremely important role for the demonstrated optical and orientational properties of the liquid crystalline material.
We propose a method to reduce sidelobes of multistage Lyot filters by substituting certain stages with two-plate fan Šolc stages. Parallel-aligned nematic liquid crystal (LC) cells are used as variable retarders to compose multistage Lyot LC tunable filters (LCTF). The simulation of a four-stage Lyot LCTF and a tunable filter, comprising two stages of Lyot filter and two stages of two-plate Šolc filter, are compared. With this method, the sidelobes are reduced and the full width at half-maximum intensity of transmission peak is also reduced. Experimental results and theoretical analysis are presented in detail to verify this method.
All 16 elements of the Mueller matrix of an optical system (sample) can be encoded onto, hence can be retrieved from, a single detected signal using a class of photopolarimeters with modulated polarizing and analyzing optics. The general theory of operation of such polarimeters is presented. We also propose a specific new photopolarimeter whose polarizing and analyzing optics are modulated by synchronously rotating two quarter-wave retarders at angular speeds ω and 5ω. When the light flux leaving such polarimeter is linearly detected, a periodic signal J = a 0 + ∑ n = 1 12 ( a n cos n ω f t + b n sin n ω f t ) is generated, with fundamental frequency ω f = 2ω. From the Fourier amplitudes a0, a n , b n , to be measured by performing a discrete Fourier transform (DFT) of the signal ℐ, the 16 elements of the Mueller matrix are simply determined.
Extension of the dynamic range of liquid crystal tunable Lyot filter is demonstrated by incorporating with it a liquid crystal variable retarder as an eliminator for the third and fourth order peaks. The filter is continuously tunable in the range 500 nm to 900 nm with a nominal width in the range 50nm-100nm. Design procedure is described including the exact solution to the LC director profile and the suitability for biomedical optical imaging applications. Flexibility in the design is proposed by applying different voltages to the different liquid crystal retarders thus compensating for small thickness deviations from the nominal values and obtaining the high dynamic range.
A Lyot–Öhman filter for imaging near the solar He i 1083-nm line is described. Fast and continuous spectral tunability is provided by nematic liquid crystals. This solid-state filter has a free spectral range of 2.35 nm and a spectral resolution of 0.135 nm at the operating wavelength of 1083 nm. A wide-fielded design was used for both static and electro-optic retarder elements, facilitating use in fast imaging systems. A first-light He i image of the Sun is presented.
Standing as the first unified textbook on the subject, Liquid Crystals and Their Computer Simulations provides a comprehensive and up-to-date treatment of liquid crystals and of their Monte Carlo and molecular dynamics computer simulations. Liquid crystals have a complex physical nature, and, therefore, computer simulations are a key element of research in this field. This modern text develops a uniform formalism for addressing various spectroscopic techniques and other experimental methods for studying phase transitions of liquid crystals, and emphasises the links between their molecular organisation and observable static and dynamic properties. Aided by the inclusion of a set of Appendices containing detailed mathematical background and derivations, this book is accessible to a broad and multidisciplinary audience. Primarily intended for graduate students and academic researchers, it is also an invaluable reference for industrial researchers working on the development of liquid crystal display technology.
Polarized light is a pervasive influence in our world-and scientists and engineers in a variety of fields require the tools to understand, measure, and apply it to their advantage. Offering an in-depth examination of the subject and a description of its applications, Polarized Light, Third Edition serves as a comprehensive self-study tool complete with an extensive mathematical analysis of the Mueller matrix and coverage of Maxwell’s equations. Links Historical Developments to Current Applications and Future Innovations This book starts with a general description of light and continues with a complete exploration of polarized light, including how it is produced and its practical applications. The author incorporates basic topics, such as polarization by refraction and reflection, polarization elements, anisotropic materials, polarization formalisms (Mueller-Stokes and Jones) and associated mathematics, and polarimetry, or the science of polarization measurement. New to the Third Edition: • A new introductory chapter • Chapters on: polarized light in nature, and form birefringence • A review of the history of polarized light, and a chapter on the interference laws of Fresnel and Arago-both completely re-written • A new appendix on conventions used in polarized light • New graphics, and black-and-white photos and color plates Divided into four parts, this book covers the fundamental concepts and theoretical framework of polarized light. Next, it thoroughly explores the science of polarimetry, followed by discussion of polarized light applications. The author concludes by discussing how our polarized light framework is applied to physics concepts, such as accelerating charges and quantum systems. Building on the solid foundation of the first two editions, this book reorganizes and updates existing material on fundamentals, theory, polarimetry, and applications. It adds new chapters, graphics, and color photos, as well as a new appendix on conventions used in polarized light. As a result, the author has re-established this book’s lofty status in the pantheon of literature on this important field.
Liquid Crystal Devices are crucial and ubiquitous components of an ever-increasing number of technologies. They are used in everything from cellular phones, eBook readers, GPS devices, computer monitors and automotive displays to projectors and TVs, to name but a few. This second edition continues to serve as an introductory guide to the fundamental properties of liquid crystals and their technical application, while explicating the recent advancements within LCD technology. This edition includes important new chapters on blue-phase display technology, advancements in LCD research significantly contributed to by the authors themselves. This title is of particular interest to engineers and researchers involved in display technology and graduate students involved in display technology research.
Monte Carlo (MC) simulations and the Mueller matrix formalism were applied to investigate electro optical properties of a LC cell with planar boundary conditions for various thicknesses. Field dependent global order parameter and the optical transmissions were analyzed in common. Three characteristic regions of the periodicity of optical transmissions as a function of polarizer angle and the external field were identified.
Liquid crystals constitute a fascinating class of soft condensed matter characterized by the counterintuitive combination of fluidity and long-range order. Today they are best known for their exceptionally successful application in flat panel displays, but they actually exhibit a plethora of unique and attractive properties that offer tremendous potential for fundamental science as well as innovative applications well beyond the realm of displays. Today this full breadth of the liquid crystalline state of matter is becoming increasingly recognized and numerous new and exciting lines of research are being opened up. We review this exciting development, focusing primarily on the physics aspects of the new research thrusts, in which liquid crystals – thermotropic as well as lyotropic – often meet other types of soft matter, such as polymers and colloidal nano- or microparticle dispersions. Because the field is of large interest also for researchers without a liquid crystal background we begin with a concise introduction to the liquid crystalline state of matter and the key concepts of the research field. We then discuss a selection of promising new directions, starting with liquid crystals for organic electronics, followed by nanotemplating and nanoparticle organization using liquid crystals, liquid crystal colloids (where the liquid crystal can constitute either the continuous phase or the disperse phase, as droplets or shells) and their potential in e.g. photonics and metamaterials, liquid crystal-functionalized polymer fibers, liquid crystal elastomer actuators, ending with a brief overview of activities focusing on liquid crystals in biology, food science and pharmacology.
We study the effect of spatial inhomogeneity of anchoring forces on real part of effective refractive index in nanosphere dispersed liquid crystal (NDLC) metamaterial at infrared frequencies using the approach of Khoo et al. [1] and Monte Carlo modeling proposed recently in Ref. [2]. Local and global characterization is made using 2D maps of spatial distribution of the index, its gradients and its modulation amplitude below and above Freedericksz threshold. We find that NDLC with step-wise modulation of anchoring forces gives rise to much larger gradients and absolute values of the effective index than NDLC with modulated external electric field as well as pure nematic liquid crystal (NLC) with inhomogeneous anchoring. This indicates that the filling factor of coated spheres in NDLC is an important design parameter which tunes the effective refractive index. We find that the results are strongly dependent on wavelength in the infrared interval 2800–2900 nm. Some potential applications to molding the flow of light are briefly mentioned.
The nematic to isotropic phase transition in a liquid crystal is investigated using Monte Carlo simulations. Effects of the rate of heating/cooling and aligning fields are studied. New parameters based on the divergence of the molecular axes are suggested to obtain information about the order in the system.
The lattice version of the Maier-Saupe model of a nematic liquid crystal, in which all molecules are restricted to be on a simple-cubic lattice with periodic boundary conditions and to interact only with their nearest neighbors through the interaction energy Eij=-ε(3/2cos2θij-1/2), is investigated using a Monte Carlo technique. The lattice is found to undergo a first-order phase transition at ε/kT=0.890±0.005 with a spontaneous order of 〈P2(cosθ)〉=0.33±0.04 at the transition.
For several years now the physics and chemistry of condensed matter attracts a great deal of attention, while also occupying an extremely important position in the research activity worldwide. Liquid crystalline materials, in particular, present numerous applications in the fields of science and technology. Since the development of the liquid crystals display (LCD) technology, a significant concern was devoted to the development and characterization of these fascinating mesophases. In the present paper we perform several Monte Carlo simulations, by using the Lebwohl-Lasher model, for investigating the molecular director configuration in a nematic liquid crystal cell having varying boundary anchoring conditions in asymmetric circumstances. For this geometry, we analyze the molecular spatial behaviour, while mapping the local order parameter distribution for a nematic phase temperature. We also characterize the shape of the transition regions which strongly depend on the distance to the boundaries, and analyze the neighboring spins behaviour throughout the bulk. Furthermore, by using the Müeller matrix approach, we simulated the transmission of light through the nematic cell at normal incidence under crossed polarizers condition. These investigations seek to enrich our scientific knowledge about the fascinating research topics homeotropic in condensed matter physics by exploring interesting issues related to the orientational and optical properties of liquid crystals in confined geometries.
We study the influence of a spatially modulated light intensity on the refractive index of a nematic liquid crystal, using Monte–Carlo simulations with a generalized version of the Lebwohl–Lasher hamiltonian. We have considered a model of 2D liquid crystal cell in which one of the electrodes is covered by a photoconducting polymeric layer. The index profiles along the cell thickness are calculated and compared with experimental data.
In this paper, mathematical models are developed to correlate the time-resolved optical transmission experiments of liquid crystals dispersion devices under the influence of an electric field. The dispersion of liquid crystal in the confining matrices is supposed to be composed of identical spherical microdroplets containing the nematic liquid crystal phase. It is proposed that the confining surface induces the formation of a gradient of the torsional molecular velocities (switching velocities) in the response to an electric field or relaxation by the removal of an electric field, along the radius of the liquid crystal microdroplets. A method is proposed to determine the probability density function of the switching velocities. Applying the Laplace transform, the time-dependent functions for the optical transmission behavior of the liquid crystal dispersions are obtained. The model was applied to the study of the dynamics of glass dispersed liquid crystals devices, showing good correlation with the experimental data.
On étudie l'influence sur la transition de Freedericks des conditions d'ancrage : 1) Angle fini d'ancrage ; 2) Energie d'ancrage finie. Cette influence se traduit par une diminution des constantes d'élasticité apparentes. The effect of loose boundary condition on the Freedericks transition is discussed : 1) Finite clamp angle ; 2) Finite clamp energy. Such conditions would decrease the apparent elascity coefficients.
Using polarization microscopy, we have investigated the director configurations of droplets of a nematic liquid crystal with negative dielectric anisotropy and perpendicular boundary conditions subjected to electric fields. The droplets were suspended in liquid poly(dimethyl siloxane) and electric fields were applied both parallel and perpendicular to the viewing direction. The resulting director pattern is deduced by comparing the experimental transmission patterns with patterns calculated from various director models. For low fields, we observe a director field which is essentially radial, but with some azimuthal twist superimposed and a radial point (hedgehog) defect at the center. At intermediate fields, the hedgehog defect moves away from the center along the electric-field direction, while at the highest fields a line defect appears which lies along the diameter parallel to the field. Comparison of the transmission patterns with model calculations yields good agreement for the low- and intermediate-field cases, and reasonable agreement for the high-field case.
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