Multiphysics Modelling of Liquid Crystal Based Adaptive Lenses
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Date
2020-09-30
Authors
Vasile, Alexandru Andrei
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
Conventional lenses are limited by their fixed shaped and optical properties. Liquid crystal adaptive lenses (LCLAs) are a promising candidate to move beyond these limitations thanks their tuneable optical properties. A difficulty of working with LCs is that their properties are the result of an experimentally un-observable structure. Thankfully, modelling is capable of providing insight into this structure. Unfortunately, progress has been hamstrung by an over-reliance on experimentation. Further, what little modelling is being done usually involves simplified models and/or close-source software packages.
This work uses a general model for thermotropic nematic liquid crystals based on Landau-de Gennes theory to study the texture of liquid crystal adaptive lenses. The most general version of this model was used, without the common simplifications such as: hard anchoring, neglecting elastic constants, or geometric symmetry. In order to find the equilibrium state for the nematic model, the Euler-Lagrange equation for the total free-energy is set to zero. This form is converted into a transient PDE in order to capture the dynamics of the system, and to evolve the texture towards its equilibrium state. The nematic model is coupled with a model for the electric field within the cell, and the two are solved simultaneously. This is accomplished by using the method of lines for temporal discretization and the finite element method for spatial discretization.
The validity of the implemented model was first verified by modelling two important LCD configurations: the TN cell and the IPS cells. The TN cell was modelled with the electrodes off and with them on. In both cases the correct equilibrium texture was obtained. Modelling light propagation with cross-polarization microscopy produced the correct results, a bright cell when the electrodes were off and a dark one when they were on. Next, the IPS cell was also modelled. Again, the correct equilibrium result was obtained; a twisted texture was when the electrodes are turned off and an untwisted texture when the electrodes are turned on. Modelling light propagation resulted in the correct dark state when the electrodes were off andthe correct bright state when they were on.
Having successful produced the expected texture and cross-polarization microscopy results, the model was applied to a LCAL. The literature review of this work identified a wide range of potential liquid crystal adaptive lenses. The final design was chosen using three criteria: 1) availability of published results, 2) modelling requirements, and 3) ease of manufacture. Based on these criteria, a design called the HMD cell was chosen. When modelled, the resulting texture and cross-polarization microscopy did not agree with previously published results. An investigation into the cause of these discrepancy was performed, but the cause has not yet been identified.
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Keywords
soft matter physics, liquid crystals, finite element, multiphysics, optics, lensing, Landau-de Gennes, nematic, Maxwell, Berreman