James, RWL; (2006) Modelling of high resolution liquid crystal devices. Doctoral thesis , UCL (University College London).

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Abstract

There is much interest in the use of liquid crystals for holographic displays or light steering in telecommunication systems. These applications require a much higher resolution than conventional displays and as a consequence the pixel size and the gaps between them shrink. The impact of the fringing fields is significant and the electric field in the inter-pixel gaps can become large enough to give rise to disclinations. There is a need for modelling of these effects not only from the point of view of device optimisation but also to find ways to use them to our advantage. For instance, defects are associated with rapid changes in the refractive index which can be relocated by an applied voltage. The first part of the work details the development of continuum theory models for liquid crystal switching. Three implementations are described (i) a finite element discretisation of the Oseen-Frank free energy using a vector representation (constant order parameter). (ii) a constant order parameter model similar to (i), but using a tensor representation and (iii) a finite element discretisation of the Qian-Sheng equations. The implementation of (iii) includes the calculation of the flow and variations in the order parameter are allowed, which typically occur on very small scales. It also includes adaptive meshing driven by an error estimate that allows significant savings in terms of degrees of freedom and a "smart time integrator, used to model the dynamic behaviour efficiently. In devices known to be free of disclinations the vector method is shown to exhibit better spatial convergence. However, when disclinations are present it becomes necessary to allow the order parameter to vary and to use a tensor representation to model their movement accurately. Results produced by these models form the second part of this work. High resolution devices can be used as diffraction devices, for holographic displays or beam steering. A Spatial Light Modulator is modelled in detail in this beam steering application. Here the use of a liquid crystal device is desirable as the connectivity of the system can be electrically reconfigured. The ability of the device to steer light in a number of different directions is evaluated in terms of the diffraction efficiency, which is limited by the pixellation and the finite extent of the elastic deformation of the liquid crystal. Of particular interest are the cases where the grating angle is oblique to the pixel grid, where reorientation of the liquid crystal in the plane parallel to the electrodes is inevitable. This twisting causes the diffraction order magnitudes to depend on the polarisation state of the incident wavefront. Choosing the surface alignment oblique to the pixel grid is found to reduce this sensitivity. As the resolution increases further there becomes a point where the switching mechanisms used in conventional display devices become ineffectual. This limit is studied for both image display and holographic applications, by applying a chequerboard pattern of voltages to a pixel array as the pixel pitch is altered. With Liquid Crystal On Silicon (LCOS) technology it is possible to move beyond this limit, with pixel pitches of the order of the cell thickness. However, the driving voltages tend to be limited to a few volts. Device designs are proposed that are able to use this limited voltage to reorient a thin layer of liquid crystal above the pixel grid, which in turn reorients the bulk. Under specific alignment conditions, the LC orientation can change abruptly in the inter-pixel gap. A large enough electric field can induce disclination lines. which can then be electrically repositioned so as to write high resolution into the liquid crystal. A new switching mechanism is proposed for the Zenithal Bistable Device that exploits the interaction between electrically induced disclinations and the grating surface without relying on the flexoelectric effect. In such high intensity fields the drift of even small concentrations of ionic impurities can influence LC switching. A study of the influence of ion migration on the switching of the LC has been performed for both planar and IPS cells. By fitting experimental to simulated results the ion distributions can be characterised. Simulations show charged particles tend to accumulate above the edges of pixels. Devices with larger pixel widths are found to be less affected by the presence of a given concentration of ionic impurities.

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