Research On The Time-domain Computational Method Of Electromagnetics For The Optical Simulation Of Liquid Crystals

As an electrically controllable anisotropic medium, liquid crystals are widely used for displays and achieved great success. Recently, the application for non-displays such as beam control, wavefront transformation, and adaptive optics has attracted much attention and step into the practical application gradually. Besides, liquid crystals are very promising in the aspect of microwave and Terahertz wave for its wide range of transmittance spectra. Numerical simulation is an essential part in the research and development of liquid crystal devices, which can predict the optical properties of the device, optimize the parameters of the device, and provide the evidence of the device design and control.Numerical simulation of liquid crystal devices includes director simulation and optical property simulation. Optical property simulation studies about the interaction between light and liquid crystals, and simulates the light propagation through liquid crystal device. Finite-difference time-domain method (FDTD), as a numerical approach for the rigorous solution of Maxwell equations, is the most widely used method for the optical simulation of liquid crystals.This thesis mainly studied 2D time-domain computational method of electromagnetics for the optical simulation of liquid crystals, and explore the algorithms suitable for inhomogeneous anisotropic media with different spatial details (compared to the wavelength of incident light). The methods studied provide theoretic foundation for design and fabrication of liquid crystal device. The following are the main contents of the study:(1) When the FDTD method is used for the scattering analysis of layered anisotropic media, the subcomponents of Dy and Hy in the Maxwell equations on 1D auxiliary grid, which propagate in the direction either parallel with or perpendicular to the planar interface, can not be discretized separately. The reason is that the components of electric field are coupled together in the arbitrary off-diagonal anisotropic media. Thus the traditional 1D auxiliary FDTD method can not be applied to calculate the incident fields of layered anisotropic media directly. Therefore, the split-field technique is introduced to solve this problem.(2) When the FDTD method is used for the liquid crystal devices with non-periodic structure, due to the asymmetry between left and right boundaries, the periodic boundary conditions for the introduction of plane waves is not applicable. Thus, it is necessary to calculate the incident fields on the left boundary and that on the right boundary independently. For this purpose, according to the viscous characteristics of liquid crystals, the problem of the calculation of the incident fields on the left and right connecting boundaries can be simplified to the calculation of the incident fields of layered anisotropic media with different dielectric tensors. Therefore, the problem of the introduction of plane waves for the FDTD analysis of non-periodic liquid crystal devices is solved.(3) To obtain accurate results, the spatial sampling rate of FDTD method must be increased as the electrical size of the structure being modeled increased, thus leads to large memory consumption. Because a fast Fourier transform algorithm is used to represent the spatial derivatives in pseudospectral time-domain method (PSTD), the spatial sampling rate of PSTD method is independent of the overall electrical size of the structure being modeled, which greatly reduces the spatial sampling rate. In order to reduce the computational cost of FDTD method, hybrid PS-FDTD method is introduced to simulate the propagation of light through liquid crystals based on the characteristics of thin plate structure of liquid crystal cells. The FDTD method is applied to the thickness direction of a cell with a small thickness and fine structures, while the PSTD method is applied to the direction, paralleled with glass substrate, of a cell with a large surface and smooth internal media.(4) The time step in FDTD method is bounded by the minimum spatial grid for the numerical stability condition, which leads to the large computational time for the solution of problem with fine-scale geometric detail. For the phase-only liquid crystal device without coupling between transverse magnetic waves and transverse electric waves in it, an unconditionally stable locally one-dimensional FDTD method is proposed to remove the restriction of time step limited by the stability condtion.According to the research above, the application problem of FDTD method in anisotropic medium such as liquid crystals is solved, and it provides the premise and approach to optical simulation of liquid crystals.