Wave Propagation in Liquid-Crystal Materials

In this dissertation, the numerical simulation of tunable liquid-crystal (LC) based radio-frequency (RF) devices is studied with specific emphasis on the anisotropic dielectric property of LC media. The well-known vector method as well as the more advanced Q-tensor method are both investigated in order to obtain the distribution of the LC director field orientation in static electric fields. The finite integration technique is applied with dedicated extensions to enable electrostatic field determination and high-frequency simulation based on LC media. Liquid crystals have been successfully applied as tunable dielectrics in the realization of tunable RF components. In order to numerically investigate such devices with high accuracy, a proper modeling which involves the LC director field in a static electric field as well as the propagation of electromagnetic fields in LC media has been set up. The determination of the resulting LC molecule orientation is based on the minimization of the total free energy and has to include the directional material parameters as well as the electrode geometry. In combination with electrostatic formulation of the finite integration technique, the Oseen-Frank vector-representation method and the Landau-de Gennes Q-tensor-representation method are both applied. On the one hand, the vector method is not sensitive to mesh density and has less computational cost so it is suitable for the simulation of a large variety of applications. On the other hand, when disclinations or topological transitions between distinct states are involved, the Q-tensor method is better suited because of its capability in describing biaxial arrangement of liquid crystal molecules. For both methods, the time dynamic equilibrium equations are formulated according to the dissipation principle. The finite integration technique is combined with the effective dielectric method to simulate the propagation of high-frequency electromagnetic fields in anisotropic dielectric media caused by inhomogeneous orientation of liquid crystal molecules. A small alteration with respect to the traditional update scheme is necessary in order to guarantee vanishing tangential electric fields on the interface between perfect electric conductor and anisotropic material. A reconfigurable waveguide polariser and a tunable phase shifter based on LC materials are simulated with the help of the implemented simulation tools. The simulation results are in good agreement with measurement data for the polarizer that have been obtained at the Institute of Microwave Engineering and Photonics