Accurate and Efficient Modelling to Calculate the Voltage Dependence of Liquid Crystal Based Reflectarray Cells

Two models that can predict the voltage-dependent scattering from liquid crystal (LC)-based reflectarray cells are presented. The validity of both numerical techniques is demonstrated using measured results in the frequency range 94-110 GHz. The most rigorous approach models, for each voltage, the inhomogeneous and anisotropic permittivity of the LC as a stratified media in the direction of the biasing field. This accounts for the different tilt angles of the LC molecules inside the cell calculated from the solution of the elastic problem. The other model is based on an effective homogeneous permittivity tensor that corresponds to the average tilt angle along the longitudinal direction for each biasing voltage. In this model, convergence problems associated with the longitudinal inhomogeneity are avoided, and the computation efficiency is improved. Both models provide a correspondence between the reflection coefficient (losses and phase-shift) of the LC-based reflectarray cell and the value of biasing voltage, which can be used to design beam scanning reflectarrays. The accuracy and the efficiency of both models are also analyzed and discussed.