A 2D finite difference/Finite Element analysis of reconfigurable mm-wave circuits in the presence of Nematic Liquid Crystals

A robust 2-D formulation for the electrical characterization of Nematic Liquid Crystals (N-LCs) under DC biasing conditions for use in reconfigurable mm-wave circuits is proposed. The finite difference (FD) method is first implemented to solve Poisson's equation in the domain of interest in order to obtain the governing DC electric field, which affects the local properties of the anisotropic material. Then, the nonlinear Euler-Lagrange differential equation, governing the orientation of the directors, is solved using a FD scheme with relaxation. Once the N-LC layer is characterized, a vector Finite Element (FE) code is used to obtain the modal propagation characteristics of a guiding structure. Tunability of the N-LC at mm-wave frequencies is illustrated for the particular geometry under a low DC bias voltage.