Analytical Approach of Director Tilting in Nematic Liquid Crystals for Electronically Tunable Devices

This paper presents an analytical expression that models the tilt angle of directors in a nematic liquid crystal (LC), depending on its elastic properties, its dielectric anisotropy, and the quasi-static electric field applied. The analytical solution obtained is fast and easily computable in comparison with numerical estimations and is of special interest in radiofrequency; for instance, for the LC modeling in full-wave electromagnetic simulators in the design process of electronically tunable devices, such as microwave phase shifters or electronically steerable antennas for satellite communications. Subsequently, a comparison is made between numerical approaches (self-implemented shooting method) and the analytical formulas when varying the parameters of the LC, being demonstrated its usefulness. The average LC director is then obtained and used to form the full permittivity tensor that completely characterizes the electrical properties of the material. Finally, an electromagnetic simulation is carried out to show the capabilities of the LC as a tunable phase shifter. It is shown that only 5 cm of a commercial 200-μm LC mixture is necessary to achieve 360° of the maximum variable phase shift at the 30-GHz band.