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

Abstract

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. INDEX TERMS Liquid crystal, nematic phase, analytical expression, microwave, phase shifting.

One-Plane Glide-Symmetric Holey Structures for Stop-Band and Refraction Index Reconfiguration

“…Since it was demonstrated that it is possible to regenerate glide symmetry from a specific non-glide configuration, the use of thin metal plates instead of dielectric material allows the possibility of breaking and regenerating symmetry by displacing alternate rows of ellipses at a distance equal to the periodicity p (see Figure 10). Another possibility is to replace the dielectric material with an anisotropic material such as liquid crystal [28], whose effective dielectric constant in the direction of propagation can be modified by applying a voltage between the parallel metal plates containing it [32]. This property would make it possible to electrically control the appearance of stop-bands and refractive index.…”

Generalized Director Approach for Liquid-Crystal-Based Reconfigurable RF Devices

“…In this section, we test the solutions obtained from the integral equations for all the parameters involved on the problem (k 11 , k 33 , V, ∆ε). We validate the results with numerical estimations and show that the error in our proposed approach is considerably reduced compared to [13]. In order to point out the implications of Section II in practical microwave designs, we will use as a reference the values measured in Merck E7 LC [16]: k 11 = 11.7 pN, k 33 = 17.1 pN, ∆ε = 0.47, ε ⊥ = 2.7.…”

“…However, a particular analytical approach can be derived from (2) when k 11 = k 33 . This fact was already exploited in [13]. However, the accuracy of the analytical approach reduces as k 33 moves away from k 11 .…”

“…[11], [12] at the expense of losing the physical insight on the properties of the material. In [13], it is recently proposed an analytical approach that takes into account these considerations. However, this approach is restricted to the case k 11 = k 22 = k 33 , commonly known in the literature as the oneconstant approximation [2].…”

“…Section II presents the derivation of the closed-form expression. Section III presents the simulation results, which are validated with numerical approaches and compared with [13]. Finally, conclusions are drawn in Section IV.…”