## 2 Microwave Liquid Crystal Technology
### Performance Metric of Microwave Liquid Crystals  
Liquid Crystals (LCs) are dielectric materials with highly anisotropic characteristics, which can be grouped into three different mesophases between solid/crystalline and liquid/isotropic states according to Figure 5. These mesophases can be separated by orientation and positional order into nematic, smetic, and cholesteric [189, 190, 191, 192]. The nematic phase is the most commonly used phase of LCs at microwaves between the melting point Tm and clearing point \(T_{c}\). Within this nematic phase, the orientation of the rod-shaped molecules, which includes a polar group that produces a dipole moment, can be changed by an external electrostatic field. This results in a highly anisotropic permittivity tensor. At the macroscopic scale, the time-averaged direction of the molecules' long axis is denoted by a director \(\overset{\rightarrow}{n}\), where the permittivity tensor reduces to the one according to Figure 6, due to the molecule's rotational symmetry. Some properties of LCs and the elastic continuum theory are given in many books and publications, e.g., in [189, 190, 188, 191, 192, 189]. Figure 5: Schematic of a nematic liquid crystal material depending on the temperature, exhibiting a perfect alignment with the order parameter S = 1 in crystalline solid state (**left**), indicating time- and space average directions of the molecules (for a Liquid Crystal (LC) unit volume element characterized by the director \(\overset{\rightarrow}{n}\)) with order parameter 0 \(<\) S \(<\) 1 in the nematic phase (**middle**) and no molecular ordering with the order parameter S = 0 in liquid state (**right**). In recent years, there have been many comprehensive studies of various high birefringence LCs, on their mesogenic and physical-chemical properties such as viscosity, birefringence, permittivity, anisotropy, and elastic constants, discussing the question of how to obtain LCs with a broad range of nematic phases. A comprehensive review of LCs dedicated for microwave application is given in [55]. In [48], dielectric properties of LC isothiacynato-tolane derivatives with fluorine atoms at various lateral positions are analyzed from 1 kHz to 3 GHz. From the same group, a composition of large birefringence nematic LC, a eutectic mixture of isothiacynato-tolane molecules are characterized from 26 to 40 GHz in a coplanar waveguide with an active part made of a central cavity with length = 3 cm and height = 100 \(\upmu\)m similar to a rectangular waveguide to determine the dielectric properties and compare them with the standard display LC K15 (SCB, cyanobiphenyl) [49]. In [50; 51; 53; 54], systematic investigations were focused on how the dielectric anisotropy in the low frequency region up to 1 GHz and the birefringence of the nematic LC phase at an optical wavelength (589 nm) influences the performance of LC mixtures at microwave frequencies. For this, the authors prepared a wide range of mixtures being nematic at room temperature and containing different classes of promising compounds. Their quasi-static and frequency-dependent dielectric properties, their birefringence, and the impact of those properties on their microwave behavior were analyzed by using the cavity perturbation method in [200; 201]. As the measuring setup, several rectangular waveguide resonator cavities are designed for a TE\({}_{102}\)-mode at 9, 30, and 38 GHz with small holes to insert empty and LC-filled PolyTetraFluoroEthylene (PTFE) tubes, respectively. Measurements were carried out over a temperature range from \(-25\)\({}^{\circ}\)C to \(135\)\({}^{\circ}\)C. External magnets were used to orient the LC molecules parallel and perpendicular to the RF field.