# Microwave Liquid Crystal Technology
## 6 Dielectric Waveguides
For characterization purposes, transitions were designed to provide a smooth mode conversion from the fundamental TE\({}_{10}\) mode of the rectangular metallic waveguide to the E\({}_{y11}\) mode of the dielectric waveguide and vice versa [42; 43]. Several tapers, such as for the cladding and core are used to achieve mode matching and for keeping losses due to radiation on a low level. The measurement setup is depicted in Figure 24. It consists of the fabricated dielectric phase shifter including two WR10-to-subwavelength fiber transitions for connection to a VNA. The phase shifter was fabricated in two parts milled out of Rexolite, being glued together by using an UV glue. By this, LC leakage can be easily avoided and two filling holes are left for later LC filling. To show the simplicity of the biasing system, adhesive copper tape was used, being directly stuck on the cladding. Furthermore, a voltage of \(\pm 550\,\mathrm{V}\) was applied to the parallel plate biasing configurations. The achieved S-parameters as well as the phase shift and FoM are given in Figure 25. It can be observed that the phase shifter is well matched with \(|S_{11}|<-15\,\mathrm{dB}\) over the whole frequency range. The insertion loss is in a range of \(3\,\mathrm{dB}\) to \(5\,\mathrm{dB}\). In comparison to the simulation, a deviation can be observed. The reason was found in the splice, which was not included in the simulation. Further, the dielectric loss of the glue itself was unknown at the time of the simulation, but it is expected to be higher than that of Rexolite. Nevertheless, with the LC GT5-26001 an FoM of around \(90^{\circ}/\mathrm{dB}\) was achieved between \(94\,\mathrm{GHz}\) to \(105\,\mathrm{GHz}\), accompanied with a differential phase shift of \(220^{\circ}\) to \(420^{\circ}\), see Figure 21:0 It is noticeable, that the simulated phase shift was not achieved in the measurement. This is due to fabrication tolerances in the milling process. With a precision of \(30\,\mathrm{\SIUnitSymbolMicro m}\), the fabricated LC cavity is slightly reduced, resulting in a reduced phase shift. Furthermore, the glue used in the assembling can flow into the cavity and can further decrease the LC volume. In addition, the LC might not be perfectly aligned. However, both insertion loss and phase shift show the same behavior independence of the biasing concept. This is an outstanding result for tunable devices based on LC, especially for in comparison to metallic waveguides. Here, electrical biasing systems always introduce additional losses and could not align the LC as properly than for the magnetic biasing. Figure 21:1 Fabricated phase shifter and measurement setup of the step-index phase shifter. Two of four electrodes are removed to enable a view of the LC core. With the design of the step-index fiber, a high-performance but bulky phase shifter was presented, which also allows a feasible phase shifter design for terahertz frequencies. However, for the integration of a dielectric waveguide phase shifter, e.g., in phased arrays, a more compact design is needed. As shown in Figure 26, a subwavelength fiber is well suited for such an application, due to its smaller dimensions. In [43] a phase shifter design was presented. The cross-section of the presented phase shifter is depicted in Figure 21:2 The main part consists of a quadratic Rexolite fiber with an edge length of 1.8 mm. For tunability, a 0.6 mm circular LC core is included. Like the step-index design, metal plates were used for the electric biasing, being placed in a large enough distance to the fiber, to not disturb the evanescent fields. The measurement setup, including the electric biasing system is shown in Figure 21:3 With a distance of the electrodes of 3 mm from the edge of the Rexolite body, the metallic plates are not disturbing the propagating wave. To ensure a proper position, Rohacell 31 HF, from Evonik Industries, Darmstadt, Germany is a special high performance foam suitable for high frequency applications.