# Potential of Liquid-Crystal Materials for Millimeter-Wave Application
## 3 Millimeter Wave Fresnel Lens Fabricated Using 3D Printer
### Magnetic Field Tunable Properties of LC Composite Fresnel Lens  
Figure 7 shows the MMW focusing properties of the combined LC Fresnel lens. The inset figures show the fabricated Fresnel lens substrate used in a demonstration of the MMW LC Fresnel  
Figure 5: **(a)** Appearance of fabricated Fresnel lens; **(b)** an example of the cross-sectional structure of the Fresnel lens; **(c)**magnified observation of the lens surface fabricated using a three-dimensional (3D) printer.  
Figure 6: MMW focusing properties of conversing lens.  
lens. The substrate had a concave structure, and the LC material was introduced into the cavity. The diverging property of the concave lens substrate without the LC material is difficult to confirm from the spatial distribution measurement of the MMW intensity; however, it is evident that a good focusing property appeared after introducing the LC material. The combined lens becomes a conversing lens, because the refractive index of the LC materials is larger than that of the plastic material used for the 3D printer filaments.  
The combined LC Fresnel lens was set at the center of the pole pieces of the electric magnet system, which was aligned horizontally. In our experiment, the horizontally launched MMW from the horn antenna was reflected vertically by a metal-plate reflector set at an angle of 45\({}^{\circ}\), and the MMW was incident on the Fresnel lens normally from the bottom surface. When a magnetic field is applied to the LC cell, the LC molecules align parallel to the magnetic field because of the anisotropic magnetic response of the LC molecules. If the electric field of the incident MMW is parallel to the applied magnetic field, the MMWs see a large refractive index according to \(n_{\mathrm{e}}\), and, if the relationship becomes perpendicular, the refractive index becomes small, corresponding to \(n_{\mathrm{o}}\).  
Figure 8 shows the measurement results of the MMW focusing properties when a magnetic field was applied (a) parallel and (b) perpendicular to the electric field of the MMW. At the initial state, the LC molecular alignment directions were random and, subsequently, the MMW experienced the mean refractive index value between \(n_{\mathrm{e}}\) and \(n_{\mathrm{o}}\). When a magnetic field was applied parallel to the MMW electric field, the refractive index of the LC layer increased, i.e., the refractive index difference between the substrate and LC layer increased. Then, the diffraction efficiency of the combined lens tended to increase, as shown in Figure 8a. On the other hand, the focusing intensity decreased when the magnetic field was applied perpendicular to the electric field of the MMW. There was a difference in the MMW intensity at B = 0 between the measurement results in Figure 8a,b. The measurement condition between them was probably a little different because we had to rotate the polarization direction of the MMW oscillator and detector system by 90\({}^{\circ}\). Although the initial intensity at B = 0 had some dispersion between the measurements, the complementary change of the MMW intensity according to the polarization direction was always clear. These results suggest that the refractive index of the 3D printer filament has a smaller refractive index than \(n_{\mathrm{o}}\) of the LC material. If we evaluate the refractive index of the filament material from the measurement data of the diffraction efficiency properties as a function of the step depth, a refractive index of about 1.6 is evaluated from the optimal depth value. This is consistent with the previously measured data of the refractive indices of 5 CB in the MMW region, which are 1.71 and 1.62 for \(n_{\mathrm{e}}\) and \(n_{\mathrm{o}}\), respectively [8].  
Figure 7: MMW focusing properties of the combined liquid-crystal (LC) Fresnel lens.