# The Role of the Directivity of Various THz Detectors in Multiplexing Systems
## 2 Materials and Methods
### Three-Focal-Spot Lenses  
Three three-focal-spot diffractive THz lenses were designed, optimized, simulated and manufactured. The first structure realizes the symmetric distribution of focal spots with respect to the optical axis of the system and is characterized by the focal length \(f=700\) mm and the design wavelength (DWL) corresponding to the frequency of 140 GHz. The second and third structures were designed to focus the radiation into three focal spots in the asymmetric configuration (one central spot and two shifted to the same side of the optical axis) at a distance of \(f=100\) mm from the structure. The DWLs of these two structures correspond to the frequencies of 140 GHz and 260 GHz, respectively. For all DOEs, the focal spots are positioned 25 mm from each other. This means that in the case of symmetric structure, the focal spot positions with respect to the optical axis are equal to (\(-25\)) mm, 0 mm and 25 mm. On the other hand, for the asymmetric structure, the focal spots are placed at 0 mm, 25 mm and 50 mm. For readability, the focal spots placed at (\(-25\)) mm, 0 mm, 25 mm and 50 mm will be referred to as R (right), M (middle), L (left) and 2L (far left), respectively.  
The geometric parameters (diameters and focal lengths) of the lenses were chosen to reflect the 3 dB acceptance cones of the highest and least directive detectors. This can be seen in Figure 2.  
The configuration presented in Figure 2b shows that in the setups with a sufficiently high ratio of the focal length to the diameter of the beam (or structure), even highly directive detectors could be applied. Such multiplexing systems, however, would be either very bulky (due to length) or suffer from low channel separability (due to the narrow beam). Therefore, geometries similar to the one presented in Figure 2a have to be considered.  
Figure 2: Simplified diagram presenting the detector field of view in relation to measured structures (MS)—(a) MS1—DOE with \(f=100\) mm and (b) MS2—DOE with \(f=700\) mm.  
All structures were fabricated using the additive manufacturing method. The photographs of the manufactured DOEs are shown in Figure 3.  
All structures were manufactured using a simple and cost-effective extrusion-based 3D printing technique. For the first DOE, polypropylene (PP Black Fiberlogy) was used, while the other two structures were fabricated from cyclic olefin copolymer (COC [TOPAS] Creamelt). The absorption coefficients of these two materials are equal to 0.21 cm\({}^{-1}\), 0.05 cm\({}^{-1}\) and 0.08 cm\({}^{-1}\) for PP @ 140 GHz, COC @ 140 GHZ and COC @ 260 GHz, respectively. Therefore, the average absorption losses introduced by these three structures are equal to 4.7%, 1.3% and 1.3%. The refractive indices of these materials in the sub-THz spectrum are close to 1.5, which translates to Fresnel losses below 5%. Additionally, in the design of the third structure (\(f=100\) mm, \(\
u=260\) GHz) a new 3D-modeling method, based on the extraction of blocks instead of triangle interpolation, was applied. This method allows for a more accurate representation of the numerically simulated bitmap in the 3D space. Such an approach is crucial for structures with high variance of the height of adjacent pixels (such as the one in Figure 3c) and has been described more closely in [23]. This article focuses mostly on the methodology of the characterization of off-axis beams with detectors of varying types and parameters and their applicability to multiplexing systems. The selection of diffractive structures used for this comparison reflects the evolution of the design and manufacturing methods we developed. Three-focal-spot structures have already been described in [18]. However, some new conclusions in this regard shall also be formulated.