# The Role of the Directivity of Various THz Detectors in Multiplexing Systems
## 3 Results
### Examination of the Three-Focal-Spot Lenses  
Three designed three-focal-spot THz lenses were experimentally verified using the detectors corresponding to the DWL. In all cases, the focal spots were observed at the desired positions. However, verifying the relative intensity of these focal spots is not trivial. Figure 6: Frequency dependence of the angular characteristics of the detectors: (**a**) QOD, (**b**) WR51, (**c**) FET and (**d**) WR34. Figure 7: Comparison of the angular acceptance characteristics of the detector in nominal position (blue line) and rotated by 180\({}^{\circ}\) (orange line). Most clearly, it can be seen by comparison of the measurements performed for structures with different focal lengths. One-dimensional cross sections along the three spots in the focal plane formed by the structure with focal length \(f=700\) mm are presented in Figure 8.  
For a focal length equal to 700 mm and a focal spot shift equal to 25 mm, the radiation deflection angle is approximately \(2^{\circ}\). However, even for such a small angle, the differences in the readings are clearly visible. When the detector faces the center of the lens from the position of one of the side focal spots (L or R), the observed relative intensity of this focal spot increases. It can also be seen that the effect is stronger for the detector with the narrower angular acceptance band--QOD (Figure 8a). Nevertheless, in such a configuration with a high ratio of the focal length to the focal point shift, the structure can be reliably verified even with strongly directive detectors. It also means that the directivity of the utilized detector would not be crucial in multiplexing systems using such multi-focal-spot lenses. The issue lies, however, in the need for the minimization of the devices. The high focal length to focal point shift ratio can be achieved either by long focal length or by small focal point shift. The first option results in a large device with a length close to a meter, while the second option does not allow the simultaneous detection of different signals with bulky detectors. Hence, the only solution is to reduce the ratio of the focal length and the focal point shift, which results in a higher deflection angle of the incoming radiation. To illustrate this issue, let us evaluate the three-focal-spot structure with a focal length \(f=100\) mm. The cross sections of the spots in the focal plane measured with the QOD and WR51 detectors placed at different angles are shown in Figure 9.  
In this case, the deflection angles of the radiation forming the L and 2L focal spots are equal to ca. \(14^{\circ}\) and \(27^{\circ}\), respectively. Therefore, the results differ much more strongly between detector types as well as the detector positions. All three lines in Figure 9a,b are in scale with each other. For the sake of clarity of comparison, all results have been normalized for the highest signal observed for a given detector. One can easily notice that in both cases the intensity of the middle focal spot is the highest for the detector facing it (perpendicular to the optical axis, marked as rotated by \(0^{\circ}\)). This is an expected result for highly directive detectors. However, the results are less intuitive for the shifted focal spots. The intensity of the L focal spot is the highest in the direct detector configuration instead of the theoretically favored tilted by \(14^{\circ}\) configuration. On the other hand, the highest intensity of the 2L focal spot has been observed exactly in the tilted by \(14^{\circ}\) configuration instead of the theoretically favored--in this case--tilted by \(27^{\circ}\) configuration. The differences between the relative intensities of the focal spots observed for different detection angles are also greater for the detector with a narrower angular acceptance band (QOD). Figure 8: Cross sections along the spots measured in the focal plane of the \(f=700\) mm structure with (**a**) QOD and (**b**) WR51 detectors.