# Arrays of Sub-Terahertz Cryogenic Metamaterial
## 5 Discussion  
The creation of receiving matrices and filtering elements in the MM and subMM wave ranges is one of the most in-demand tasks today, as such structures can be applied in various fields from radio astronomy research to the creation of scanning matrices for security systems. Figure 23: Experimental setup for spectral evaluation of cryogenic detectors comprising cryostat with optical windows, filters, calibration detectors, BWO source, chopper, and pyroelectric detector [29]. Figure 24: Measured spectral response of arrays of half-wave (**a**) and electrically small (**b**) antennas from [29], black as it is from detector voltage response, and red after corrections from the reference channel (not averaging). The methodology for modeling, manufacturing, and measuring such devices has become relevant. Matrices based on half-wave unit cells are the most popular building blocks. To create a broadband receiving structure, it is important to develop electrically small antennas with a characteristic element size \(\lambda/10\) or less--an analogue of a distributed absorber. With an increase in the frequency range and a decrease in the size of single elements and the period, the calculation of the characteristics of such structures becomes a complex computational problem. A modern approach is numerical simulation in software packages such as CST STUDIO SUITE and HFSS. However, the results obtained by the numerical simulation method do not always reflect the real (or close to real) electrodynamic picture of the matrices being developed. In the pursuit of a decrease in computing power and a reduction in computation time, a modeling technique is used with Floquet ports, infinite matrices, and periodic unit cell boundary conditions. The condition that the electromagnetic field in a single cell differs only by a complex component can be applicable only for the case of phased antenna arrays, or filtering devices in the absence of dissipation. In the case of antenna arrays with integrated SINIS detectors, we observe a more complex electrodynamic picture. This is especially important for receiving matrices consisting of electrically small elements, since in this case, the mutual influence of the adjacent elements on each other is significant, which is not taken into account when calculating the unit cell. As an example, Figure 25 shows the simulated spectral responses of the matrices of electrically small antennas using two methods: a single cell with Floquet ports and an entire matrix consisting of 81 ring antennas, each of which is integrated with four SINIS detectors. As noted above, the simplified method for calculating a unit cell is quite applicable for studying the characteristics of filters based on periodic structures. The difference between the calculated and experimental results of the study (a small shift in frequency and bandwidth) of filtering devices (Figures 4, 8, 9 and 13) is due to the following: the imperfect size and shape of the fabricated structures and the difference in the basic characteristics (mainly dielectric constant) used in the substrate materials in a practical and simulated case. Considering the results of modeling filters on thick substrates (quartz 100 \(\upmu\)m and Teflon 800 \(\upmu\)m, Figure 4a), \"parasitic resonances\" can be explained by the fact that the resonance of the etched structures (crosses) is combined with the Fabri-Perot resonance on a plane-parallel plate. The evaluation and comparison of the theoretical and experimental characteristics of receiving matrices with integrated superconducting detectors, in contrast to filtering devices, is a more difficult task, as on the path \"source-receiver\", there are multiple reflections both on the windows of the cryostat and inside it that will require huge computing power and supercomputers to simulate. In addition, it should be noted that the power level of the signal source (in our case, the backward wave oscillator) is significantly nonuniform.