# Arrays of Sub-Terahertz Cryogenic Metamaterial
## 3 Metamaterial Matrices of Microwave Filters: Design, Fabrication, and Experimental Studies
### Capillary High-Pass Filters
This periodic lattice was simulated for the characteristic cell dimensions with periodic boundary conditions. The cross size was 40 \(\upmu\)m, width was 5 \(\upmu\)m, film thickness was 0.3 \(\upmu\)m, and substrate thickness was 240 \(\upmu\)m. The simulation projects were calculated both in CST STUDIO SUITE and HFSS programs (see a view of the model in Figure 11). The calculated transmission spectral results are presented in Figure 12 in the frequency range 100-1000 GHz. The main resonant transmission feature was present at a frequency of approximately 300 GHz and harmonics at 600 and 900 GHz. A slight downshift of maxima from the expected frequency was related to the so-called \"sagging electric field\" effect in the grids and is more pronounced at higher frequencies. For the first version of the filter, the grids were made of gold on quartz substrates with a thickness of 240 \(\upmu\)m, a diameter of 25 mm, a gold thickness of 300 nm, a stripe width of 5 \(\upmu\)m, and a period of 40 \(\upmu\)m. The transmission was measured by the substitution method in a transmission BWO spectrometer. A holder with meshes was installed in a four-lens beam guide (Figure 7) in the waist of the formed Gaussian beam, where the wave front is the flattest. The results of the experimental study are shown in Figure 13a. In addition, the aluminum filter on the glass substrate was investigated (Figure 13b). Figure 11: Design view of unit cell for numerical modeling. Figure 10: Tunable interferometer: (**a**) golden mesh evaporated on quartz substrate; (**b**) mechanical parts of the gadget; and (**c**) assembled interferometer. \[\gamma=(2\pi/\lambda_{\text{cr}})\ \sqrt{(\lambda_{\text{cr}}/\lambda)^{2}-1} \tag{2}\]0 Calculated dependence of the interferometer transmission spectrum for 4 distances between meshes. \[\gamma=(2\pi/\lambda_{\text{cr}})\ \sqrt{(\lambda_{\text{cr}}/\lambda)^{2}-1} \tag{2}\]1 Results of the theoretical and experimental study of the transmission of an interferometer depending on the distance between the grids: (**a**) measurements of a gold filter on a quartz substrate from the radiation source of the avalanche diode at 232 GHz (red) and 95 GHz (blue); and (**b**) measurements of an aluminum filter on a glass substrate carried out by changing the distance between the filter grids. Such a filter was used to measure the response of the SINIS bolometer [27]. A \"fast\" blackbody radiation source on a sapphire substrate was used as the emitter, which made it possible to operate at a modulation frequency of 20 Hz. To move the meshes inside the cryostat, the design of a worm drive connected to the filter draft by a long shaft made of a thin-walled stainless tube was developed (see Figure 14). The operation of the filter was demonstrated with a SINIS bolometer mounted at the 273 mK stage in a helium-3 Helixo-AC-V sorption cryostat. Reduced and broadened spectrum for black body source is due to broad illumination angle for such wide aperture and corresponding different resonant distances for different angles of incidence. Similar to [28], the Fabry-Perot resonance is dependent on incidence and polarization angles. With our black-body radiation source placed close to interferometer, these angles vary from normal to meshes to about \(\phi\) = 30\({}^{\circ}\) from normal. The corresponding resonant distance varies from actual distance d for normal incidence to d/cos\(\phi\) and brings broadening of transmission spectrum by about 15%.