# Arrays of Sub-Terahertz Cryogenic Metamaterial
## 3 Metamaterial Matrices of Microwave Filters: Design, Fabrication, and Experimental Studies
### Capillary High-Pass Filters
The filters were placed in the waist of a quasi-optical beam guide comprising (Figure 7) a backward wave oscillator (BWO) radiation source, a corrugated horn, four Teflon lenses (focal length 20 cm and 40 cm), and a Goley cell detector. The transmission was measured in the frequency range 150-550 GHz. For an inner diameter of a capillary of 0.54 mm and a length of 3 mm, the attenuation of such a filter was over 40 dB at frequencies below 200 GHz. At frequencies above 350 GHz, attenuation does not exceed 5 dB. The results of the measurements are presented in Figures 8 and 9. Figure 5: The results of measurements of Al foil filter (1) and Al filter on Mylar substrate (2). Measurements from [23]. Figure 8: Investigation of capillary filter 200 and 350 GHz band: (**a**) schematic image of modeled structure; and (**b**) results of numerical modeling and experimental tests. Experimental curves are shifted to higher frequencies presumably due to slight pressing capillaries in the fabrication process and deformation. Figure 6: Capillarity filter: (**a**) fabrication process; and (**b**) photo of capillary filter. Figure 7: Photo and schematic view of experimental setup for filter evaluation: 1—BWO, 2, 4—lenses, 3—chopper, 5—filter under test, and 6—pyroelectric detector. As we mentioned above, our experimental curves are shifted to higher frequencies presumably due to slight pressing capillaries in fabrication process and some deformation. Squeezing capillary diameter in fabrication leads to reducing effective diameter in the middle and increasing of the cut-off frequency. Cryogenic Tunable Filter-Interferometer of Fabry-Perot Type with Grid Meslues below 1/8 Wavelength Period  
For developing a cryogenic measuring system and performing spectral measurements, it is very appealing to use a broadband calibrated cryogenic thermal radiation source combined with a tunable high-Q filter inside the cryostat. This solution makes it possible to significantly simplify the optical path in comparison with the use of a BWO source and a set of lenses at room temperature, as well as to remove multiple reflections and irregularities arising on the optical windows of the cryostat. As a tunable filter, a mesh filter of the Fabry-Perot interferometer type can be used [26]. One of the requirements for the implementation of such a design is a good reflectivity of the meshes. In our experiment, metal film grid filters on quartz substrates were used as meshes (interferometer mirrors). A photo of the golden mesh is presented in Figure 10a. For a backlash-free tuning of distance between meshes, we fabricated a gadget with magnetic pushers made from SmCo magnetic rods. The mandrels  
Figure 9: Investigation of dependence of filter’s characteristic on capillary length: (**a**) the results of modeling; and (**b**) the results of measurements of thick (4 mm long) and thin (2 mm long) filters. were facing each other with the same poles, so that pushing the mandrels back and forth was smooth, without sticking or backlash. For photos of the mechanical parts of such a tunable interferometer, see Figure 10b. The assembled tunable filter consisted of two metal film meshes on quartz substrates that could be pushed apart by the rotation of ring diaphragms in the M50 \(\times\) 0.75 screw. One complete revolution of the mesh ring corresponded to a movement of 0.75 mm. The initial gap between the meshes was 0.1 mm. The meshes were oriented facing the metallic film sides and dielectrics oriented outside. The transmission of one such grid in the 500 GHz band was below 4%, which fulfills the requirements of interferometer meshes. The frequency response of such a filter tuned to a frequency of 300 GHz was calculated. The calculation was carried out in the following configuration: the grids on the substrates faced each other, the distance between the grids was 500 \(\upmu\)m, which corresponded to half the wavelength at a given frequency. Optical quartz for the substrate and gold for the grating material were chosen as reference materials for numerical simulations.