# Arrays of Sub-Terahertz Cryogenic Metamaterial
## 3 Metamaterial Matrices of Microwave Filters: Design, Fabrication, and Experimental Studies
### Thin-Film Filters  
Metal film filters can be fabricated by various fabrication methods: evaporation, sputtering, etching, or lifting-off. Advanced designs are multilayer structures, as in [21; 22]. For frequencies below 1 THz, such filters can be made of free-standing thin metal foil instead of thin film on a dielectric substrate.  
We fabricated a series of band-pass filters for the central frequencies of 300, 450, 600, and 750 GHz [23]. Such filters were fabricated with chemical etching of 50 \(\upmu\)m of thick copper foil, 20 \(\upmu\)m of thick aluminum foil, chemical etching of copper-plated Teflon (35 \(\upmu\)m of copper on 800 \(\upmu\)m of Teflon carrier), and chemical etching of aluminum-plated Kapton. The shape of the openings was transferred to an S1813 photoresist from a photomask (Figure 2a) with dimensions ratios of period:length:width as P:L:W = 10:8:1. To avoid oxidation, copper foil was electrolytically gold plated. A photo of such a filter is presented in Figure 2b. The copper filters were etched in a solution of hydrogen peroxide and salt acid, and the aluminum was etched in orthophosphoric acid or in potassium hydroxide. Such filters were modeled in the CST STUDIO SUITE with Floquet ports and \"unit cell\" boundary conditions. Schematic images of some modeled filters are presented in Figure 3.  
The spectral characteristics were measured with a BWO transmission spectrometer, a Fourier spectrometer (BECKMAN IR-720M), and an IR spectrophotometer (Shimadzu IR-460). At lower frequencies, better characteristics were obtained for copper foil filters,  
Figure 3: Schematic image of modeled structure: (**a**) foil filters; and (**b**) copper filter on Mylar substrate.  
Figure 2: (**a**) Unit cell and (**b**) photo of fabricated 600 GHz filter with 625 \(\upmu\)m period.  
and at higher frequencies for thin-film filters evaporated on Mylar or Kapton. The best transmission losses were as low as \(-0.13\) dB. The losses in the cascade of four filters was \(-0.9\) dB. The cascade of four filters separated by filter paper was \(-1.5\) dB. The fine alignment and tuning of the cascade filter can improve the Q-factor. Filters on thick Teflon inserted additional losses of about 1 dB due to the reflections from two air-Teflon boundaries. Filters made of 0.4 \(\upmu\)m of aluminum on Kapton have additional losses of 5 dB that can be attributed to resistive losses in the thin aluminum film on top of an adhesion layer of 5 nm chromium. Furthermore, using the IR spectrophotometer, we measured the transmission of the filters in the IR band. Losses in this region are over 10 dB. The results of the measurements of the different filters in the frequency band 100-600 GHz are presented in Figure 4.  
The out-of-band attenuation in a single filter at infrared (Figure 5) was above \(-11\) dB in the wave range 2-20 \(\upmu\)m; that is, more than the geometrical factor equal to the area of etched-away opening to the area of unit cell equals, which is \(-8.2\) dB.  
The operation of cryogenic bolometers is only possible at a strong suppression of the background IR radiation. For this purpose, special cold low-pass filters (for example, fluorogold) are used. The attenuation of the IR background by a band-pass filter outside its working band reduces the requirements for low-pass filters. The band-pass spectra of the grid filters in the 2.5- to 25-\(\upmu\)m IR wavelength range are shown in Figure 5. Deep transmission minima at 6 and 13 \(\upmu\)m relate to reflections and absorptions in the Mylar film, on which this filter is based. The filters can be efficiently staged in the IR wave range in contrast to the submillimeter range, since the mutual darkening of the holes of subsequent grids leads to the fact that the total transmission is much smaller than products of the transmissions of single filters. In our spectrometer, the signal transmitted through two filters was below the noise level, i.e., the attenuation exceeded 20 dB.