# Arrays of Sub-Terahertz Cryogenic Metamaterial
## 2 Frequency-Selective Surfaces  
A frequency-selective surface [8] usually consists of periodic simple metallic elements that interact with incoming microwave radiation. For GHz bands, metallic components are preferred. The FSS unit cell in general does not contain only metallic elements, as it can be made out of semiconductor-dielectric and all-dielectric components [9]. The silicon-dielectric and metal-dielectric FSSs are also promising for mid-IR domain, see [10] and also [11].  
The FSS structure is equivalent to the reactance for propagating waves. It can reflect, transmit, or absorb radiation in a specific frequency range. A metallic grid FSS is common in millimeter and submillimeter wave ranges. Grid structures can be divided into main groups of inductive, capacitive, and combined types depending on the choice of unit element of the grid. In Figure 1, the main basic FSS types are presented. Modern advanced FSS structures can be much more complicated, as in [12; 13]. FSSs with required spectral characteristics can be integrated with superconducting detectors, as in [14], and develop receivers for several frequency bands. Besides conventional half-wavelength antenna elements [6], wideband detectors with electrically small elements [5; 15] can be developed. Another important application of FSSs is in developing spectral filters for background radiation power load suppression. The fabrication technique for such structures is well developed using a lift-off technique and the chemical etching of thin metallic films and foils.  
In one of the first detailed analytical and experimental studies of cross-shape filters [16], it was found that peak transmission is determined by the length of the crossarm (and not by period itself), while the bandwidth is determined chiefly by coupling between the crosses. These results are qualitatively consistent with coupled-dipole model.  
A comprehensive historical review of metal mesh filters is presented in [17]. Besides review of published results of research groups, authors also refer to some companies that can fabricate and sell different terahertz metal mesh filters (high-pass, low-pass, and band pass transmission). Among them, the most known are BRLABS [BR-labs [[http://www.br-labs.com](http://www.br-labs.com)]([http://www.br-labs.com](http://www.br-labs.com)) accessed on 10 October 2021] with bandpass filters between 0.4 to 10 THz, QMC Instruments [QMC instruments [[http://www.terahertz.co.uk](http://www.terahertz.co.uk)]([http://www.terahertz.co.uk](http://www.terahertz.co.uk)) accessed on 10 October 2021] with low-pass filters with edges between 0.3 to 20 THz, Virginia diodes with bandpass filters between 0.35 to 5 THz [Virginia diodes [[http://www.vadiodes.com](http://www.vadiodes.com)]([http://www.vadiodes.com](http://www.vadiodes.com)) accessed on 10 October 2021], and Mutsumi corporation [Mutsumi corporation http://In [18], authors measured characteristics of single-mesh cross-shaped filters dependencies on incident angle and polarization. Broadband resonances correspond to slot apertures, and series of narrowline resonances of Fabry-Perot type. It was demonstrated the possibility of tuning narrow-band resonances by adjusting the incidence and polarization angles, while the fundamental broadline resonance is not significantly affected.  
Among the best laboratory-made filters can be mentioned [19] with free-standing metal-mesh bandpass filters with central frequencies ranging from 0.585 to 2.1 THz. Filters are made of a 12 um thick copper foil, power transmission 97-100% at their center frequency, and stop-band rejection in excess of 18 dB.  
A combination of Fabry-Perot and guided mode resonances provides creating flat-top filter with less than 3 dB losses at central frequency 300 GHz, a 5 GHz flat-top, 19 GHz bandwidth at \(-15\)dB, that means high out-of-band rejection [20].