# Cascaded Frequency Selective Surfaces with Matryoshka Geometry for Ultra-Wideband Bandwidth
## 1 Introduction
### Review
When compared with the cascaded FSS of matryoshka geometry design in the present work, they are not as suitable for the 1 to 5 GHz range, where many applications are in use. There are also other FSSs that have several modern applications. An example is found in the work of [PERSON] et al. [23], which addresses how FSSs can contribute to buildings with architecture covered by many panes of glass, reducing the consumption of electricity involved in cooling and heating while leading to adequate transmission of electromagnetic waves carrying telecommunications signals through the windows. Low-emissivity (low-e) windows have been proposed as a solution to minimize energy use as they are capable of reflecting external heat radiation, thus reducing cooling loads when compared to conventional windows. Low-e windows have been used in both architectural and automotive sectors to block ultraviolet (UV) and infrared (IR) radiation from the sun. The windows are made with thin multilayer coatings (metallic and dielectric layers), which are highly transparent to visible light but reflect infrared radiation (heat). However, metallic layers attenuate telecommunications signals, such as radio frequency (RF) and microwave signals. Due to the demand for reliable mobile communications coverage, those windows need to be transparent to waves in the frequency ranges of these signals. One technology that can solve this problem is frequency selective surface (FSS), which can be incorporated into the surface of windows to selectively filter electromagnetic waves. Another application of FSSs is presented in [24], in which the authors propose a flexible and reconfigurable monopole antenna design with FSS for Internet of Things (IoT) applications. To improve the antenna gain, a simple FSS was designed to be placed under the antenna at a distance of 15 mm. FSS operates efficiently in the 2 to 4.5 GHz band and has improved antenna gain. Maximum gains of 6.5 dBi, 7.52 dBi, and 7.91 dBi were achieved in the three frequency bands under consideration. In [25], an FSS is associated with a microstrip antenna to obtain ultra-wideband (UWB). The antenna contains a hexagonal patch with multiple inserted stubs to provide an ultra-wideband range from 5 GHz to 17 GHz. Results show that the aforementioned approach is a strong candidate for future high-gain, high-bandwidth wireless devices. A radiating element consisting of a modified circular patch is proposed in [26] for MIMO arrays in 5G millimeter-wave applications. The radiating elements of the proposed 2 \(\times\) 2 antenna array are configured orthogonally to each other to mitigate mutual coupling that would otherwise degrade the performance of the MIMO system. Due to the low coupling between the radiating elements, its envelope correlation coefficient (ECC) is less than 0.002, and its diversity gain (DG) is greater than 9.99 dB in the 5G operating band centered at 28 GHz between 26.5 GHz and 29.5 GHz. An aperture antenna array shared between the Ku and Ka frequency bands, with high performance provided by an FSS, is evaluated in [27] in terms of gain, efficiency, and isolation between frequency bands. The antenna consists of two dipole arrays, one 8 \(\times\) 8 for the Ka-band and the other 4 \(\times\) 4 for the Ku-band. The proposed structure is composed of the 8 \(\times\) 8 array printed on the top face of the substrate, a low-pass FSS printed on the opposite face of the substrate, and the 4 \(\times\) 4 array printed on the top face of a second substrate so that the two arrangements form a sandwich with the FSS. The proposed antenna array presents an impedance bandwidth of \(-\)10 dB equal to 19.07% from 14.47 GHz to 17.52 GHz and 23.66% from 30.19 GHz to 38.29 GHz, with peaks gain of 18.9 dBi at 16 GHz and 24.85 dBi at 35 GHz, respectively. A band-pass FSS with low insertion loss and angular stability, in relation to the variation of the horizontal angle of incidence of the wavefront, composed of three metallic layers, is proposed in [28].