# Cascaded Frequency Selective Surfaces with Matryoshka Geometry for Ultra-Wideband Bandwidth
## 1 Introduction
### Review
The metallic surface of the FSSs is modified into a resistive material for two layers and into a conductive material for the other two. The resistive layer is a dielectric material covered with a thin film of nickel-phosphorus, while the conductive surface is a simple copper material. Simulations were carried out, and measures were obtained of the cascaded FSS for two different spacings between the layers, 5 mm and 10 mm, with comparisons between the spacings and between simulated and measured results. The design in [17] is an absorber cascaded FSS of four layers for a frequency range from 2.48 GHz to 6.13 GHz and a bandwidth higher than 3 GHz. The main advantage of the structure presented by [PERSON] [17] is the absorption of signals for the entire industrial, scientific, and medical (ISM) radio band from 2.4 GHz to 2.4835 GHz, 5G at 3.5 GHz, and unlicensed national information infrastructure (UNII) from 5 GHz to 6 GHz. The cascaded FSS with matryoshka geometry proposed in the present paper presents a range that covers 2.0 GHz, the ISM band, and 5G at 3.5 GHz with only two layers and is easier to fabricate with only metallic layers. These advantages are especially useful for applications requiring a large bandwidth at lower frequencies. The development of a cascaded FSS is presented in [18] with a geometry of two concentric square rings to provide a large bandwidth with only two layers of FSS, a characteristic portrayed here in this paper. However, in [18], a 5 cm gap between the layers is proposed, and the bandwidth for the measured result is from 3 GHz to 11.64 GHz, a wide range of more than 8 GHz that influences frequencies beyond 10 GHz. However, this wide range comes with a larger spacing between the layers. The cascaded FSS with matryoshka geometry in the present work does not have such a wide range, but it uses only 12 mm spacing, more than four times less space, and includes the earlier frequencies of 1.8 GHz. In a paper by [PERSON] et al. [19], a design is presented of a three-layer cascaded FSS with patch and slotted patch geometry and 10 mm spacing between the layers. This structure allows obtaining a band-stop for ultra-wideband (UWB) applications with a bandwidth of 7.5 GHz between 3.10 GHz and 10.6 GHz. The paper shows the analysis of the resonant frequencies of the individual FSS layers and their influence on the cascaded FSS, as well as comparisons between the simulated designed model and the measurement of the fabricated FSSs. When comparing the design in [19] with the cascaded FSS with matryoshka geometry in the present paper, the design of [17] shows a larger bandwidth, but only for frequencies above 3 GHz, and a total gap of 20 mm between all three layers. There are also examples that explore dual-band operation [20; 21], in which the resonance frequencies occur in two different bands, and innovative uses, such as a three-dimensional origami-like FSS [20] or a curved metal FSS [21]. The FSS presented in [20] reaches smaller bandwidths of less than 600 MHz, and the FSS design in [21] has a resonance frequency of 10 GHz. The designed cascaded FSS with matryoshka geometry in our paper presents an optimized way to reach an ultra-wideband from 1.8 GHz to 3.8 GHz frequency range with only two layers spaced by 12 mm. Another innovative FSS structure is presented in [22], in which a metasurface filter of vanadium dioxide (VO2) with a switchable mode of transmission/reflection for electromagnetic shielding applications is designed. The paper by [PERSON] et al. [22] shows a design with hybrid layers and its components, as well as numerical analysis by finite element method (FEM). There is also a study of the equivalent circuit model (ECM) in which the FSS geometry can be analyzed as a circuit composed of inductors and capacitors. Although this is an innovative design, its bandwidth and applications are for terahertz frequencies, ranging from 0.1 THz to 3.78 THz.