# Frequency Selective Surfaces: A Review
## 4 Types of FSSs
### FSS Based on Array Elements
#### 4.1.3 Fractal Based FSSs
(2) Research on Fractal FSS  
Fractal FSS surfaces design based on the Minkowski islands, inset crossed dipole periodic cells, and Sierpinski carpet fractals were investigated in [29]. The simulation methods incorporating periodic boundary conditions allow for periodic arrays of complex elements to be analyzed. These include periodic MoM, which gives liberty to simulate tilted FSS surfaces for varying incidence angles and periodic finite difference time domain (FDTD) technique by which complex periodic arrays elements can efficiently be simulated. It is observed that the two later kinds of fractals provide multiband responses with a superior relationship between the structure geometry and the prediction of stop bands, while former fractal gives most closely spaced resonances. Conversely, transmission in the passband between the two stop bands is relatively lossy which can be made constructive for some applications. Importantly, a number of bands with the desired bandwidth are possible, and the passband performance can be improved by making a trade off among geometric shape, periodicity, and supporting dielectrics substrate. An interesting property of fractals is the opportunity of acquiring arbitrarily longer curvature confined in a specified area/volume. This characteristic has been effectively utilized in reducing the inter-element spacing between the resonating shapes of FSS. The fascinating feature of \"self-similarity\" facilitates to realize a multiband performance. However, a truly multiband FSS design encounters a major limitation, i.e., appearance of grating lobes, which can be overcome by minimizing the spacing between neighboring elements as compared to the free space wavelength. On the other hand, the inter-elements spacing cannot be smaller than their length. The Sierpinski dipole exhibits a multiband response that is known after the invention of Sierpinski gaskets or Sierpinski triangles [69]. Earlier, it is proved by [PERSON] et al. that Sierpinski fractal FSS without dielectric substrate can merely show dual band behavior [77]. This is to note that in Sierpinski gasket, a scale ratio exists between a triangle and the triangles built in the subsequent iterations of one half. The Sierpinski dipole shape gives enough freedom to modify its geometry and tune frequency response [73]. It is recognized in this research that the resonant frequencies are related to the span length of the dipole edge (2*h) instead of its height. As a result, the resonant frequency becomes low at a certain height when the flare angle of dipoles is widened, as seen in the trend graph of Figure 8b. Additionally, the distance between the first and the second resonance roughly remains the same with the variation of flare angle. It has been examined that by suitably perturbing the shape i-e the scale factor, the ratio between resonant frequencies can be modified. Trends of the resonant frequency in Figure 8c shows the effect of different scale factors, and it can be inferred that it is possible to adjust the frequency response to a definite extent for a Sierpinski dipole FSS. Gosper hexagonal and Durer pentagon patch fractals were proposed in designing of compact FSS based filters in [78; 79]. Stopband filtering with dual-band responses and broad bandwidth is exhibited by these spatial structures. Their EM performance parameters (resonant frequency and bandwidth) can be adjusted without modifying their original size. The tuning at the required frequencies range is possible because resonant frequency decreases by increasing the number of fractal iterations. Also, with an increase in the periodicity of the structure, the resonant frequency is lowered while narrowing the bandwidth. Nonetheless, a reduced effect is pronounced when the fractal iteration is increased. Metallic Koch fractal with two-dimensional periodic array elements is reported in [80] for miniaturization of FSS. Recently, fractals have been used to design compact and angularly stable FSSs [81].