# Frequency Selective Surfaces: A Review
## 4 Types of FSSs
### FSS Based on Array Elements
#### 4.1.3 Fractal Based FSSs
Promising and desirable FSS performance characteristics with Peano pre-fractals is claimed in [82], for instance, adjustable transmission features, compact designs, higher frequency compression factor, stable frequency responses for oblique angles of incidence wave, and multiband behavior. Any fractal geometry whose fractal dimension (SFD) is equal to 2 is named as Peano curve [68]. Originally, Peano curve consists of a base-motif fractal, which makes use of a line segment for its base. Figure 9a shows Peano fractals (k = 1 and k = 2) with an octagonal base of metallic patches printed on a single layer of fiber glass has been used for reconfiguration which is an attractive feature for some antenna systems and transmission management in buildings requiring wireless applications [82]. The possibility of FSS reconfiguration is facilitated by assuming particular switches to be turned off (S1-S8). As seen in Figure 9b, with the increase of iteration level, the number of resonances increases from 3 to 7. Analysis of increasing the inter-element spacing shows that for k = 0, the resonance frequency lessens and the BW narrows down, as depicted in Figure 9c. However, for k = 1 and k = 2, a slight increase in resonant frequency is examined. Figure 9d gives the trend graph of varying angle of incidence and shows stability for fractal level 1 and 2, while deviations of 33% and 0.49% in resonance frequencies are found for k = 0 and k = 2, respectively. Similarly, an increase in BW is seen for higher oblique angles with level 1 and 2 as compared to level 0 and tendency is shown in Figure 9e. Such flexible fractal patch element can provide many combinations of reconfigurations, though the drawback is that a reconfigured patch loses its symmetry and hence dual polarisability. Fractal elements can also be employed in designing FSSs for wireless security and mobile communication especially to protect security staff in buildings against harmful EM radiation in L or S-band. In this band of frequencies, FSS proposed in [81] demonstrates good reflection characteristic to screen out the EM energy; while at 900/1800/1900 MHz and 5.2/5.8 GHz, this fractal structure works as a good transmitter (a passband filter). The design made by regular hexagonal patches and equilateral triangle shaped array while using a fractal structure can efficiently reduce the unit size and maintains the stopband characteristic of this ring shaped FSS. Through proper symmetric configuration and a small gap between the two adjacent cells, the resonance frequency can be diminished by using high permittivity material, as revealed in Figure 9f. With resonance frequency in vacuum f0 and relative permittivity \(\epsilon_{\mathrm{r}}\), the resonance frequency f\({}_{\mathrm{r}}\) can be calculated by (9). \[\mathbf{f}_{\mathrm{r}}=\
icefrac{{\mathrm{f}_{0}}}{{\sqrt{(\epsilon_{\mathrm{ r}+1})/2}}} \tag{9}\]  
Desired resonance frequency in reject-band can conveniently be gained by using the certain dielectric material, for screening out the WiMax, WLAN, mobile communication, and other unwanted signals. Usually, self-similarity feature of fractal structures increases the number of resonances by augmenting the fractal iteration. One such fractal configuration, named as the SZ curve, is utilized in miniaturizing the FSS element giving two passbands (in S and C band) [83]. The element in slot shape is joined by four symmetric SZ curves of the second iteration, giving it a meandered aperture appearance. Figure 8: **(a)** Koch curve generation [76]. Effect on resonant frequency for the Sierpinski dipole FSS with (**b**) variation of flare angle (**c**) variation of scale factors [73]. An improvement in the FSS bandwidth can be achieved by cascading two or multiple layers of fractal elements. Another approach to develop double or multiband FSSs is by creating geometries with dissimilar fractal array elements as compared to those geometries with identical fractal elements.