# Fractal Metasurfaces and Antennas: An Overview for Advanced Applications in Wireless Communications
## 4 Fractal Metasurfaces
### Fractal Metamaterial Absorbers
#### 4.1.2 Examples of Fractal-Based MAs  
The Minkowski fractal geometry proposed in [53; 54] can be used to create small absorber cells that are suitable for mitigating multipath phenomena in the European RFID UHF band. The compact size of fractal geometries has been exploited to design a dual-band microwave absorber operating in the UHF band [54]. The MA unit cell, shown in Figure 16a, consists of two pairs of Minkowski patches arranged alternately. The fractal elements in the pairs were synthesized to operate at specific resonant frequencies, namely 878 MHz and 956 MHz, resulting in absorption peaks greater than 99%. An absorber plate measuring 125 mm \(\times\) 125 mm and composed of 18 \(\times\) 18 fractal elements was prototyped and experimentally validated (see Figure 16b). The configuration achieved perfect absorption in the dual-frequency operating mode, despite being thinner and smaller than standard microwave absorber configurations [54]. Furthermore, the panel exhibited stable angular behavior (see Figure 16b). Another example of fractal MAs is the polarization-independent metamaterial energy harvester (EH) proposed in [55]. Metamaterial structures are a promising alternative to conventional rectennas for RF energy harvesting systems. They offer significant advantages in terms of increased harvested power and a greater efficiency in the initial RF-to-AC power conversion stage [65; 66; 67; 68; 69]. Figure 17a shows a metamaterial cell consisting of a miniaturized Minkowski fractal element printed on a thin grounded dielectric layer. The cell is loaded with two resistive loads that model the rectification circuitry. The unit cell analyzed in [55] provides high absorption rates, good angular stability, and high polarization independence in the 2.45 GHz Wi-Fi frequency band. In addition, a 9 \(\times\) 9 metamaterial EH was designed and simulated, demonstrating a high RF-to-AC efficiency of 96.5% (see Figure 16b). Moreover, the finite-size harvester exhibits polarization-insensitive behaviour, making it highly attractive for the development of eco-friendly energy-harvesting solutions. Figure 16: UHF fractal MA unit cell [54]: (**a**) cell layout and free-space measurement setup with the particulars of the fabricated MA absorber, (**b**) comparison between measured and simulated reflection coefficients. In [56], a circular fractal structure was proposed to design a tri-band polarization-insensitive metamaterial absorber for stealth technology. The MA was printed on an FR4 dielectric substrate and backed by a metallic layer. The proposed fractal construction process starts with an initiator circle (iteration 0). Next, four small circles, tangent to each other, are inserted into the initiator (Figure 18a). This shape represents the first iteration of the fractal geometry and is called the generator. As shown in Figure 18a, the subsequent iterations are generated by repeating the process described above. In particular, in [56], the construction process was stopped at iteration 2 to design the MA cell shown in Figure 18b, resulting in the measured absorption coefficient in Figure 18c. Figure 17: Minkowski MA unit cell for ambient power harvesting [55]: (**a**) top view and 3D view, (**b**) RF-to-AC efficiency of a 9 \(\times\) 9 harvester for different polarization angles \(\phi_{\text{inc}}\) at normal incidence. Figure 18: Circular fractal-based MA: (**a**) fractal construction, (**b**) circular fractal MA unit cell, (**c**) measured absorption coefficient (Adapted with permission from [56], IET, 2016). Reference [57] proposes a fractal-based metamaterial structure with lumped resistors, using a combination of the Sierpinski curve and Minkowski fractal (see Figure 19). The structure is printed on a 1.6 mm thick FR4 substrate with an air gap of 12.5 mm. This geometry enables the design of a perfect tri-wideband metamaterial absorber that covers the frequency bands of 1.7 to 2.6 GHz, 4.56 to 5.59 GHz, and 12.37 to 13.29 GHz (Figure 18c), at the expense of a thick structure.