# Fractal Metasurfaces and Antennas: An Overview for Advanced Applications in Wireless Communications
## 4 Fractal Metasurfaces
### Fractal Metamaterial in Antenna Applications  
Over the last two decades, metamaterials have become increasingly popular in the antenna community due to their ability to improve the performance of antenna systems. They offer advantages such as bandwidth enhancement, gain improvement, miniaturization, stealth capabilities, and reductions in mutual coupling [73; 74; 75; 76; 77; 78; 79; 80]. Combining fractal metamaterials with antennas is an innovative approach in EM technology. Actually, fractal metamaterials have unique properties (e.g., miniaturization) that can improve the functionality of antennas. Below are some examples of antennas that use fractal metamaterials [81; 82; 83; 84; 85].  
In [81], a compact single-feed circularly polarized (CP) patch antenna was proposed and investigated based on the combined use of meta-surfaces and meta-resonators for gain enhancement (see Figure 23a). A complementary crossbar fractal tree slot was used as a meta-resonator to enable the antenna to radiate circularly polarized (CP) waves in single-band or dual-band operation and to facilitate further miniaturization.  
A novel miniaturized CP microstrip antenna operating in the UHF band (920-925 MHz) was designed in [82]. The antenna miniaturization was achieved by a special cross-shaped fractal metamaterial structure inserted between the patch and the ground plane (see Figure 23b).  
In [83], a strategy was proposed to reduce the cross-polarization (XP) radiation of a microstrip antenna by using the fractal-perturbed mushroom structure shown in Figure 23c. This method achieved XP suppression over several operating bands (1.5 GHz, 2.96 GHz, and 7.7 GHz) without compromising the co-polarization patterns, such as the antenna gain and directivity.  
Hilbert-shaped magnetic waveguide metamaterials to reduce the electromagnetic coupling of microstrip antenna arrays were proposed and developed in [84], showing a high decoupling efficiency (Figure 23d).  
Recently, metamaterials have also been used to fabricate lenses for microwave applications, including beam shaping, beam steering, and imaging. The literature presents bulk lenses made of 3D metamaterials or planar lenses made of metasurfaces [86; 87; 88; 89; 90]. Several interesting configurations using fractal meta-elements for lens antennas have also been presented [88; 89; 90]. In addition, in 2018, Fractal Antenna Systems Inc. was granted a US patent for a planar lens that uses fractal metamaterials to bend electromagnetic waves [91]. In [88], a left-handed fractal material-based three-dimensional superlens was proposed for C-band operation using second-order iteration Sierpinski fractal curves. In [89], a broadband three-dimensional (3D) emission system was proposed for beam-shaping and  
Figure 22: Metamaterial fractal polarizers: (**a**) dual-band circular polarizer using a twisted Hilbert chiral metamaterial [71], (**b**) H-shaped tree-like fractal metamaterial polarizer [72].  
beam-steering applications. The system comprises an omnidirectional source antenna and multiple lenses with a 3D gradient index of refraction (GRIN). The lenses are based on a Sierpinski fractal ring meta-element, as shown in Figure 23e. The same fractal metamaterial element was used in [90] to design an octave bandwidth half-Maxwell fish-eye (HMFE) lens antenna for C-band operation.