# Fractal Metasurfaces and Antennas: An Overview for Advanced Applications in Wireless Communications
###### Abstract  
This paper provides an overview of fractal antennas and metasurfaces, exploring their design principles, performance, and applications. Fractal antennas, incorporating self-similar geometric shapes, offer several advantages, such as their multiband operation, compact size, and improved performance. Metasurfaces, on the other hand, are two-dimensional structures composed of subwavelength unit cells and are designed to achieve advantageous and unusual electromagnetic properties by enabling precise control over electromagnetic waves. This paper discusses the fundamental concepts of fractal antennas and metasurfaces, compares their characteristics, and presents the latest advances in research. Additionally, it highlights applications in wireless communications, energy harvesting, sensing, and beyond. fractal antennas; reflectarray; metasurfaces; microwaves; metamaterial absorbers +
Footnote †: journal: _Applied_  
0000-0001-5000-0000-0000-0000-0000-0000-0000-0000-0000-00000-0000-0000-0000-00000  
widely used in the following application fields, which are just a few examples of their wide-ranging applications:  
* computer graphics and animation, to generate realistic and visually appealing natural landscapes, trees, clouds, and textures;
* data compression techniques, to reduce the size of digital files;
* image and signal processing, to extract features from images, detect patterns, and provide efficient methods for image compression and reconstruction;
* biology, to describe the growth of plants and the organization of neurons in the brain;
* antenna theory and metamaterials, to design compact/multiband antennas and innovative metasurfaces. Currently, fractal geometry continues to find new and innovative uses across various scientific, artistic, and technological disciplines. In electromagnetic (EM) technology, fractal shapes are proving very interesting for applications requiring miniaturization, from antennas to metamaterials and frequency selective surfaces (FSSs). The use of fractal geometries in conventional antennas can increase their electrical length, thus reducing the overall size of resonant structures. Moreover, the self-similar nature of fractal shapes makes them ideal for achieving multiband or broadband resonant structures. The inherent miniaturization capabilities of fractals are particularly attractive for the design of reflectarrays, phased array antennas, metamaterial absorbers, and metasurfaces for various applications. Indeed, the use of very small array elements can offer several advantages, such as the reduction in mutual coupling or the ability to work with an array lattice with very small inter-element spacing, ensuring good scanning performance and a higher level of angular stability. For all the above reasons, fractal antennas and metasurfaces represent two fascinating research areas in the field of electromagnetics that have attracted considerable attention in recent years [8; 9; 10]. Both concepts offer unique ways to manipulate and control electromagnetic waves, leading to a wide range of applications in wireless communications, radar systems, and sensing [11; 12]. Their self-similarity property enables them to be compact in size, while maintaining excellent electromagnetic responses. This compactness is particularly advantageous in space-constrained applications, such as mobile devices, RFID tags, and aerospace systems [11; 12]. Figure 1: Examples of fractal shapes/curves: (**a**) Cantor set, (**b**) Sierpinski triangle, (**c**) Koch curve, (**d**) Mandelbrot set. The use of fractal antennas and metasurfaces has the potential to significantly improve wireless communications, imaging, and radar systems by enabling compact, high-performance devices with enhanced functionalities. Furthermore, fractal geometries are increasingly used in designing microwave sensors for materials diagnostics due to their ability to operate in multiple frequency bands and their miniaturization capabilities [13; 14; 15; 16; 17].