# Optimization Design for Sparse Planar Array in Satellite Communications
## 3 Sparse Surface Array and Material Design
### Sparse Planar Array Material Design  
In sparse planar array optimization design, the array material is a crucial factor influencing array performance and cost. [PERSON]'s equations and constitutive relationships are important physical bases for designing materials in the field of array material design. [PERSON]'s equations and their constitutive relations establish that materials significantly influence the propagation of electromagnetic waves. Antenna array polarization serves as a parameter describing the spatial directivity of the electromagnetic wave vector radiated by an antenna array. As per [PERSON]'s theory, alternating electric and magnetic fields intersect perpendicularly. During electromagnetic wave transmission, when the direction of the electric field vector remains fixed or rotates according to specific rules, this wave is referred to as a polarized wave. The polarization direction of an antenna array refers to the direction of the generated electric field. When the receiving and transmitting antennas share identical polarization modes, the highest receiving efficiency and signal level are  
Figure 10: Array layout: (**a**) sparse planar arrays; (**b**) thinned planar arrays. obtained. In satellite communication scenarios, patch antennas or slot feeding are commonly used to achieve the desired polarization mode. Alternatively, in the design of polarized reconfigurable antennas, the polarization mode can be switched through array material and feed network adjustments. Ultimately, hybrid multi-polarization can be achieved. When designing spaceborne antenna pattern reconfigurable antennas, two design approaches are generally adopted. One is to design a parasitic unit around the main radiation unit of the antenna and change the beam width and antenna gain of the antenna by increasing the physical size of the antenna aperture. Another is to add parasitic layers and etching gaps or use partial reflective surface antennas to change the beam width and antenna gain of the antenna without changing the physical size of the antenna aperture. In recent years, metamaterial technology has reached new heights and has become one of the most investigated frontier technologies. Metamaterial technology can break through the traditional thought of material design, enabling artificial composite structures or composite materials with extraordinary physical properties that natural materials do not have. The unique properties of metamaterials make them well-suited for the development of functional devices, including antennas. It is worth noting that atoms serve as the smallest unit of traditional materials, and both the permittivity \(\varepsilon\) and the permeability \(\mu\) are positive, while metamaterials analogize periodic units to atoms, which can achieve negative values of \(\varepsilon\) and/or \(\mu\). Metamaterial technology has found application in optimizing the design of satellite arrays for use in satellite communication scenarios. For instance, in [15], a high-impedance surface (HIS) structure was utilized to improve the surface wave and wide beam radiation performance of a single antenna element, enhance the wide scanning performance of phased arrays, increase gain while improving the scanning angle range, and facilitate a low-profile array design. In [16], the authors employed an artistic magnetic conductor structure (AMC) to design a broadband planar phased array antenna, broaden bandwidth, enhance phased array beam steering performance, and reduce array size and cost. Similarly, in [17], the electronic bandgap (EBG) structure was used to design a sparse planar array with broadband and wide-angle scanning capabilities, enabling lightweight array design and reduced array fabrication costs. Metamaterial technology offers new possibilities for developing optimization ideas for sparse planar arrays.