This study explores the topology optimization technique to design lightweight and compact antennae. The primary objective of this antenna design is to enable its operation across a broad and extensive frequency bandwidth. The optimization process revolves around manipulating the material distribution within the structure. This endeavor successfully yields a novel material distribution characterized by refractive indices spanning the range of 3 to 4. Subsequently, the antenna structure undergoes a binarization process, reducing its constituent features in size, thereby streamlining the fabrication process. The antenna design is accomplished by utilizing the commercial software platform COMSOL Multiphysics, specifically leveraging its optimization module. This scientific approach and methodology contribute to the advancement of metasurface antenna technology.