The current frontier of human exploration is space. We have achieved sending rovers to planets and probes throughout the Solar System and beyond into interstellar space, yet the stars seemed to be out of reach. The current fastest man-made object would take thousands of years to travel to the nearest star, Proxima Centauri. However, Breakthrough Starshot presents an engineering challenge to reach it in a generation's time. Recent technological advancements make this possible through ultralight spacecraft equipped with mirror-like sails, known as Lightsails. Due to their structure, these sails could be propelled by lasers up to 20% light speed, or over 200 million km/h. To achieve the required efficiency, the sails need to exhibit high reflectivity and low mass on the scale of 1g, while covering a surface area of ∼10m2. Some materials and membranes explored in literature have exhibited high reflectivity, but their mass did not comply with the necessary requirements. The most promising current design is a photonic crystal, which interacts with light in a way that maximizes reflectivity and removes material by incorporating cavities into the surface, effectively reducing overall mass. Current research into photonic crystal Lightsails primarily focuses on the reflectivity of a small segment of a flat lattice. While this is essential, the literature suggests that the full-scale structures will probably behave like traditional sails on sailboats, tending to billow. This prompts us to consider not only the problem of reflectivity on curved surfaces but also mechanical deformations and stresses within a membrane that's 1000 times thinner than a human hair. This thesis investigates the full-scale design of the Lightsail from both the structural and electromagnetic sides. Firstly, the material, microstructure, and macrostructure of the Lightsail are analyzed to determine stresses and deformations, as well as the optimal shape for stress distribution and efficiency. Then, through topology optimization of shell elements, the main load-carrying "backbone" of the sail is identified. Secondly, optimization of unit cell photonic crystal cavities is performed across the curvature of the sail derived from the previously obtained shape, maximizing the reflectivity. Finally, the thesis proposes a design of the Lightsail that integrates all findings, which is then used to obtain a Figure of Merit value for comparison with designs in existing literature.