Lightweight photophoretic flyers with germanium coatings as selective absorbers

The goal of ultrathin lightweight photophoretic flyers, or light flyers for short, is to levitate continuously in Earth's upper atmosphere using only sunlight for propulsive power. We previously reported light flyers that levitated by utilizing differences in thermal accommodation coefficient between the top and bottom of a thin film, made possible by coating their lower surfaces with carbon nanotubes (CNTs). Such designs, though successful, had relatively high thermal emissivity (>0.5), which prevented them from achieving high temperatures and resulted in their transferring relatively low amounts of momentum to the surrounding gas. To address this issue, we have developed light flyers with ultrathin undoped germanium layers that selectively absorb nearly 80% of visible light but are mostly transparent in the thermal infrared, with an average thermal emissivity of 0.1. Our experiments show that germanium-coated light flyers could levitate at up to 43% lower light irradiances than mylar-CNT disks with identical sizes. In addition, we simulated our experiments using a semiempirical model, which allowed us to predict that our 2-cm-diameter disk-shaped germanium-coated light flyers can levitate in the mesosphere (altitudes 67--75 km) under the natural sunlight (1.36 kW/${\mathrm{m}}^{2}$). Similar ultrathin selective-absorber coatings can also be applied to three-dimensional light flyers shaped like solar balloons, allowing them to carry significant payloads and thereby revolutionize long-term atmospheric exploration of Earth or Mars.