Analyzing the acceleration time and reflectance of light sails made from homogeneous and core-shell spheres

Deciding on appropriate materials and designs for use in light sails, like the one proposed in the Breakthrough Starshot Initiative, is a topic that requires much care and forethought. Here, we offer a feasible option in the form of metasurfaces made of periodically arranged homogeneous and core-shell spheres. Using the re-normalized T-matrix from Mie theory, we explore the reflectance, absorptance, and acceleration time of such metasurfaces. We focus on spheres made from aluminum, silicon, silicon dioxide, and combinations thereof. Since the light sails are foreseen to be accelerated using Earth-based laser arrays to 20% of the speed of light, one needs to account for relativistic effects. As a result, a high broadband reflectance is essential for effective propulsion. We identify metasurfaces that offer such properties combined with a low absorptance to reduce heating and deformation. We highlight a promising extension to the case of a metasurface made from homogeneous silicon spheres, as already discussed in the literature, by adding a layer of silicon dioxide. The high broadband reflectance of the silicon and silicon dioxide combination is explained by the favorable interference of the multipolar contributions of the outgoing field up to quadrupolar order. We also consider the impact of an embedding material characterized by different refractive indices. Refractive indices up to 1.13 maintain over 90% reflectance without re-optimizing the light sail.

💡 Research Summary

The paper addresses the design of light sails for the Breakthrough Starshot initiative, focusing on metasurfaces composed of periodically arranged homogeneous or core‑shell spheres. Using a renormalized T‑matrix formalism derived from Mie theory, the authors calculate the reflectance (R), absorptance (A), and acceleration time (τ) of such metasurfaces when illuminated by a ground‑based laser array (intensity I = 10 GW m⁻²) intended to accelerate gram‑scale probes to 0.2 c.

A key feature of the analysis is the inclusion of relativistic Doppler shift: as the sail accelerates, the incident wavelength in the sail’s frame stretches from λ₀ = 1 µm to λ′ = λ₀(1 + β)/γ(β), where β = v/c and γ is the Lorentz factor. The authors sample β in 50 equally spaced points over the interval