Modelling and numerical optimisation of refractive surface patterns for transmissive solar sails

Transmissive solar sail designs have been proposed with performance and utility benefits over traditional solar sails, particularly in low Earth orbit. The functional element of these new sails is their refractive or diffractive surface pattern. This paper explores the design of refractive sail patterns using numerical optimisation, and explores the validity of using model-free reinforcement learning algorithms for this purpose. In particular, the performances of triangular prism and semi-cylindrical lightfoil patterns from prior literature are iteratively improved. To do this, a ray tracing optical simulation was developed that models the solar radiation pressure and torque per unit area of illuminated, refractive patterns in a vacuum. Meanwhile, a numerical optimiser was developed to iteratively improve upon simulated patterns according to user-defined fitness functions. Depending on their purpose, patterns were optimised for either tangential-to-sail solar radiation pressure or self-stabilising corrective torque at a Sun-pointing attitude, or range of attitudes. The optimiser was shown to be capable of substantially improving the performance of optical elements, particularly through the harnessing of total internal reflection. In one case, the numerical optimiser was shown to improve the maximum tangential radiation pressure of an analytically optimised polystyrene prism pattern by 58%. In another case, the optimiser improved the peak corrective torque of a pattern of polyethylene terephthalate lightfoils by 74%. • Numerical optimiser uses internal reflections to improve refractive sail performance. • User-defined fitness functions enable automated, mission-specific sail optimisation. • Analytically optimal micro-prism patterns improved further by numerical optimisation. • Alternative lightfoil geometries improve peak torque but reduce stable angle range. • Lightfoil self-stabilisation behaviour the same for single element and patterned sail.