Asymptotic stability of laser-driven lightsails: Enhancement by optical dispersion engineering in gratings

Lightsails are promising spacecraft that can traverse interstellar distances within decades via radiation-pressure propulsion from high-power lasers. The envisioned missions crucially rely on the sail being confined within the propelling laser beam, requiring restoring and damping mechanisms for both translational and rotational degrees of freedom. Here, we use a two-dimensional rigid model to show that full asymptotic stability of planar nanophotonic sails can be achieved through purely optical, relativistic forces and torques, which damp all unstable degrees of freedom. By judiciously optimizing the angular and frequency dispersion of diffraction gratings, we find that damping can be substantially enhanced compared to plane-mirror sails. Over the full operating band for $0.2c$ missions it is several times larger, while over narrow wavelength bands, the enhancement is by three orders of magnitude. Therefore, relativistic effects can, in principle, provide comprehensive and realistic control over lightsail motion.