Asymptotic stability of laser-driven lightsails: Orders of magnitude enhancement by optical dispersion engineering in gratings

Abstract

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 enhanced by orders of magnitude compared to plane-mirror sails. Therefore, relativistic effects can, in principle, provide comprehensive and realistic control over lightsail motion.

Figures (6)

• Figure 1: Plane reflectors or designs that are marginally stable (experience restoring mechanisms but not damping) are ejected from the beam due to continual perturbations. Restoring and damping mechanisms arising from a fully relativistic treatment can be harnessed in judiciously patterned membranes, ensuring the lightsail acquires its target velocity.
• Figure 2: (a) Axes, angles and velocity definitions. The sail depicted here consists of two diffraction gratings connected at the center of mass, $\mathbf{O}'$. Each grating has a unit cell comprising two rectangular resonators (shown in green and pink). The two gratings are mirror symmetric at $\mathbf{O}'$ with respect to the normal axis $\hat{\mathbf{g}}_1'$, forming a "bigrating". (b) Relativistic transformation of light momentum between (i) sail and (ii) laser reference frames. In (i), the incident laser momentum $\mathbf{p}_\text{inc}'$ is relativistically aberrated with non-zero angle $\theta'$ relative to $\hat{\mathbf{x}}'$ and appears Doppler redshifted compared to the laser light in (ii). (c) Damping torque on a planar mirror due to position-dependent Doppler shift.
• Figure 3: Comoving integration from time step $n$ to time step $n+1$ while recording position and velocity information in frame $\mathcal{L}$. In frame $\mathcal{L}$, the sail is nonrigid and nonuniformly Lorentz contracted. Note: $\mathcal{M}_n$ is defined by a Lorentz boost with no spatial translation, so the spatial origins of frame $\mathcal{M}_n$ and frame $\mathcal{L}$ coincide at $t^\mathcal{L}=t^\mathcal{M}=0$. However, for clarity, we have drawn axes where the origin of frame $\mathcal{M}_n$ coincides with the sail CoM.
• Figure 4: Bigrating sail, unit cell and optimization parameters.
• Figure 5: (a) Restoring coefficients, (b) damping coefficients, (c) real-part of eigenvalues and (d) imaginary part of eigenvalues over velocity/wavelength for the bigrating whose optimized relative permittivity profile is shown in the inset. The units of the restoring terms are: $[k^y_\phi] = m\per\square s\per rad$, $[k^\phi_y] = rad\per m\per\square s$, $[k^y_y] = [k^\phi_\phi] = \per\square s$, while the corresponding damping terms have the same units multiplied by 1s.