Optomechanical Self-Stability of Freestanding Photonic Metasurfaces

We develop an analytical framework for self-stabilizing optical manipulation of freestanding metasurfaces in three dimensions. Our framework reveals that the challenging problem of stabilization against translational and rotational perturbations in three dimensions is reduced to a simpler scattering analysis of the metasurface unit cell in two dimensions. We derive universal analytical stiffness coefficients applicable to arbitrary three-dimensional radial metasurfaces and radial beam intensity profiles. The analytical nature of our framework facilitates highly efficient discovery of optimal optomechanical metasurfaces. Such use of metasurfaces for mechanical stabilization enables macroscale and long-range control in collimated, but otherwise unfocused light beams, and could open up new avenues for manipulation beyond traditional optical tweezing and transport.