  We propose the optical trapping of Rayleigh particles using tailored
anisotropic and hyperbolic metasurfaces illuminated with a linearly polarized
Gaussian beam. This platform permits to engineer optical traps at the beam axis
with a response governed by nonconservative and giant recoil forces coming from
the directional excitation of ultra-confined surface plasmons during the light
scattering process. Compared to optical traps set over bulk metals, the
proposed traps are broadband in the sense that can be set with beams
oscillating at any frequency within the wide range in which the metasurface
supports surface plasmons. Over that range, the metasurface evolves from an
anisotropic elliptic to a hyperbolic regime through a topological transition
and enables optical traps with distinctive spatially asymmetric potential
distribution, local potential barriers arising from the momentum imbalance of
the excited plasmons, and an enhanced potential depth that permits the stable
trapping of nanoparticles using low-intensity laser beams. To investigate the
performance of this platform, we develop a rigorous formalism based on the
Lorentz force within the Rayleigh approximation combined with anisotropic
Green's functions and calculate the trapping potential of nonconservative
forces using the Helmholtz-Hodge decomposition method. Tailored anisotropic and
hyperbolic metasurfaces, commonly implemented by nanostructuring thin metallic
layers, enables using low-intensity laser sources operating in the visible or
the IR to trap and manipulate particles at the nanoscale, and may enable a wide
range of applications in bioengineering, physics, and chemistry.
