  Tunable directional scattering is of paramount importance for operation of
antennas, routing of light, and design of topologically protected optical
states. For visible light scattered on a nanoparticle the directionality could
be provided by the Kerker effect, exploiting the interference of electric and
magnetic dipole emission patterns. However, magnetic optical resonances in
small sub-100-nm particles are relativistically weak. Here, we predict
inelastic scattering with the unexpectedly strong tunable directivity up to
5.25 driven by a trembling of small particle without any magnetic resonance.
The proposed optomechanical Kerker effect originates from the vibration-induced
multipole conversion. We also put forward an optomechanical spin Hall effect,
the inelastic polarization-dependent directional scattering. Our results
uncover an intrinsically multipolar nature of the interaction between light and
mechanical motion. They apply to a variety of systems from cold atoms to
two-dimensional materials to superconducting qubits and can be instructive to
engineer chiral optomechanical coupling.
