  Controlling light scattering by nanoparticles is fundamentally important for
the understanding and the control of light with photonic nanostructures, as
well as for nanoparticle scattering itself, including Mie scattering. Here, we
theoretically and numerically investigate the possibility to manipulate
nanoparticle scattering by wavefront shaping that was initially developed to
control light scattered by large numbers of nanoparticles in nanophotonic
media. By employing a scattering matrix analysis, we find that even a single
nanoparticle supports multiple strongly scattering eigenchannels, suggesting
wavefront shaping as a promising tool to manipulate scattered light of a single
nanoparticle. By sending in shaped wavefronts, we selectively excite
eigenchannels, as is apparent from the distinct field distributions. These
scattering eigenchannels are related to different resonant leaky modes of the
scatterer, that reveal remarkable localized "hot spots" where the field is
substantially enhanced. Moreover, we investigate the backscattered spectra; to
this send in wavefronts relevant for a particular eigenchannel, and observe
that the backscattered spectrum reveals not only the excited channel but also
several others. This result points to the existence of short and long-range
spectral correlations for an eigenchannel. Our work offers a flexible tool to
manipulate light scattering of a single nanoparticle, and thus opens new
possibilities to control field patterns and light-matter interactions in a
nanoparticle, as well as to explore new features of nanoparticle scattering
such as the spectral correlation and temporal response of light scattered by
nano scatterers, including Mie spheres.
