  We report on a chiral nanostructure, which we term a "butterfly nanoantenna,"
that, when used in a metasurface, allows the direct conversion of a linearly
polarized beam into a nonlinear optical far-field of arbitrary complexity. The
butterfly nanoantenna exhibits field enhancement in its gap for every incident
linear polarization, which can be exploited to drive nonlinear optical emitters
within the gap, for the structuring of light within a frequency range not
accessible by linear plasmonics. As the polarization, phase and amplitude of
the field in the gap are highly controlled, nonlinear emitters within the gap
behave as an idealized Huygens source. A general framework is thereby proposed
wherein the butterfly nanoantennas can be arranged on a surface to produce a
highly structured far-field nonlinear optical beam with high purity. A third
harmonic Laguerre-Gauss beam carrying an optical orbital angular momentum of 41
is demonstrated as an example, through large-scale simulations on a
high-performance computing platform of the full plasmonic metasurface with an
area large enough to contain up to 3600 nanoantennas.
