  We show that nonlinear multipolar interference allows achieving not only
unidirectional, but also non-reciprocal nonlinear generation from a
nanoelement, with the direction of the nonlinearly produced light decoupled
from that of at least one or several of the excitation beams. Alternatively, it
may allow inhibiting the specified nonlinear response in a nanoelement or in
its periodic arrangement by reversing the direction of one of the pumps. The
described phenomena exploit the fact that, contrary to the linear response
case, nonlinear magneto-electric interference stems from a combination of
additive and multiplicative processes and includes an interference between
various terms within the electric and magnetic partial waves themselves. We
demonstrate the introduced concept numerically using an example of a plasmonic
dimer geometry with realistic material parameters.
