  Simultaneous scattering invisibility and free-space field enhancement have
been achieved based on multipolar interferences among all-dielectric
nanoparticles. The scattering properties of all-dielectric nanowire quadrumers
are investigated and two sorts of scattering invisibilities have been
identified: the trivial invisibility where the individual nanowires are not
effectively excited; and the nontrivial invisibility with strong multipolar
excitations within each nanowire, which results in free-space field enhancement
outside the particles. It is revealed that such nontrivial invisibility
originates from not only the simultaneous excitations of both electric and
magnetic resonances, but also their significant magnetoelectric
cross-interactions. We further show that the invisibility obtained is both
polarization and direction selective, which can probably play a significant
role in various applications including non-invasive detection, sensing, and
non-disturbing medical diagnosis with high sensitivity and precision.
