  Dual scatterers preserve the helicity of an incident field, whereas antidual
scatterers flip it completely. In this setting of linear electromagnetic
scattering theory, we provide a completely general proof on the non-existence
of passive antidual scatterers. However, we show that scatterers fulfilling the
refractive index matching condition flip the helicity of the fields very
efficiently without being in contradiction with the law of energy conservation.
Moreover, we find that this condition is paired with the impedance matching
condition in several contexts of electromagnetism and, in particular, within
Fresnel's and Mie's scattering problems. Finally, we show that index-matched
media induce a resonant helicity mixing on the propagating electromagnetic
waves. We reach to this conclusion by identifying that the refractive index
matching condition leads to the phenomenon of avoided level-crossing. Our
contribution not only closes a historical discussion within the Nanophotonics
community, but also opens up new possibilities in the fields of Metamaterials
and Particle Physics.

Optics