  Recently, the coupling of two different modes of a homogeneous plasmonic
particle and their sharply varying spectra were elucidated as Fano resonances;
an 'interference' of two spatially orthogonal modes driving each other. On the
other hand, the scattering (and extinction) cross-section of a non-absorbing
dielectric particle is always the sum of the cross-sections of all mode
numbers; and this rules out any such Fano type interference between two
different mode numbers. So delectric particles exhibit an interference
structure in their extinction spectra only if it manifests in the individual
modes describing the scattered field of the particle. We show that in a
all-dielectric core-shell particle such strong interferences in multiple mode
numbers can be attained, and notably even as a spectral region of transparency
and directional scattering of incident light. Here interference between the
complementary normal modes of the nanoshell and core regions can be realized
for each mode number, resulting in a sharp interference structure in the
extinction of the particle. This manifests as spectral regions of
minimal/maximal interaction with the incident electromagnetic field. Such
spectral properties are significant for many applications where the
non-radiative losses of plasmonic structures are a liability. Note that this
behaviour is useful for optical antennas, cloaking materials and a quantum
mechanical interpretation of this classical effect may be signicant for
single-photon based applications.
