  Optical properties of nanoparticles attract continuous attention owing to
their high fundamental and applied importance across many disciplines. Recently
emerged field of all-dielectric nanophotonics employs optically induced
electric and magnetic Mie resonances in dielectric nanoparticles with a high
refractive index. This property allows obtaining additional valuable degrees of
freedom to control optical responses of nanophotonic structures. Here we
propose a conceptually distinct approach towards reaching optical resonances in
dielectric nanoparticles. We show that lacking conventional Mie resonances,
low-index nanoparticles can exhibit a novel anisotropy-induced family of
non-Mie eigenmodes. Specifically, we investigate light interactions with
calcite and vaterite nanospheres and compare them with the Mie scattering by a
fused silica sphere. Having close permittivities and same dimensions, these
particles exhibit significantly different scattering behavior owing to their
internal structure. While a fused silica sphere does not demonstrate any
spectral features, the uniaxial structure of the permittivity tensor for
calcite and non-diagonal permittivity tensor for vaterite result in a set of
distinguishable peaks in scattering spectra. Multipole decomposition and
eigenmode analysis reveal that these peaks are associated with a new family of
electric and magnetic resonances. We identify magnetic dipole modes of
ordinary, extraordinary and hybrid polarization as well as complex electric
dipole resonances, featuring a significant toroidal electric dipole moment. As
both vaterite and calcite are biominerals, naturally synthesized and exploited
by a variety of living organisms, our results provide an indispensable toolbox
for understanding and elucidation of mechanisms behind optical functionalities
of true biological systems.
