  Engineered core-shell cylinders are good candidates for applications in
invisibility and cloaking.In particular, hyperbolic nanotubes demonstrate
tunable ultra-low scattering cross section in the visible spectral range. In
this work we investigate the limits of validity of the condition for
invisibility, which was shown to rely on reaching an epsilon near zero in one
of the components of the effective permittivity tensor of the anisotropic
metamaterial cavity. For incident light polarized perpendicularly to the
scatterer axis, critical deviations are found in low-birefringent arrangements
and also with high-index cores. We demonstrate that the ability of anisotropic
metallodielectric nanocavities to dramatically reduce the scattered light is
associated with a multiple Fano-resonance phenomenon. We extensively explore
such resonant effect to identify tunable windows of invisibility.
