  The study of invisibility of an infinite dielectric rod with high refractive
index is based on the two-dimensional Mie scattering problem, and it suggests
strong suppression of scattering due to the Fano interference between
spectrally broad nonresonant waves and narrow Mie-resonant modes. However, when
the dielectric rod has a finite extension, it becomes a resonator supporting
the Fabry-Perot modes which introduce additional scattering and eventually
destroy the invisibility. Here we reveal that for shorter rods with modest
values of the aspect ratio r/L (where r and L are the radius and length of the
rod, respectively), the lowest spectral window of the scattering suppression
recovers completely, so that even a finite-size resonator may become invisible.
We present a direct experimental verification of the concept of switchable
invisibility at microwaves using a cylindrical finite-size resonator with high
refractive index.
