  A broad class of planar dielectric media with complex permittivity profiles
that are fully invisible, for both left and right incidence sides, is
introduced. Such optical media are locally isotropic, non-magnetic and belong
to the recently discovered class of Kramers-Kronig media [{\it Nature Photon.}
9, 436 (2015)], i.e. the spatial profiles of the real and imaginary parts of
the dielectric permittivity are related each other by a Hilbert transform. The
transition from unidirectional to bidirectional invisibility, and the
possibility to realize sharp reflection above a cut-off incidence angle, are
also discussed.
