  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. 
Bidirectional invisibility in Kramers-Kronig optical media