Diffractionless propagation through Kapitza stratified media

We show that in the presence of a rapidly modulated dielectric permittivity with a large modulation depth (Kapitza medium) a novel and robust regime of diffractionless electromagnetic propagation occurs. This happens when the mean value to depth ratio of the dielectric profile is comparable to the small ratio between the modulation period and the wavelength. We show that the standard effective medium theory is inadequate to describe the proposed regime and that, its occurrence is not substantially hampered by medium losses. We check the feasibility of the proposed regime by means of a large modulation depth metal-dielectric layered medium whose subwavelength imaging properties are analytically investigated.