  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.
