  Electromagnetic waves in vacuum and most materials have transverse
polarization. Longitudinal electromagnetic waves with electric field parallel
to wave vector are very rare and appear under special conditions in a limited
class of media, for example in plasma. In this work, we study the dispersion
properties of an easy-to-manufacture metamaterial consisting of two
three-dimensional cubic lattices of connected metallic wires inserted one into
another, also known as an interlaced wire medium. It is shown that the
metamaterial supports longitudinal waves at extremely wide frequency band from
very low frequencies up to the Bragg resonances of the structure. The waves
feature unprecedentedly short wavelengths comparable to the period of the
material. The revealed effects highlight spatially dispersive response of
interlaced wire medium and provide a route toward generating electromagnetic
fields with strong spatial variation.
