Longitudinal electromagnetic waves with extremely short wavelength

Electromagnetic waves in vacuum and most materials have transverse polarization. Longitudinal electromagnetic waves with an electric field parallel to the wave vector are very rare and appear under special conditions in a limited class of media, for example, in plasmas. In this Letter, 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 an 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 a spatially dispersive response of the interlaced wire medium and provide a route toward generating electromagnetic fields with strong spatial variations.