  We demonstrate numerically the diffraction-free propagation of sub-wavelength
sized optical beams through simple elements built of metal-dielectric
multilayers. The proposed metamaterial consists of silver and a high refractive
index dielectric, and is designed using the effective medium theory as strongly
anisotropic and impedance matched to air. Further it is characterised with the
transfer matrix method, and investigated with FDTD. The diffraction-free
behaviour is verified by the analysis of FWHM of PSF in the function of the
number of periods. Small reflections, small attenuation, and reduced Fabry
Perot resonances make it a flexible diffraction-free material for arbitrarily
shaped optical planar elements with sizes of the order of one wavelength.
