  The propagation and transmission of Bessel beams through nano-layered
structures has been discussed recently. Within this framework we recognize the
formation of unguided diffraction-free waves with the spot size approaching and
occasionally surpassing the limit of a wavelength when a Bessel beam of any
order n is launched onto a thin material slab with grazing incidence. Based on
the plane-wave representation of cylindrical waves, a simple model is
introduced providing an exact prescription of the transverse pattern of this
type of diffraction-suppressed localized waves. Potential applications in
surface science are put forward for consideration.
