generation of invariant wavefields along with a finite axial distance. The estimation of such limits is similar for example to that corresponding to Bessel beams propagating in free space [1, 2], and therefore they are not discussed here. However we point out the decisive role of the structured medium in order to achieve the subwavelength beamsizes: these wavefields cannot be sustained in free space for ranges longer than a wavelength. Relevant aspects in near-field subwavelength nondiffracting beams are exhaustively investigated by Kukhlevsky and co-workers [40–43]. Finally, material losses are neglected in our analysis. Since Im( ϵ ) = 0 leads to wave damping in an unbounded dissipative system, absorption in the medium should be accounted for assuming a limited number of slabs. We have performed numerical simulations showing that the superresolving effect along the y -axis is practically maintained for a small absorption coefficient of the metallic medium and a moderate number of layers, whereas the peak slightly gets wider along the x -axis. Even assuming that the focus is placed at an interface near the center of the system, boundary effects and also tunnelling effects cannot be ignored. For instance, setting ϵ$_{m}$ = − 15 + i 0 . 15 we may excite a diffraction-free beam with a propagation constant β = 9 µ m − 1 and a central peak of Δ$_{x}$ = 139 nm and Δ$_{y}$ = 43 nm in a medium composed of 20 unit cells. The deterioration in resolution power along the x -axis is mainly caused by a selective increment in Im( K ) within the allowed spectral bands, an effect that is specially dramatic in the highest band. We have estimated that the central peak is also enlarged to a lesser extent by increasing the number of layers. Under these unfavourable conditions the beamsize is still surpassing the diffraction limit along the direction of the periodicity. On other hand, a significant attenuation of the focal intensity is also evident. In our numerical simulation, in-focus intensity decreases down to 18% (down to 6%) from its original value if Im ( ϵ$_{m}$ ) = 0 . 15 and the number of unit cells is 10 (20). A manuscript containing an extended analysis with further details is in preparation. 17