of the excited field in the linear medium is ideally maintained for infinitely-long distances. Let us consider a monochromatic nondiffracting beam propagating in a multilayered medium. The y -axis is set such that it is perpendicular to the surfaces separating the metallic media and the adjacent dielectric media, so that n = ˆ y . In Fig. 1 we show schematically the multilayered system. The width of a metallic slab is w , an element periodically replicated at a distance p along the y -axis. We also assume that beam propagation is directed along the z -axis, so that we may cast the electromagnetic fields as being ω the frequency of the monochromatic radiation. The homogeneity of the wave field in the coordinate z is explicitly parametrized in terms of the propagation constant β . More specifically, we study TM waves where H exists only onto planes parallel to the metal- dielectric interfaces, and therefore which component h$_{y}$ vanishes. Later on we additionally consider wave confinement around the origin ( x, y ) = (0 , 0) in any given transverse plane. The Maxwell’s equations provide some relations between the transverse fields e and h . The electric field e may be derived from h by means of the equation ∇ × H = − iωϵ$_{0}$ϵ E , where ϵ ( y ) is the relative dielectric constant of the foliar structure. Thus we have From the equation ∇ ( µ$_{0}$ H ) = 0 we also find so that h$_{x}$ is the scalar wavefield from which we may describe the nondiffracting beam unambiguously. Let us point out that alternate routes for the description of electromagnetic diffraction-free beams may be found elsewhere [15–17]. 3 h$_{z}$ = iβ − $^{1}$∂$_{x}$ h$_{x}$, (3) e$_{x}$ = i ( ωϵ$_{0}$ϵ ) − 1 ∂$_{y}$h$_{z}$, (2a) e$_{y}$ = i ( ωϵ$_{0}$ϵ ) − $^{1}$( iβh$_{x}$ − ∂$_{x}$h$_{z}$ ) , (2b) e$_{z}$ = − i ( ωϵ$_{0}$ϵ ) − 1 ∂$_{y}$h$_{x}$. (2c) E ( x, y, z, t ) = e ( x, y ) exp ( iβz − iωt ) , (1a) H ( x, y, z, t ) = h ( x, y ) exp ( iβz − iωt ) , (1b) II. IN-PLANE PROPAGATION OF DIFFRACTION-FREE BEAMS IN METALLO- DIELECTRIC LAYERED MEDIA