content_image/341601.jpg content_image/341600.jpg content_image/341599.jpg
of the excited field in the linear medium is ideally maintained for infinitely-long distances. 

## II. IN-PLANE PROPAGATION OF DIFFRACTION-FREE BEAMS IN METALLO- DIELECTRIC LAYERED MEDIA 

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 

<img src='content_image/341601.jpg'>

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 

<img src='content_image/341600.jpg'>

<img src='content_image/341599.jpg'>

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]. 

