The two-dimensional Helmholtz equation may be of help in order to find any localized solution of the field h$_{x}$ . However it is preferable an alternative approach. Based on the Bloch theorem [18], we may describe the propagating wavefield h$_{x}$ as a superposition of Bloch modes having the form Assuming that sources are sufficiently far from the focal region of the localized beam, the role of evanescent waves [19] is negligible in our analysis and, therefore, they are disregarded setting a$_{K}$ = 0 if Im( K ) = 0. In this sense we also neglect material losses imposing that the relative dielectric constant of the medium is a real parameter of the problem [Im( ϵ ) = 0]. We point out that this is not strictly true in a realistic problem; plasma-like media with ϵ < 0 are necessarily dispersive since energy density considerations lead to the condition d ( ωϵ ) /dω > 0, and the presence of dispersion in general signifies dissipation of energy [20]. However, it is possible to neglect the absorption in a transparency window where the imaginary part of ϵ is very small in comparison with its real part. where k$_{x}$ is the (real) component of a wave vector along the x -axis, and K is the so-called Block wave number, which generally is multivalued for a given k$_{x}$ . Moreover, h$_{K}$ ( y + p ) = h$_{K}$ ( y ) is a periodic function, which is normalized as h$_{K}$ (0) = 1 for convenience, and a$_{K}$ is simply a field amplitude. In the case of the stratified medium shown in Fig. 1, the periodic function is conveniently written as the addition of two independent terms, h$_{K}$ = h + K + h − $_{K}$. Using the column vector we may write [21] where α is an integer that refers to a unique slab. The domains R$_{α}$ ≡ ( y$_{α}$$_{−}$$_{1}$, y$_{α}$ ] where y$_{0}$ = 0, y$_{1}$ = w and y$_{α}$$_{+2}$ = y$_{α}$ + p ; for instance, R$_{α}$ is associated with a region where the 4 h$_{K}$ ( y ) = exp ( − iKy ) T$_{α}$ ( y − y$_{α}$ ) v$_{α}$ , for y ∈ R$_{α}$, (7) h$_{K}$ =   h + K h − K   , (6) h$_{x}$ ( x, y ) = ∑ K ∫ ∞ −∞ a$_{K}$h$_{K}$ ( y ) exp ( ik$_{x}$x + iKy ) dk$_{x}$, (5) ( ∂ 2 x + ∂ 2 y + ω $^{2}$µ$_{0}$ ϵ$_{0}$ϵ − β $^{2}$) h$_{x}$ = 0 . (4)