conditions, it cannot be found a point other than the origin from the xy plane where such a phase matching holds. As a consequence, a strong localization of the nondiffracting beam is expected to occur around the z -axis, such a line unquestionably constituting a focus. At this point of our analysis it is interesting to review the concept of focus wavefields in a system such as the uniform dielectric medium, where nondiffracting solutions of the wave equation are well known. Obviously we are speaking of Bessel beams [1]. Such a system would result from setting w = 0 in the layered medium of Fig. 1 to remove the metallic films from the dielectric host. In this case Eq. (18) leads trivially to the solutions K$_{±}$ = ± k$_{yd}$ . Also h$_{K}$ ( y ) = 1 in the whole xy plane. The phase matching condition at the origin is also observed over a radially-symmetric transverse pattern if in addition a$_{K}$ is in direct proportion to | dφ/dk$_{x}$ | = | − 1 /K | , where φ is the polar angle in the k$_{x}$K plane. Thus inserting the transverse wave number and r the radial spatial coordinate. See Ref. [10] for further details. We point out that excitations of the type a$_{K}$ = 1 / | K | [if Im ( K ) = 0, a$_{K}$ = 0 otherwise] also provide paraxial Bessel beams in periodic media [11] and in anisotropic crystals [24]. A field spectrum like that of Eq. (24) may be experimentally attained using an opaque screen, with a centered extremely-thin transparent annulus, placed at the front focal plane of a perfect lens [4]. Highly-efficient approaches may be found using conical lenses [25, 26] and mirrors [27], Fabry-Perot interferometers [28], leaky screens [29–31], and diffractive optical elements [32–34]. Using such devices as external sources in our system would excite the required diffraction-free wavefields in the layered medium. For simplicity we assume that the spectral strength of such nondiffracting beams has a form following Eq. (24), and a$_{K}$ = 0 if | k$_{x}$ | ≥ γ . 10 a$_{K}$ = 1 √ γ 2 − k 2 x , for | k$_{x}$ | < γ, (26) k$_{⊥}$ = √ β 2 c − β 2 (25) a$_{K}$$_{±}$ =   1 √ β 2 $_{c}$− ( k 2 $_{x}$+ β 2 $_{)}$, if | k$_{x}$ | < √ β 2 c − β 2 0 , otherwise (24)  into Eq. (5) yields the Bessel wavefield h$_{x}$ = 2 πJ$_{0}$ ( k$_{⊥}$r ) provided β < β$_{c}$ [see Eq. (19)], being