Let us consider that β and γ may be tuned at convenience. Thus β ≤ k$_{‖}$ < √ β 2 + γ 2 so that we might apply any spectral band (i.e. ordinates in Fig. 2) arbitrarily. In our model it is reasonable to think of √ β 2 + γ 2 denoting the cut-off frequency ¯ β$_{c}$ = 2 $_{π}$√$_{¯}$ ϵ$_{d}$/λ$_{0}$ associated with the uniform external medium of dielectric constant ¯ ϵ$_{d}$ where the source field is driven. In a great number of examples given below ¯ β$_{c}$ = β$_{max}$ yielding ¯ ϵ$_{d}$ = 2 . 89; in this medium the wavelength ¯ λ$_{d}$ = λ$_{0}$$_{/}$√$_{¯}$ ϵ$_{d}$ = 324 nm and the minimum spot size of the zero-order Bessel beam is (Δ$_{x}$)$_{min}$ = 2 . 253 /γ = 116 nm where the maximum value of γ = ¯ β$_{c}$ at β = 0. In other hand, our model neglects filtering (apodizing) effects and aberrations on the wave fields induced at the boundaries of the system [10]. However, conventional techniques for its compensation might be employed in order to find a good agreement with our results. Otherwise the theory remains valid leaving the appropriate estimation of the spectrum a$_{K}$ . To illustrate the focus generation along the z -axis, we perform a numerical simulation in the periodic layered medium of p = 450 nm (and ϵ$_{d}$ = 2 . 25) with metallic films of w = 50 nm and ϵ$_{m}$ = − 15 . 0. In Fig. 5 we show the field intensity | h$_{x}$ | 2 for a nondiffracting beam of propagation constant β = 18 . 90 µ m − 1 ( β = β$_{c}$$_{1}$ ), which spatial spectrum is given by Eq. (26) with γ = 4 . 462 µ m − 1 ( γp = 2 . 008). Thus the maximum value of k$_{‖}$ reaches a value coinciding with β$_{max}$ , i.e. β$_{c}$$_{1}$ ≤ k$_{‖}$ < β$_{max}$ corresponding to the first band of allowed frequencies shown in Fig. 2. The isofrequency curve K = K ( k$_{x}$ ) is also depicted in the inset of the figure, where excited frequencies k$_{x}$ are shaded in blue. The intensity is maximum at the origin but the pattern exhibits no radial symmetry. The field distribution along the abscissa, resembles that of the source field that would propagate in the homogeneous dielectric medium of ¯ ϵ$_{d}$ = 2 . 89. We point out that some discrepancies arise in Eq. (27) if some spatial fre- quencies k$_{x}$ are excited but, because of the presence of a gap, they do not contribute to the resulting propagating wavefield; this case will be treated ahead. From Eq. (27) we derive that the FWHM of the intensity peak along this direction is inversely proportional to γ following Δ$_{x}$ = 2 . 253 /γ . In our case Δ$_{x}$ = 505 nm, which is above the wavelength in the dielectric host λ$_{d}$ = λ$_{0}$/ √ ϵ$_{d}$ (= 367 nm). However, the behavior along the ordinate is signif- 11 h$_{x}$ ( x, y = 0) = 2 ∫ π/ 2 − π/ 2 cos ( γx cos φ ) dφ = 2 πJ$_{0}$ ( γx ) , (27) IV. SUBWAVELENGTH TRANSVERSE PATTERNS: NUMERICAL RESULTS