interference (nearly in-phase) of the Bloch modes from the second band. On other hand, self-collimation is attributed exclusively to the stationary points ( k$_{xs}$, K$_{s}$ ) = (0 , ± π/p ) giving θ = ± 48 deg ( φ$_{s}$ = ± 42 deg as seen above). Setting γp = 3 . 148 as shown in Fig. 7(b), the bandgap β$_{c}$$_{2}$ < k$_{‖}$ < β$_{c}$$_{1}$ is encountered, that is frequencies satisfying γ$_{c}$$_{1}$ < | k$_{x}$ | < γ$_{c}$$_{2}$ are frustratedly excited (being γ$_{c}$$_{1}$p = 2 . 552 and γ$_{c}$$_{2}$p = 3 . 148), so that the optical system behaves like a low-pass filter. In this case and C ( c 1) 0 = 4 φ$_{c}$$_{1}$ . We point out that J$_{2}$$_{m}$ (0) = 0 for m = 0 so that in the vicinities of the focal point we have h$_{x}$ ≈ (2 π − 4 φ$_{c}$$_{1}$ ) J$_{0}$ ( γx ). However the central peak stretches slightly, specifically Δ$_{x}$ = 459 nm, whereas sidelobes are altered significantly as expected. Moreover, FWHM in the direction of the periodicity Δ$_{y}$ = 61 . 58 nm and self-collimation angles θ = ± 48 deg are also maintained is spite of bandgaps. Finally, arriving at γp = 3 . 734 we are able to excite every allowed spatial frequency in the first band since ( k$_{‖}$ ) max = β$_{max}$ . The intensity | h$_{x}$ | 2 is depicted in Fig. 7(c) showing notable differences from the cases previously analyzed. For instance, the FWHM along the x -axis is Δ$_{x}$ = 277 nm, which is close to the value we would obtain if we ignore the bandgap. In this case Δ$_{x}$ is lower than the radiation wavelength in the dielectric λ$_{d}$ = 367 nm; however this subwavelength size is still higher than λ$_{d}$/ 2 in the same order than a regular Bessel beam. Here we may evaluate the wavefield by where γ cos φ$_{c}$$_{2}$ = γ$_{c}$$_{2}$ . Sidelobes are also strongly attenuated in all directions; even at those associated with self-collimation. Here θ = ± 48 deg ( φ$_{s}$ = ± 42 deg) and also θ = ± 17 deg ( φ$_{s}$ = ± 73 deg); as a consequence, sharing the power radiated in this large number of directions leads to the weakening of the photon-focusing effect. More importantly, the high sidelobe appearing previously in the y -axis seems to be wiped out completely. This effect h$_{x}$ ( x, y = 0) = 2 πJ$_{0}$ ( γx ) − h$_{xc}$$_{1}$ ( γx ) + h$_{xc}$$_{2}$ ( γx ) , (34) C ( c 1) m = 4 ( − 1) m sin (2 mφ$_{c}$$_{1}$ ) m , for m = 0 , (33) being 0 ≤ φ$_{c}$$_{1}$ < π/ 2 such that γ cos φ$_{c}$$_{1}$ = γ$_{c}$$_{1}$ , where h$_{x}$ ( x, y = 0) = 2 πJ$_{0}$ ( γx ) − h$_{xc}$$_{1}$ ( γx ) , (31) h$_{xc}$$_{1}$ ( γx ) = 2 ∫ φ$_{c}$$_{1}$ − φ$_{c}$$_{1}$ cos ( γx cos φ ) dφ = ∞ ∑ m =0 C ( c 1) m J$_{2}$$_{m}$ ( γx ) (32) 14