We theoretically analyze Airy beams by solving the exact vectorial Helmholtz equation using boundary conditions at a diffraction aperture. As result, the diffracted beams are obtained in the whole space; thus, we demonstrate that the parabolic trajectories are larger than those previously reported, showing that the Airy beams start to form before the Fourier plane. We also demonstrate the possibility of using a new type of Airy beams (SAiry beams) with finite energy that can be generated at the focal plane of the lens due to diffraction by a circular aperture of a spherical wave modified by a cubic phase. The finite energy ensured by the principle of conservation of energy of a diffracted beam.

In this paper, we describe a photopolymerizable silica glass based on acrylamide (AA) and N,N’-methylenebisacrylamide (BMA) as monomers, triethanolamine (TEA) as coinitiator and yellowish eosin (YE) as photoinitiator. We studied different compositions, analyzing the diffraction efficiency, energetic exposure and effective thickness obtained in the holographic gratings. A diffraction efficiency of 60 % with an energetic exposure of 139 mJ/cm ² and an effective thickness of 1.1 mm were obtained. Also, by varying the photopolymerizable composition of the material diffraction efficiencies higher than 80 % can be reached with an energetic exposure of 10 mJ/cm ² and an effective thickness of 113 µm. These values are similar to those obtained in conventional photopolymer systems in polyvinylalcohol and better than the values reached in other sol-gel compositions. Also, 9 holograms were angular multiplexed with diffraction efficiencies between 6 and 12 % and total exposure time shorter than 150 ms, with a dynamic range M/#=2.4.

We analyze the near-field focalization properties of perfect black Fresnel Zone Plates (FZPs) through the exact solutions of Maxwell equations for radially polarized fields obtained by means of Luneburg vector diffraction theory. The electromagnetic fields are computed assuming Hermite-Gauss and Bessel-Gauss beams as boundary conditions at the FZP plane z=0, which allows us to demonstrate that the total intensity is necessarily focused at z=0 and thus there is not much improvement of the intensity resolution at the focal plane. On the other hand, the Poynting vector exhibits multiple vortices and saddle points in the near-field region while its z component vanishes at the FZP axis and has a large focal depth as well as several residual contributions outside the focal region. These facts suggest that perfect black FZPs do not focus radially polarized fields at the designed focal length when such length is comparable to the wavelength (or smaller). Our results are very similar to the ones obtained for phase FZPs and they are in good agreement with FDTD simulations.