Near-Field Electromagnetic Analysis of Perfect Black Fresnel Zone Plates Using Radial Polarization

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.