Abstract
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 <i>z</i>=0, which allows us to
demonstrate that the total intensity is necessarily focused at <i>z</i>=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 <i>z</i> 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.
© 2011 IEEE
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