Near-field focusing properties of perfect black Fresnel zone plates are analyzed by solving Maxwell equations using the vectorial angular spectrum representation and the equivalent Rayleigh diffraction formulae of the first kind given by the Luneburg vector diffraction theory. Linear and circular polarizations are compared. As a result, an exact analytical expression for axial intensity is obtained showing that, in the near field, the shift of focal length is inherent in the diffraction process and independent of incident field polarization. The numerical intensity distribution of the electromagnetic field is also obtained, which allows us to demonstrate that when vectorial analysis of the system is performed, subwavelength focusing cannot be achieved for very short focal distances. This result is valid for linearly and circularly polarized incident fields. Finally, it is shown that symmetry of the focalized field is strongly dependent on the polarization of the incident field and that the vectorial diffraction theory can be a good alternative to finite-difference time-domain methods.
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