Vectorial approach to Huygens's principle for plane waves: circular aperture and zone plates.

A vectorial equation that describes the Huygens principle was reported, and an expression for the secondary-spherical-wave energy density was found. With a vectorial formulation, we performed an exact calculation for the relative axial intensity of the wave diffracted by an illuminated circular aperture. The off-axis intensity in Fresnel's and Fraunhofer's approximations was calculated. The zone plate was also studied by vectorial formulation. We showed that with increasing number of rings, the intensity maxima magnify as (2n + 2)(2), their full widths decrease, their positions remain unchanged, and secondary maxima appear, in a behavior similar to that for diffraction gratings.