Focusing property of high numerical aperture photon sieves based on vector diffraction

Photon sieves (PS) vector diffraction model and focus property with polarized illumination are proposed for the first time. The existing PS theories are limited to the scale diffraction. And for its special structure, the PS vector diffraction property is different from that of traditional optical elements and hard to be calculated. In order to describe the property of the PS with high numerical aperture (NA) exactly, the optical field of PS based on vector diffraction is proposed. Based on the vector diffraction model, simulations are carried out to analyze the focus property of the high NA PS while the illumination polarizations are linear, radial, and azimuthal. It shows that the focus property of the high NA PS changes with the polarization of the illumination. Therefore, in the applications of high NA PS, the illumination polarization needs to be considered. Furthermore, to describe the property of high NA PS, the vector diffraction model must be used instead of the scalar one. The vector diffraction model and polarization property of the PS proposed in this study not only improve the existing PS theories, but can also be used in the further design and analysis of the high NA PS.