Design of DOE for generating a needle of a strong longitudinally polarized field

A needle of strong longitudinally polarized field with homogeneous intensity along the optical axis, long depth of focus, and subdiffraction beam size can be generated by focusing a radially polarized light with a high-NA lens and a diffractive optical element (DOE) with belts. A method combining the global-search-optimization algorithm and the tight focusing properties of the radially polarized light is proposed to design the DOE. Based on the tight focusing properties, the light incident on the lens is divided into two parts: areas A and B. We discover that the longitudinal field in the focal region is mainly dependent on the number of belts in area B but not the total number of belts in the DOE.