Focus shaping of tightly focused axially symmetric polarized beams by diffractive optical elements

We study the focus shaping of tightly focused axially-symmetric polarized beams by diffractive optical elements, introduce the basic theory of beam shaping and derive the mathematical expressions of focusing field in a high-NA focusing system. We further design two DOEs to achieve an optical chain and an optical distribution of multiple ultrasmall focused spots with a long depth of focus respectively, which may find wide applications in optical tweezers, optical storage, microscopy and so on.