Shaping the focal field of radially/azimuthally polarized phase vortex   with Zernike polynomials
  The focal field properties of radially/azimuthally polarized Zernike polynomials are studied. A method to design the pupil field in order to shape the focal field of radially or azimuthally polarized phase vortex is introduced. With this method, we are able to obtain a pupil field to achieve a longitudinally polarized hollow spot with a depth of focus up to $12\lambda$ and $0.14\lambda$ lateral resolution for a optical system with numerical aperture 0.99; A pupil field to generate 8 circularly polarized focal spots along the optical axis is also obtained with this method. 
Lei Wei, H. Paul Urbach
physics.optics