Longitudinally polarized beams have unique properties that are different from a traditional transversely polarized beam. By modulating the amplitude, phase and polarization of the incident beam, various longitudinal polarization fields can be obtained in a large-numerical aperture focusing system. Here we propose a simple and efficient method to generate longitudinally polarized light needle with pure phase element and radially polarized Gaussian beam. The phase element is designed with simulated annealing algorithm. The high purity longitudinally polarized light needle formed near the focal point has a horizontal full width at half maximum of 0.39λ and a non-diffraction distance of 4λ. This method can be employed to design other pure phase elements for generating beams with special longitudinal polarization distributions.
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