Generation of a sub-wavelength sized optical needle with arbitrary longitudinal rotation

We show that under tight focusing conditions, arbitrarily rotating the longitudinally polarized optical needle in space is possible. Applying the Richards and Wolf vector diffraction methods, the explicit expressions underlying the simultaneous control depth of focus (DoF), intensity suppression of the sidelobes, as well as the orientation of the optical needle can be obtained, and then the strength vectors of the three-dimensional electromagnetic fields can be calculated. Calculations reveal that the sidelobe suppression ratio reaches 5.35% of the principal lobe, the optimal DoF is 5.1λ, and the maximum length is about 18.2λ. In addition, we specify the necessary conditions for rotating the sub-wavelength sized optical needle in the longitudinal field. Such an optical needle with controllable length, purity, and orientation can provide a flexible approach and additional degree of freedom for 3D precise fabrication and some other potential application areas.