Generation of optical needle and dark channel by tight focusing of radially polarized circular partially coherent beams

We theoretically investigate the tight focusing of radially polarized circular partially coherent (RPCPC) beams through a high numerical aperture objective. The sub-wavelength super-long optical needle and dark channel can be obtained near the focus, by engineering the source coherent length of the incident RPCPC beams. The length of the optical needle and the dark channel can be adjusted, and the obtained maximal lengths of the optical needle and the dark channel are both 22λ. The full width at half maximum of the optical needle and the dark channel are 0.6λ and 0.48λ, respectively.