Super-Diffraction Longitudinally Polarized Optical Needle With Ultra-Long Focal Depth Generated by a Radially Polarized High-Dimensional Circular Hollow Sinh-Gaussian Beam

In this paper, the incident beam called high-dimensional circular hollow sinh-Gaussian (HD-CHsG) beam with a novel wavefront is proposed, which is determined by three parameters (
m
,
σ
₀
,
σ
₁
). Based on the Richards-wolf vector diffraction theory, it can be focused into a longitudinal polarized optical needle through a high numerical aperture lens. The effects of the three parameters (
m
,
σ
₀
,
σ
₁
) on the resolution and depth of focus of the longitudinally polarized optical needle are simulated and analyzed. In the condition of (
m
,
σ
₀
,
σ
₁
) = (8, 0.6, 0.125), a super-diffraction longitudinal optical needle with ultra-long focal depth (resolution 0.40
λ
, focal depth 18.36
λ
, depth-to-width ratio 45.9:1) is generated. In addition, compared with a radially polarized incident beam whose amplitude distribution is Gaussian and circular hollow sinh-Gaussian (CHsG) distribution, the resolution and depth of focus of the longitudinally polarized optical needle obtained by focusing the HD-CHsG beam are higher. Both simulations and experiments are carried out to demonstrate the availability of our method. Our findings are of great significance to the production, manipulation, and application of longitudinally polarized optical needle.