Through modulating the Bessel–Gaussian radially polarized vector beam by the cosine synthesized filter under a reflection paraboloid mirror system with maximum focusing semi-angle of π/2 , arbitrary-length super-Gaussian optical needles are created with consistent beam size of 0.36λ (full width at half maximum) and the electric field being pure longitudinally polarized (polarization conversion efficiency greater than 99%). Numerical calculations show that the on-axis intensity distributions are super-Gaussian, and the peak-valley intensity fluctuations are all within 1% for 4λ , 6λ , 8λ , and 10λ long light needles. The method remarkably improves the nondiffraction beam quality, compared with the subwavelength Gaussian light needle, which is generated by a narrow-width annular paraboloid mirror. Such a light beam may suit potential applications in particle acceleration, optical trapping, and microscopy.
Focusing of the plane wave with radially polarized electric field by an arbitrary opening paraboloid mirror is analyzed
using a rigorous vectorial diffraction theory, i.e., Stratton-Chu integral. In the vicinity of the focus, far-field
approximation conditions are used to simplify the derived integrals with sufficiently high accuracy. It is found that a
noticeable deviation of the approximate integral, as characterized by a phenomenon of focal shift, from the exact integral
can be observed when the maximum focusing semi-angle α below π/9. For α=π/2, the radial spot size reduces to below
0.40λ if cutting off the central segment, larger than π/4, of the paraboloid mirror. The sharp focusing property of the
paraboloid mirror has the potential application in super-resolution confocal scanning microscopy. Specific confocal
scanning arrangements are provided and remarked.