Tightly focusing vector beams containing V-point polarization singularities

Abstract

We show theoretically and numerically that an n-th order vector light field containing the central V-point singularity of indefinite linear polarization with polarization singularity index n, with a 'flower' 2(n – 1)-petal polarization pattern centered on it, produces an intensity pattern with 2(n – 1) local maxima at the tight focus. Meanwhile, a vector light field with polarization singularity index –n, leading to a 'web' of polarization singularities composed of 2(n + 1) cells, is tightly focused into an intensity pattern with 2(n + 1) intensity maxima. At the intensity nulls at the focus, either 2(n – 1) or 2(n + 1) V-points with alternating + 1 or –1 indices are produced. In addition, we study more general vector fields of the order (n, m) and analytically derive their Poincare-Hopf indices for many values of n and m. Application areas of such light fields with polarization singularities are laser information technologies, laser material processing, microscopy and optical trapping.