Tightly focusing vector beams containing V-point polarization singularities. (January 2022) - Kotlyar, Victor V.; Kovalev, Alexey A.; Stafeev, Sergey S.; Nalimov, Anton G.; Rasouli, Saifollah
Highlights: Field with n -order polarization vortex has a V-point with Poincare-Hopf and Stokes indices n and 2 n . When tightly focused, such a vector field produces 2( n – 1) local intensity maxima on a circle. Between these maxima, 2( n – 1) V-point singularities exist with alternating indices + 1 and –1. An intensity null, or a V-point with the index –( n – 2), occurs at the center in the focal plane. In a number of cases for an ( n, m )-order field, indices of V-points have been derived analytically. 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.