Sharp Focusing of a Hybrid Vector Beam with a Polarization Singularity

The key result of this work is the use of the global characteristics of the polarization singularities of the entire beam as a whole, rather than the analysis of local polarization, Stokes and Poincare–Hopf indices. We extend Berry’s concept of the topological charge of scalar beams to hybrid vector beams. We discuss tightly focusing a new type of nth-order hybrid vector light field comprising n C-lines (circular polarization lines). Using a complex Stokes field, it is shown that the field polarization singularity index equals n/2 and does not preserve in the focal plane. The intensity and Stokes vector components in the focal plane are expressed analytically. It is theoretically and numerically demonstrated that at an even n, the intensity pattern at the focus is symmetrical, and instead of C-lines, there occur C-points around which axes of polarization ellipses are rotated. At n = 4, C-points characterized by singularity indices 1/2 and ‘lemon’-type topology are found at the focus. For an odd source field order n, the intensity pattern at the focus has no symmetry, and the field becomes purely vectorial (with no elliptical polarization) and has n V-points, around which linear polarization vectors are rotating.

Error Analysis and Optimization of a Sky Full-Polarization Imaging Detection System

An accurate sky polarization field map is a prerequisite for polarization navigation applications. In this article, a detector for sky full-polarization imaging detection is described, the major error-influencing factors (MEIFS ) are obtained, and the error propagation is modeled and analyzed. We reveal the relationship between the error of the inversed Stokes vector and the condition number of the detector matrix, which shows that the error of the inversed Stokes vector is affected by the Stokes vector of the incident light itself and the MEIFS together, with the MEIFS playing a decisive role. With the MEIFS optimized, the impact of detector error on the inversed Stokes vector is attenuated. A control equation for system calibration is also deduced which can establish the connection between the detector matrix design and calibration process. The work in this article provides a reference for optimization and calibration of sky full-polarization imaging detectors.