Sharp focusing of beams with V-point polarization singularities

It is theoretically and numerically shown that when tightly focusing an n-th order vector light field that has the central V-point (at which the linear polarization direction is undetermined), the polarization singularity index n, and a "flower"-shaped intensity pattern with 2(n-1) lobes it forms a transverse intensity distribution with 2(n-1) local maxima. At the same time, a vector light field with the polarization singularity index -n, which has the form of a "web" with 2(n+1) cells generates at the sharp focus a transverse intensity distribution with 2(n+1) local maxima. In the focal spot, either 2(n-1) or 2(n+1) V-point polarization singularities with alternating indices +1 or -1 are formed at the intensity zero.

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.

An Online Contaminant Classification Method Based on MF-DCCA Using Conventional Water Quality Indicators

Emergent contamination warning systems are critical to ensure drinking water supply security. After detecting the existence of contaminants, identifying the types of contaminants is conducive to taking remediation measures. An online classification method for contaminants, which explored abnormal fluctuation information and the correlation between 12 water quality indicators adequately, is proposed to realize comprehensive and accurate discrimination of contaminants. Firstly, the paper utilized multi-fractal detrended fluctuation analysis (MF-DFA) to select indicators with abnormal fluctuation, used multi-fractal detrended cross-correlation analysis (MF-DCCA) to measure the cross-correlation between indicators. Subsequently, the algorithm fused the abnormal probability of each indicator and constructed the abnormal probability matrix to further judge the abnormal fluctuation of indicators using D–S evidence theory. Finally, the singularity index of the cross-correlation function and the selected indicators were used to classification by cosine distance. Experiments of five chemical contaminants at three concentration levels were implemented, and analysis results show the method can weaken disturbance of water quality background noise and other interfering factors. It effectively improved the classification accuracy at low concentrations compared with another three methods, including methods using triple standard deviation threshold and single indicator fluctuation analysis-only methods without fluctuation analysis. This can be applied to water quality emergency monitoring systems to reduce contaminant misclassification.