Aberration-resistible topological charge determination of annular-shaped optical vortex beams using Shack-Hartmann wavefront sensor.

Determining topological charge (TC) of optical vortex (OV) beams is important for many applications, such as optical measurement and information transmission through long-distance propagation. In this application, the OV beams usually have an annular intensity profile at the receiving end and are inevitably distorted by aberrations during propagation. In this paper, we propose a simple, direct, and aberration-resistible method to determine the TC value of this annular-shaped OV beam with a Shack-Hartmann wavefront sensor (SH-WFS). Our approach involves finding a closed-path along the annular intensity distribution ridge, and then determining the TC value by a discrete circulation calculation with only the phase-slope vectors along the closed-path. Verification experiments were performed using a phase-only spatial light modulator to generate OV beams and aberrations, while SH-WFS to measure the intensity profile and phase-slopes. The results show that our method can determine the TC value of up to ± 20. The robustness against wavefront aberration and simulated atmospheric turbulence was evaluated. We also verified the proposed closed-path's superiority to other circular closed-paths for TC determination.

Dichlorido(ethanol-κO)[2-(1,3-thia-zol-4-yl-κN)-1H-benzimidazole-κN(3)]copper(II).

In the title complex, [CuCl(2)(C(10)H(7)N(3)S)(C(2)H(5)OH)], the Cu(II) ion is five-coordinated in a distorted square-pyramidal geometry by two N atoms from a 2-(1,3-thia-zol-4-yl)-1H-benzimidazole ligand, one O atom from an ethanol mol-ecule and two Cl atoms. In the crystal, O-H⋯Cl and N-H⋯Cl hydrogen bonds link the complex mol-ecules into a layer parallel to (100). π-π inter-actions between the thia-zole rings are observed [centroid-centroid distance = 3.749 (3) Å].

Poly[[µ(2)-aqua-µ(3)-(4-carb-oxy-2-propyl-1H-imidazole-5-carboxyl-ato-κN,O:O:O)-sodium] hemihydrate].

In the title compound, {[Na(C(8)H(9)N(2)O(4))(H(2)O)]·0.5H(2)O}(n), the Na(+) ion is coordinated by two bridging water mol-ecules, one N atom and three O atoms from three 4-carb-oxy-2-propyl-1H-imidazole-5-carboxyl-ate (H(2)pimdc) ligands. Adjacent Na(+) ions are linked alternately by two water O atoms and two carb-oxy O atoms into a chain along [001]. These chains are connected through the coordination of the carboxyl-ate O atoms to the Na(+) ions, forming a three-dimensional structure. An intra-molecular O-H⋯O hydrogen bond and inter-molecular N-H⋯O and O-H⋯O hydrogen bonds are present in the crystal structure.