Tight focusing effect of annular obstructed incident beam in the focal region of high NA lens

Focusing properties of the azimuthally polarized axisymmetric Bessel-modulated Gaussian beam with Quadratic Bessel Gaussian (QBG beam) and annular aperture are investigated theoretically by vector diffraction theory. Simulation results show that the intensity distribution in focal region of the azimuthally polarized axisymmetric QBG beam can be shifted along optical axis considerably by changing parameter (C). On introducing annular aperture (δ), focal pattern at the focus extends along optical axis. In this paper, we have shown the generation of focal hole and focal shifting in the axial direction of incident beam propagating through aligned optical system which is suitable for application such as optical manipulation and optical trapping.     

Tight focusing properties of radially polarized Lorentz–Gaussian beam

Focusing properties of radially polarized Lorentz–Gauss beam with one on-axis optical vortex was investigated by vector diffraction theory. Results show that intensity distribution in the focal region can be altered considerably by charge number of the optical vortex and the beam parameters. Many novel focal patterns may occur, Such as Peak-centered, donut focal shapes which is potentially useful in optical tweezers, material processing and laser printing.     

Generation of sub wavelength focal spot with large depth of focus generated by radially polarized beam

We investigate the focusing properties of a radially polarized Bessel Gaussian beam by a high numerical aperture (NA) lens based on vector diffraction theory. We observe that our proposed system generates a sub wavelength focal spot of 0.42λ having large uniform focal depth of 6.45λ. The authors expect such a long depth of focus have great potential for use in optical, biological, high-resolution and atmospheric sciences.     

Synthesis and photoluminescence properties of NaPbB5O9:Dy phosphor materials for white light applications

Given the recent increased interest in phosphor materials and their applications, we analyzed a new NaPbB₅O₉:Dy³⁺ phosphor material with different concentrations of Dy³⁺. In particular, we investigated the crystal structure, morphology, and luminescence properties of these materials. X-ray diffraction analyses confirmed the formation of NaPbB₅O₉:Dy³⁺ phosphor powder. The functional groups present in the phosphor materials were examined by Fourier transform infrared spectroscopy. Scanning electron microscope images showed that the size of the grains was in the micrometer range. Photoluminescence spectra were recorded at different excitation wavelengths for the phosphor materials and we analyzed the variation in the intensity of the emission bands with different concentrations of Dy³⁺ ions. The color co-ordinates were calculated and used to characterize the color of the phosphor. We found that the emission colors of the Dy³⁺-doped NaPbB₅O₉ powders depended on the Dy³⁺ ion doping concentration and the excitation wavelength.     

On the excitation temperature of pulsed plasma produced from washer plasma gun in a compact plasma system

The washer plasma gun is widely used to produce pulsed plasma and has various applications in plasma physics. A washer plasma gun and a Guillemin-E type pulse forming network are designed and fabricated in the laboratory to produce pulsed argon plasma in the Compact Plasma System. The spectroscopic signals of pulsed plasma are taken through toughened float glass at a distance of about 0.3 m from the plasma gun by a USB4000 digital spectrometer. Assuming the gun plasma is in Local Thermodynamic Equilibrium, Boltzmann plot method and the line ratio method are used to measure the excitation/electron temperature of pulsed plasma with different base pressure varying from 0.2 mbar to 1 mbar. The excitation/electron temperature of the plasma increases slightly with increasing base pressure within the range of 0.2 mbar to 0.8 mbar and then decreases slightly at a pressure of 1 mbar. Both methods produce almost similar results in temperature measurement, but the Boltzmann Plot method is most accurate than line ratio method and widely used method to obtain the excitation/electron temperature of plasma in Local Thermodynamic equilibrium condition.     

Study of Alpha Decay Chains of Superheavy Nuclei and Magic Number Beyond Z = 82 and N = 126

We study various $\alpha $ -decay chains on the basis of the preformed cluster decay model. Our work targets the superheavy elements, which are expected to show extra stability at shell closure. Our computations identify the following combinations of proton and neutron numbers as the most stable nuclei: $Z=112$ , $N=161, 163$ ; $Z=114$ , $N=171, 178, 179$ ; and $Z=124$ , $N=194$ . We also investigate the alternative of heavy cluster emissions in the decay chain of ³⁰¹120, instead of $\alpha $ decay. Our study of cluster radioactivity shows that the half-life for ¹⁰Be decay in ²⁸⁹114 is larger, indicating enhanced stability at $Z=114$ , $N=175$ . Similar calculations concerning the emission of $\ ^{14}{\rm C}$ and $\ ^{34}{\rm Si}$ from ³⁰¹120 find the more stable combinations $Z=114$ , $N=173$ , and $Z=106$ , $N=161$ , respectively. From the same parent, ³⁰¹120, the emission of a $\ ^{49-51}{\rm Ca}$ cluster yielding a $Z=100$ , $N=152$ daughter is the most probable.     

Crystal structure,dielectric properties of (K0.5Na0.5)NbO3 single crystal grown by flux method using B2O3 flux

Lead free piezoelectric single crystals of sodium potassium niobate (K_0.5Na_0.5)NbO₃ (KNN) were grown by high‐temperature solution method using two different fluxes; one with a mixture of NaF and KF and other with addition of B₂O₃ along with the mixture. In the present study, the growth of KNN crystals without B₂O₃ flux and the same with B₂O₃ flux were compared. It was found that additions of small amounts of B₂O₃ lowered the melting temperature of the solid solution and enabled better dielectric properties. Phase analysis showed that all samples were crystallized in pure orthorhombic perovskite phase. AFM morphological studies showed that the addition of B₂O₃ flux increased the roughness of the grown crystal. Further, addition of B₂O₃ flux slightly decreased the orthorhombic to tetragonal phase transition temperature T_(O—T) and the Curie temperature T_C. The ferroelectric behaviour of KNN single crystal has been investigated at room temperature. The crystal grown using B₂O₃ flux exhibited a remanent polarization (P_r) ∼ 32 μC/cm² and coercive field (Ec) of ∼11.8 kV/cm whereas the crystal grown without the use of B₂O₃ flux had a remanent polarization (P_r) ∼ 36 μC/cm² and coercive field (Ec) of ∼14.6 kV/cm.     

Trumping and Power Majorization

Majorization is a basic concept in matrix theory that has found applications in numerous settings over the past century. Power majorization is a more specialized notion that has been studied in the theory of inequalities. On the other hand, the trumping relation has recently been considered in quantum information, specifically in entanglement theory. We explore the connections between trumping and power majorization. We prove an analogue of Rado’s theorem for power majorization and consider a number of examples.     

Two modes of O—H...O hydrogen bonding utilized in dimorphs of racemic 6‐O‐acryloyl‐2‐O‐benzoyl‐myo‐inositol 1,3,5‐orthoformate

The title compound, C₁₇H₁₆O₈, yields conformational dimorphs [forms (I) and (II)] at room temperature, separately or concomitantly, depending on the solvent of crystallization. The yield of crystals of form (I) is always much more than that of crystals of form (II). The molecule has one donor –OH group that can make intermolecular O—H...O hydrogen bonds with one of the two acceptor C=O groups, as well as with the hydroxyl O atom; interestingly, each of the options is utilized separately in the dimorphs. The crystal structure of form (I) contains one molecule in the asymmetric unit and is organized as a planar sheet of centrosymmetric dimers via O—H...O hydrogen bonds involving the OH group and the carbonyl O atom of the acryloyl group. In the crystal structure of form (II), which contains two independent molecules in the asymmetric unit, two different O—H...O hydrogen bonds, viz. hydroxyl–hydroxyl and hydroxyl–carbonyl (benzoyl), connect the molecules in a layered arrangement. Another notable feature is the transformation of form (II) to form (I) via melt crystallization upon heating to 411 K. The higher yield of form (I) during crystallization and the thermal transition of form (II) to form (I) suggest that the association in form (I) is more highly favoured than that in form (II), which is valuable in understanding the priorities of molecular aggregation during nucleation of various polymorphs.     

Probing the supramolecular interaction synthons of 1‐benzofuran‐2,3‐dicarboxylic acid in its monoanionic form

1‐Benzofuran‐2,3‐dicarboxylic acid (C₁₀H₆O₅) is a dicarboxylic acid ligand which can readily engage in organometallic complexes with various metal ions. This ligand is characterized by an intramolecular hydrogen bond between the two carboxyl residues, and, as a monoanionic species, readily forms supramolecular adducts with different organic and inorganic cations. These are a 1:1 adduct with the dimethylammonium cation, namely dimethylammonium 3‐carboxy‐1‐benzofuran‐2‐carboxylate, C₂H₈N⁺·C₁₀H₅O₅⁻, (I), a 2:1 complex with Cu²⁺ ions in which four neutral imidazole molecules also coordinate the metal atom, namely bis(3‐carboxy‐1‐benzofuran‐2‐carboxylato‐κO³)tetrakis(1H‐imidazole‐κN³)copper(II), [Cu(C₁₀H₅O₅)₂(C₃H₄N₂)₄], (II), and a 4:1 adduct with [La(H₂O)₇]³⁺ ions, namely heptaaquabis(3‐carboxy‐1‐benzofuran‐2‐carboxylato‐κO³)lanthanum 3‐carboxy‐1‐benzofuran‐2‐carboxylate 1‐benzofuran‐2,3‐dicarboxylic acid solvate tetrahydrate, [La(C₁₀H₅O₅)₂(H₂O)₇](C₁₀H₅O₅)·C₁₀H₆O₅·4H₂O, (III). In the crystal structure, complex (II) resides on inversion centres, while complex (III) resides on axes of twofold rotation. The crystal packing in all three structures reveals π–π stacking interactions between the planar aromatic benzofuran residues, as well as hydrogen bonding between the components. The significance of this study lies in the first crystallographic characterization of the title framework, which consistently exhibits the presence of an intramolecular hydrogen bond and a consequent monoanionic‐only nature. It shows further that the anion can coordinate readily to metal cations as a ligand, as well as acting as a monovalent counter‐ion. Finally, the aromaticity of the flat benzofuran residue provides an additional supramolecular synthon that directs and facilitates the crystal packing of compounds (I)–(III).