Generalized dark hollow sine-Gaussian beam and its propagation properties.

A model of the generalized dark hollow sine-Gaussian beam (GDHsGB) is proposed to uniformly describe both conventional dark hollow beams (DHBs) and anomalous dark hollow beams (ADHBs) with circular or elliptic geometrical patterns. Using the Collins formula, we derive the analytical expression for GDHsGBs propagating in ABCD paraxial optical systems. We analyze the evolution of the intensity pattern and beam width of circular ADHBs, as well as the ellipticity of elliptic ADHBs, providing mathematical expressions for these physical quantities. The results reveal various evolution forms based on beam parameters, with elliptic ADHBs exhibiting more intricate propagation behavior compared to circular ADHBs. By controlling parameters, the intensity pattern of elliptic ADHBs undergoes a transformation into a petal-like distribution in the near field, later reverting to its original elliptic configuration but rotated 90° from its initial orientation on the source plane in the far field.

Accelerating finite-energy generalized Olver beams.

We propose a new, to the best of our knowledge, and very general finite power beam solution to the paraxial wave equation (PWE) in Cartesian coordinates by introducing an exponential differential operator on the existing PWE solution and term it as the "finite-energy generalized Olver beam." Applying the analytical expressions for the field distributions, we study the evolution of intensity, centroid, and variance of these beams during free-space propagation. Our findings demonstrate that these new beams exhibit a diffraction-resistant profile along a curved trajectory when specific beam conditions are met. Using numerical methods, we further demonstrate the ability to adjust the self-accelerating degree, sidelobe profile, and stability of the central mainlobe by manipulating the transforming parameters. This research presents a versatile approach to controlling beam properties and holds promise for advancing applications in various fields.

Complex source point theory of paraxial and nonparaxial elliptical Gaussian beams.

Using the operator transformation technology, we extend the circular Gaussian beam based virtual (complex) sources method to investigate the paraxial and nonparaxial propagation properties of the elliptical Gaussian beams (EGBs) with planar or cylindrical wavefronts travelling in free space. The paraxial approximation analysis reveals the self-reappearance and self-focusing propagation features for the EGBs with cylindrical wavefront under proper parameter conditions. We further introduce the nonparaxial theory to derive the analytical expressions for the field distribution of an EGB in free space, and confirm that these intriguing propagation features can still be observed with added nonparaxial correction. Comparing with the paraxial approximation results, it is worth noting that there is a clear deviation of the on-axial intensity and phase distributions near the self-focusing position on the basis of nonparaxial correction solution. Our results reveal that the anisotropic diffraction of light propagating through homogeneous medium or free space is possible. The approach in this work can easily be generalized to other beam models with elliptical geometry, which allows us to correctly predict some important information about their near field propagation characteristics for various applications.

Synthesis of Polyurethane Hydrogel and Polyurethane Thermoplastic Elastomer Composite Based Separation Membranes.

A series of polyurethane hydrogel and polyurethane thermoplastic elastomer composite based separation membranes were successfully prepared via wet phase inversion method. The morphology, chemical structure, phase transition temperature and crystallinity of the polyurethane (PU) membranes were characterized by SEM, FTIR, DSC, and XRD, respectively. The SEM observation showed that the PU membranes exhibited irregular porous structure on the surface and path of the hole was flexural and asymmetrical in cross-section. The FTIR analysis demonstrated that thermalsensitive groups and pH-sensitive components (-N(CH3)-) were incorporated into the PU network. The DSC experiment and XRD experiment showed that the regular arrangement of PU network was destroyed partly due to the introduction of polyurethane thermoplastic elastomer. The equilibrium swelling ratio (ESR) and water flux (J) for PU membranes clearly decreased and increased with functional groups and sophisticated structure of PU membranes, respectively. In addition, the permeation experiments indicated that the permeation percentage (P) of the glycine was strongly affected by the external temperature and pH value.

In-situ preparation of silver salts/collagen fiber hybrid composites and their photocatalytic and antibacterial activities.

To promote the utilization of collagen fiber, silver salts/collagen fiber hybrid composites with photocatalytic and antibacterial activities were successfully prepared in this study via the in-situ organic-inorganic process. The surface morphology, chemical composition and structure were discussed. Scanning electron microscopy (SEM) observation showed that the silver salts/collagen fiber hybrid composites were successfully prepared with silver salt particles (300-500 nm) distributing evenly on the surface of collagen fiber. X-ray diffraction (XRD) patterns and Fourier transform infrared spectroscopy (FTIR) analysis provided strong evidence for the successful coating of silver salts on the surface of collagen fiber and the hybrid mechanism was subsequently discussed. The photocatalytic activity was evaluated by degrading methyl orange (MO) under ultraviolet (UV) light and visible light, respectively. The results indicated that AgCl/Collagen Fiber showed the most efficient photocatalytic activity under UV and visible light irradiation. Furthermore, the introduction of Ag+ endowed the photocatalysts with antibacterial performance, which was investigated by measuring the width of the bacteriostatic belts. The results indicated the antibacterial activity of the composites, proving that the photocatalysts were durable and reusable.

Virtual sources for coherent combination beams consisting of off-axis Gaussian beams.

Based on the operator transformation technique, the multiple complex point sources required to generate a coherent superposition of waves are introduced and a closed-form analytical expression is derived for this composite wave. From the expression of the composite wave, the paraxial approximation and the nonparaxial corrections of all orders for the corresponding paraxial beam are determined. The paraxial composite beam uniformly represents off-axis Gaussian beams (GBs), sin(cos)-GBs, sinh(cosh)-GBs, nth-order modified Bessel-GBs, and Bessel-GBs with topological charge.

Vortex characteristics of Fraunhofer diffractions of a plane wave by a spiral phase plate limited by pseudoring polygonal apertures.

We introduce a multilevel spiral phase plate (SPP) limited by a pseudoring polygonal aperture (PRPA). Such an SPP has the advantages of easier fabrication and greater suppression of the sidelobes of the diffraction field over that generated with a polygonal aperture (PA). The Fraunhofer diffraction fields generated by an SPP with a PRPA or with a PA have the same topological charge features and a similar diffraction pattern. Numerical evaluations show that the maximum bright annular-intensity difference between the diffraction patterns for the SPP with a PRPA and that of a PA does not exceed 3% under optimal design parameters.