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The transformation of (l,n)th mode Laguerre-Gaussian (LG) laser beam, in the process of its diffraction by a curved fork-shaped grating with topological charge p, is theoretically studied. The analytical solutions for the diffracted wave field amplitudes are derived in the Fresnel regime and in the back focal plane of a convergent lens. The zeroth-diffraction order is found as (l,n)th mode LG beam. The higher, (± m) th diffraction-order beam is described in the radial direction through a product of the Gauss-doughnut function by the double sum of hypergeometric Kummer functions. Its topological charge can be increased or reduced compared to that of the incident beam, or it can be equal to zero. The radial intensity distributions are plotted and compared to the corresponding ones valid when a fork-shaped grating is used. The results are specialized for the cases of incident LG beams of modes (l, n = 0), (l = 0,n) and (l = 0,n = 0) i.e. Gaussian mode. [ABSTRACT FROM AUTHOR]

Based on the vector angular spectrum representation and stationary phase method, analytical far-field vectorial expressions of a noncanonical vortex dipole Airy beam, namely, a pair of noncanonical vortices with opposite charges embedded in an Airy beam are derived and used to investigate the phase singularities and energy flux distributions of the corresponding beam in the far-field regime, where the noncanonical characteristic of vortex is stressed. It is shown that the noncanonical strength, off-axis distance, and aperture coefficient affect the position and number of phase singularities, and the motion, creation, and annihilation of phase singularities are found by adjusting these parameters. For a low aperture coefficient, the energy flux distributions exhibit different numbers and orientations of lobes by varying the noncanonical strength. With increasing aperture coefficient, the symmetries of lobes are broken, and the energy flux distributions gradually become ellipses and the directions of their major axes vary with different noncanonical strengths. Finally, the energy flux distributions of an Airy beam carrying a single noncanonical vortex are discussed and compared. [ABSTRACT FROM AUTHOR]

The evolution behavior of two edge dislocations passing through an astigmatic lens is studied. It is shown that the edge dislocations are unstable in general. They may vanish or decay into vortices under certain conditions. The appearance, disappearance and motion of phase singularities may take place by varying the off-axis distance of the edge dislocations, the astigmatic coefficient of the lens, the angle between two edge dislocations, and the propagation distance. Vortices or edge dislocations may appear at the geometrical focal plane for two perpendicular edge dislocations, whereas no phase singularities occur for two parallel edge dislocations. [ABSTRACT FROM AUTHOR]

The phase singularities and spectral switches of focused higher-order Bessel-Gauss pulsed beams are studied. Numerical calculation results are given to illustrate the dependence of phase singularities and spectral switches of focused higher-order Bessel-Gauss pulsed beams on the truncation parameter, topological charge, spatial parameter and propagation distance. It is shown that there always exists an optical vortex at the center of focused higher-order Bessel-Gauss pulsed beams and the topological charge is conserved during the propagation. The spectral switch appears in the neighborhood of the zero- or minimum-intensity position. With increasing topological charge or spatial parameter, the size of the vortex core increases and the spectral transition height decreases. [ABSTRACT FROM AUTHOR]