Transformation of optical-vortex beams by holograms with embedded phase singularity

Abstract

a b s t r a c tSpatial characteristics of diffracted beams produced by the ''fork" holograms from incident circular Laguerre-Gaussian modes are studied theoretically. The complex amplitude distribution of a diffracted beam is described by models of the Kummer beam or of the hypergeometric-Gaussian beam. Physically, in most cases its structure is formed under the influence of the divergent spherical wave originating from the discontinuity caused by the hologram's groove bifurcation. Presence of this wave is manifested by the ripple structure in the near-field beam pattern and by the power-law amplitude decay at the beam periphery. Conditions when the divergent wave is not excited are discussed.The diffracted beam carries a screw wavefront dislocation (optical vortex) whose order equals to algebraic sum of the incident beam azimuthal index and the topological charge of the singularity imparted by the hologram. The input beam singularity can be healed when the above sum is zero. In such cases the diffracted beam can provide better energy concentration in the central intensity peak than the Gaussian beam whose initial distribution coincides with the Gaussian envelope of the incident beam. Applications are possible for generation of optical-vortex beams with prescribed properties and for analyzing the optical-vortex beams in problems of information processing.

Fraunhofer diffraction of a Laguerre–Gaussian laser beam by fork-shaped grating

“…In [24] the incident beam enters into the forked grating plane normally, but, differing from [23], its waist is shifted a distance z=ζ from the grating. The higher-diffraction-order beams in the far-field approximation are found as [24] …”

“…LG l n≠ In [23] the Fresnel diffraction of a Laguerre-Gaussian beam with zeroth radial mode number and arbitrary azimuthal index by forked grating has been treated. The incident beam propagation axis is orthogonal to the diffraction grating plane and intersects it exactly in the centre of the grating bifurcation point, while the beam waist is in the grating plane.…”

Localization and migration of phase singularities in the edge-diffracted optical-vortex beams

“…This expression is similar to the formal asymptotic of the Kummer function [41] modified with account for the non-zero wavefront curvature of the incident Gaussian beam [32]; however, in the considered range of   Now both summands of (A11) should be substituted into the integral term of (A1). The first summand yields the corresponding summand of the integral term, which with omitted coordinateindependent coefficients obtains the representation (cf.…”

Measuring the Orbital Angular Momentum of Electron Vortex Beams Using a Forked Grating

“…order beams are −9 and −11 , respectively. Our experimental results indicate that the forked grating with a Burgers vector of b = 1 transfers not only linear momentum but also OAM, where the electron OAM transfer of the nth-order diffracted electron beam is n [15][16][17][18].…”