Two-dimensional Talbot effect of the optical vortices and their spatial evolution

Abstract

We report on the experimental and theoretical study of the near-field diffraction of optical vortices (OVs) at a two-dimensional diffraction grating. The Talbot effect for the optical vortices in the visible range is experimentally observed and the respective Talbot carpets for the optical vortices are experimentally obtained for the first time. It is shown that the spatial configuration of the light field behind the grating represents a complex three-dimensional lattice of beamlet-like optical vortices. A unit cell of the OV lattice is reconstructed using the experimental data and the spatial evolution of the beamlet intensity and phase singularities of the optical vortices is demonstrated. In addition, the self-healing effect for the optical vortices, which consists in flattening of the central dip in the annular intensity distribution, i.e., restoring the image of the object plane predicted earlier is observed. The calculated results agree well with the experimental ones. The results obtained can be used to create and optimize the 3D OV lattices for a wide range of application areas.

Remote state preparation of single-photon orbital-angular-momentum lattices

“…Using this correspondence, a lattice of spin-orbit states originally developed for neutrons has been implemented with photons. Optical lattices have led to studies of optical Talbot physics of structured orbital angular momentum (OAM) light beams [6,7], optical lattice structure shaping [8,9], and direct detection of optical spin-orbit states by the human eye [10,11]. By translating the physics of a periodic structure of spinorbit states further in photonics, we can take advantage of additional capabilities such as multi-particle entanglement.…”

Production of orbital angular momentum states of optical vortex beams using a vortex half-wave retarder with double-pass configuration

“…Another approach is to make use of the near-field diffraction phenomenon known as the Talbot effect 47 to characterize optical vortices and their topological charges 26 , 27 . Two-dimensional Talbot effect of the optical vortices has also been reported 48 . It was demonstrated later that the Talbot patterns resulting from an overlapping grating configuration can provide high optical vortex detection efficiency 31 , 49 .…”

3D Optical Vortex Lattices

“…When a plane wave passes through a periodic grating, the near‐field interference of the diffracted waves leads to the self‐reproduction of the intensity distribution (image) at distances multiple of the Talbot length , where Λ is the grating period and λ is the wavelength of the incident wave. This effect is well‐known as the Talbot effect [ 26 ] ; it has been shown that this effect is retained for OVs in the visible [ 24 ] and terahertz ranges. [ 21,23 ] It means that the Talbot effect can be used to create the 3D OVLs by illuminating a 2D amplitude diffraction grating with an OV as shown in Figure 1 a.…”

“…The 3D intensity distribution can be calculated using the approach proposed in ref. [24]. In the case of a squared regular grating, the light field diffracted behind the grating can be presented in the form Here, and , , k is the wavevector, w is the beam spot radius, is the reciprocal lattice vector, and the subscripts are integers.…”

“…[22] it was proposed a method for producing a close‐packed 2D OV lattice with a controllable structure in the far‐field. So far, the investigations of the OV arrays have been limited to the cross sections of the 3D spatial distributions, [ 21,23 ] except for the 3D reconstruction of a unit cell, [ 18,24 ] although 3D optical lattices without TCs have been intensively studied. [ 9,25 ] A spatial array of the OVs regular in the three dimensions (a 3D lattice) is of particular interest, since it offers unique possibilities for light‐matter interactions, which cannot be obtained using optical lattices without TCs.…”