An astigmatic transform of a fractional-order edge dislocation

Through theoretical calculation, the analytical expression for the cross-spectral density function of vortex beam with and without edge dislocation during transmission in turbulent atmosphere and free space is obtained. The calculation result is used for researching the influences of edge dislocation on optical vortex transmission. The research shows that due to the edge dislocation, when the optical vortex's topological charge is greater than +1, the optical vortex will no longer carry out steady transmission in the free space transmission. Instead, it will divide into two optical vortices, and the distance between them will gradually increase as the transmission distance increases. Optical vortex will split in turbulent atmosphere propagation. Due to the edge dislocation, when the topological charge of optical vortex is greater than +2, it is found that the distance between one optical vortex and other optical vortices is much larger than that between other optical vortices. Besides, when there's an edge dislocation, the greater the light wavelength and the structure constant are, the smaller the distance between the optical vortex and the edge dislocation on the source plane is, and the evolution of the optical vortex will be accelerated.

This work presents an investigation of tight focusing of optical vortices, which produce regions where the Poynting vector is directed opposite to the beam's propagation direction-known as areas of reverse energy flow. We study both phase optical vortices and polarization optical vortices (cylindrical vector beams). For phase optical vortices, it is shown that the emergence of reverse energy flow as well as splitting of the initial optical vortex depends on the handedness of the circular polarization and the phase of the initial optical vortex. An optical vortex with an initial topological charge of $m\; \le \; - {3}$ splits into three optical vortices with topological charges $m + {2}$, ${-}{1}$, and ${-}{1}$ when the polarization is right circular. In contrast, under left-hand circular polarization, a vortex with the topological charge $m$ is preserved at the focus. The reverse-flow regions are located between the centers of phase singularities (screw dislocation points). As the topological charge of the phase vortex increases, the region of reverse flow along the radial coordinate widens, and the distance from the vortex center to the optical axis also increases. In the focusing of cylindrical vector beams (polarization optical vortices), the reverse energy flow region is also observed, but screw dislocations are absent.

All diffractive optical element setup for creating and characterizing optical vortices with high topological charges: Analytical models and numerical results

We present a model based on the Fresnel diffraction scheme for the spatial coherence function of random fields created by scattering optical vortex and perfect vortex beams. By using the spatial coherence function we showed analytically, numerically, and experimentally the dependence and independence of the speckle size of an optical vortex and perfect optical vortex (POV) with a topological charge, respectively. We also showed in both cases the linear dependence of speckle size on the distance of propagation. Furthermore, we describe a regime in which the spatial coherence function is nonevolving for the optical vortex beam and the POV beam with the propagation distance.

We model the effect of the off-axis distance of edge dislocation on the transmission of mixed higher order optical vortex–edge dislocations in atmospheric turbulence. We find that when mixed dislocations beams propagate through atmospheric turbulence, the higher order optical vortex will break down, and the topological charge is conserved in the process; an edge dislocation evolves into a pair of optical vortices with the opposite topological charge. With the increase of the propagation distance, one of the optical vortices that are broken down and one of the optical vortices that are evolved will annihilate. And the bigger the off-axis distance of edge dislocation is, the bigger the annihilation distance of optical vortices is. The results illustrate that as the off-axis distance of edge dislocation increases, the transmission of mixed dislocations propagating through atmospheric turbulence becomes better.

Space-division multiplexing (SDM) has emerged as a promising technology for both classical and quantum communications. Twisted light, particularly in the form of orthogonal optical vortex beams, offers significant potential for SDM by enhancing the capacity and performance of optical communication systems. A critical component in such systems is a twisted light (de)multiplexer, which enables scalable and efficient (de)multiplexing of twisted light to meet the demands of high-capacity optical communications. In this work, we propose and experimentally demonstrate quasi-wavelet conformal mapping microstructures for efficient twisted light demultiplexing. These microstructures, specifically designed and fabricated for this experiment, successfully demultiplex 11 optical vortex beams with a low crosstalk below −20.9 dB at the target wavelength. Moreover, the microstructures exhibit a broad operational bandwidth (1525–1570 nm), maintaining crosstalk levels under −13 dB. To further validate their performance, the microstructures are also tested in the demultiplexing of various configurations of multiplexed two-channel optical vortex beams. The presented quasi-wavelet conformal mapping microstructures with compact size and exceptional demultiplexing performance hold great promise for applications in high-capacity optical communication systems using twisted light.

Optical vortices are a new kind of laser beam and receiving more and more attention currently.The complex amplitudes of optical vortices comprise a helical term exp (il),with l being the topological charge and the azimuthal angle.Each photon in optical vortices carries the orbital angular momentum (OAM) with a value of lħ,where ħ is the Planck's constant divided by 2.The topological charge l is the eigenvalue of optical vortices,and determines the helical wavefront distribution,thus also known as OAM state.Moreover,such an OAM state can be an infinite integer state. And vortices with various OAM states are orthogonal to each other,making it possible to be employed in high capacity data-transmission system.In addition,the above unique features contribute to their widely applications in lots of areas such as optical tweezers and spanners,rotation detection,quantum entanglement,etc.In these applications,detecting OAM states is basic,and greatly significant.Recently researchers have developed lots of approaches to detecting the OAM states,including the methods of interference,diffraction gratings,metasurface,etc.Of such approaches,the scheme of diffraction gratings is the simplest and most widely used,where one or more diffraction gratings are employed. When optical vortices propagate through such gratings,the OAM states are acquired immediately through capturing and analyzing the distinct OAM-related diffraction patterns.In this review,we focus on the techniques of detecting OAM states through diffraction gratings,which have been demonstrated by our group and other researchers.Some of the main detection gratings,including double-slit,triangle aperture and slit,angular slit,cylindrical lens,graduallychanging-period grating,annular grating,are introduced.In addition,schemes like composite fork grating,Dammann vortex grating and integrated Dammann grating,are presented to detect the OAM state for coaxial multiplexed vortices. Besides diagnosing OAM state,measuring the intensity proportion of each OAM channel,known as OAM spectrum, in multiplexed vortices is also necessary in some cases.Therefore we also introduce the ways to measure the OAM spectrum,e.g.the OAM mode sorter,the gray-scale algorithm.

In the present presentation, we report the experimentally and theoretically investigated spatial wavefront conversion properties of an optical vortex (OV) generation system including azo-dye doped liquid crystal (ADDLC) polymer composite and vector beam illuminator, focusing on the abilities of flexibility and achromaticity. Threedimensional anisotropic structure was induced by recording vector beam in ADDLC and it can convert a polarized Gaussian beam into polarized OVs whose topological charge is depending on the structure of anisotropy. The photo-induced anisotropic structure can be re-initialized by turning it off and changing the illuminating polarization pattern of vector beam. Numerical simulations and experimental results showed that our anisotropic structure can generate OV with broadband spectrum.

Formation of optical vortices with topological charge [formula omitted] and [formula omitted] by use of the S-waveplate

Construction of special multi-mode annular optical vortex

In a number of theoretical (J. Opt. 6, 259 (2004)) and experimental (Opt Express 19, 5760 (2011)) works, an original fractional-TC optical vortex (with TC standing for topological charge) was shown to evolve into an integer optical vortex whose TC is equal to the nearest (i) smaller integer, if the fractional part is smaller than 1/2, and (ii) larger we show that the initial fractional optical vortex evolves into an integer optical vortex with TC equal to the nearest (i) smaller integer, if the fractional part is smaller than 0.12, and (ii) larger integer, if the fractional part is larger than 0.12. This can be explained by the fact that the additional center integer, if the fractional part is larger than 1/2. In this work, using numerical simulation, of singularity is generated on the beam periphery characterized by near zero-intensity (a millionth of the maximum), thus prohibiting the experimental detection, but allowing a numerical assessment.

Nonlinear propagation effects on high-power optical-vortex pulses in anisotropic crystals is reported. Nonlinear effects on optical-vortex pulse generation through the spin-orbit interaction and its propagation in an anisotropic crystal is investigated.The beam of the left-circularly-polarized optical vortex pulse is focused on one of the surfaces of a LiNbO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> or rutile crystal (NC) by a convex lens L1. After propagating along the optic axis of the crystal, the beam is collimated by another convex lens L2.

Vortex beams, known as a typical form of structured light, possess numerous applications in various fields. Their widespread application prospects have then sparked an in-depth analysis of the generation and manipulation of vortex modes in an active cavity, as well as the development of high-performance vortex lasers. In this paper, we report on a new class of highly efficient and high-power Nd:YAG vortex lasers in a robust and compact configuration, which allows direct generation of vortex beams with an easily controllable topological charge both in the continuous-wave and pulsed operation regimes. The on-demand generation of intracavity vortex modes is realized based on a Q-plate by controlling the geometric phase inside the laser resonator. The maximum output power in the continuous-wave regime is 4.11 W with a slope efficiency of 37.9%. Besides, the vortex pulses are also achieved by including a Cr:YAG crystal in the cavity as a saturable absorber. The shortest pulse width is 142.8 ns at a pulse repetition rate of 232.6 kHz, with a maximum average output power of 1.05 W. Vortex modes with other topological charges can be obtained by simply changing the corresponding Q-plate without sacrificing the lasing efficiency. The experimental results can shed some light on the design and building of highly efficient and high-power vortex lasers together with a well-defined controllable topological charge, aiming at some specific applications.

A photon can carry orbital angular momentum equal to an integer number of the reduced Planck’s constant. This principle expresses itself in geometrical quantization of optical vortex beams, which thus can propagate only in the form of fields having a helically wavefront characterized by an integer valued topological charge. However, one can create an optical vortex beam of an effective fractional charge by combining multiple integer vortices. Here, we investigate this apparent violation of the geometrical quantization of orbital angular momentum of light. Our approach relies on observation of the light-induced motion of a microscopic particle, which thus acts as an optomechanical probe for the optical vortex beam. A fractional topological charge corresponds to an abrupt jump in the helical phase front of the beam. This singularity expresses itself as an off-axis disturbance in the intensity profile, and thus complicates the optomechanical probing. We overcome this problem by distributing the disturbance along the vortex ring, so that a microparticle can continuously orbit due to the orbital angular momentum transfer. We demonstrate theoretically that whatever effort is put into smoothing the fractional vortex ring (as long as the net topological charge is fixed), the particle’s orbital motion cannot be as uniform as in the case of an integer vortex beam. We support this prediction by experimental proof. The experimental technique benefits from the recently introduced “perfect” vortex beams which allow an optically trapped particle to orbit along a constant trajectory irrespective of any topological charge.

A full comparative analysis of the chain of phase singularities generated when a quasi-plane wave and a Gaussian beam pass a double-phase-ramp (DPR) converter is presented based on the theoretical and experimental data. The overall output beam structure includes a system of interrelated optical vortices (OVs) whose linear trajectories form a threedimensional singular skeleton which can be applied for the trapping and guiding of microparticles. An internal structure of each individual phase singularity is characterized by the OV topological charge and by the morphology parameters of the equal intensity ellipses in the OV-core area. The rectilinear equidistant OV trajectories form a chain in the transverse cross section, and their identical morphology parameters can be useful for the applications to metrology and micromanipulation. As a separate result, we consider the DPR-induced transformations of the incident Laguerre-Gaussian beams of the lowest orders and show that the incident multicharged OVs are transformed into small sub-chains of the OVs located in the near-axial region.