A highly efficient element for generating elliptic perfect optical vortices

We study perfect optical vortices with an elliptic shape. Like the conventional circular perfect vortices, elliptic perfect optical vortices (EPOVs) have diameters that are independent on the topological charge. A pure-phase optical element is proposed for efficient generation of such EPOV. Intensity of EPOV generated by this element is order of magnitude higher than that of the EPOV generated by the Fraunhofer diffraction of an elliptic Bessel beam. We obtain exact analytical expressions for the orbital angular momentum (OAM) of the EPOV. These expressions show that the OAM of the EPOV can be fractional and it always exceeds the OAM of the conventional circular perfect optical vortex, which equals the topological charge. EPOVs can be used for movement of microscopic particles along an ellipse with acceleration, as well as for generation of OAM-entangled photons.

Optical vortex beams are profiled as helical wavefronts with a phase singularity carrying an orbital angular momentum (OAM) associated with their spatial distribution. The transverse intensity distribution of a conventional optical vortex has a strong dependence on the carried topological charge. However, perfect optical vortex (POV) beams have their transverse intensity distribution independent of their charge. Such “size-invariant” POV beams have found exciting applications in optical manipulation, imaging, and communication. In this paper, we investigate the use of POV modes in the efficient generation of high-dimensional quantum states of light. We generate heralded single photons carrying OAM using spontaneous parametric downconversion (SPDC) of POV beams. We show that the heralding efficiency of the SPDC single photons generated with a POV pump is greater than that with normal optical vortex beams. The dimensionality of the two-photon OAM states is increased with POV modes in the pump and projective measurements using Bessel–Gaussian vortex modes that give POV, instead of Laguerre–Gaussian modes.

Experimental generation and orbital angular momentum properties of focused field for vector vortex beams on Hybrid-order Poincaré sphere

We have demonstrated a holographic grating, the far-field diffraction pattern of which is a perfect optical vortex (POV) array. The diffraction order, as well as the topological charge of each spot in the array, is controllable. By setting different parameters when designing the hologram, the spot in different diffraction orders will be changed, resulting in the variance of the POV array. During the experiment, we uploaded holograms of different design on a phase-only spatial light modulator. We then observed POV arrays with different dimensions and topological charges using a CCD camera, which fit well with the simulation. This technique provides the possibility to generate multiple POVs simultaneously, and can be used in domains where multiple POVs are of high interest such as orbital angular momentum multiplexed fiber data transmission systems.

Based on the expansions of the Lorentz distribution and the aperture function, an analytical expression of Lorentz–Gauss vortex beams with a topological charge of ±1 diffracted by a rectangular aperture is derived. One can judge the sign of the topological charge from the normalized intensity and the phase distributions. The effects of the rectangular aperture on the orbital angular momentum density and the spiral spectrum are investigated, respectively. When the length and the width of the rectangular aperture are not equal, the orbital angular momentum density distribution becomes twisted and tilted. When the size of the rectangular aperture increases, the magnitude of the orbital angular momentum density and the weight coefficient of the dominant spectrum both increase, while the weight coefficients of other minor spectra decrease. In addition, the expansion of the spiral spectrum in the case of rectangular aperture is smaller than that in the case of the single slit. The difference between the adjacent spectra in the case of the rectangular aperture is four, which is twice the difference in the case of the single slit. Moreover, the weight coefficient of the dominant spectrum in the case of the rectangular aperture is relatively larger. To measure the topological charge of the diffracted Lorentz–Gauss vortex beam, this research denotes that the rectangular aperture is superior to the single slit.

Optical vortex lattices (OVLs) with diverse modes show potential for a wide range of applications, such as high-capacity optical communications, optical tweezers, and optical measurements. However, vortices in typical regulated OVLs often exhibit irregular shapes, such as being narrow and elongated. The resulting increase in asymmetry negatively impacts the efficiency of particle trapping. Additionally, the vortex radii expand with an increase in topological charge (TC), limiting the TC value of the vortices and hindering their ability to fully utilize orbital angular momentum (OAM). Herein, we propose an alternative approach to custom OVLs using off-axis techniques combined with amplitude modulation. Amplitude modulation enables the precise generation of an OVL with perfect vortex properties, known as a perfect off-axis OVL. Further, the number of vortices in the perfect off-axis OVL, the off-axis distances, and the TC can be freely modulated while maintaining a circular mode. This unique OVL will promote new applications, such as the complex manipulation of multi-particle systems and optical communication based on OAM.

An analytical expression for a Lorentz-Gauss vortex beam passing through a fractional Fourier transform (FRFT) system is derived. The influences of the order of the FRFT and the topological charge on the normalized intensity distribution, the phase distribution, and the orbital angular momentum density of a Lorentz-Gauss vortex beam in the FRFT plane are examined. The order of the FRFT controls the beam spot size, the orientation of the beam spot, the spiral direction of the phase distribution, the spatial orientation of the two peaks in the orbital angular momentum density distribution, and the magnitude of the orbital angular momentum density. The increase of the topological charge not only results in the dark-hollow region becoming large, but also brings about detail changes in the beam profile. The spatial orientation of the two peaks in the orbital angular momentum density distribution and the phase distribution also depend on the topological charge.

Perfect optical vortices (POVs) provide a solution to address the challenge induced by strong dependence of classical optical vortices on their carried topological charges. However, traditional POVs are all shaped into bright rings with a single main lobe along the radial direction. Here we propose a method for enhanced control on the ring profile (the radial intensity profile of circular rings) of POVs based on modulated circular sine/cosine radial functions, which is realized by a circular Dammann grating embedded with a spiral phase. Specifically, a type of “absolute” dark POVs surrounded by two bright lobe rings in each side is presented, which provides a perfect annular potential well along those dark impulse rings for trapping low-index particles, cells, or quantum gases. In addition, several POVs with different ring profiles, including conventional POVs with bright rings, the dark POVs mentioned above, and also POVs with tunable ring profiles, are demonstrated. This work opens up new possibilities to controllably tune the ring profile of perfect vortices, and this type of generalized POVs will enrich the content of singular optics and expand the application scope of perfect vortices in a range of areas including optical manipulation, both quantum and classical optical communications, enhanced optical imaging, and also novel structured pumping lasers.

In this paper, the circular Airy derivative beams carrying rotationally-symmetric power-exponent-phase vortices are proposed for the first time, whose evolutionary properties are explored by theoretical analysis as well as experimental verification. The intensity and phase distributions of this kind of beam can be flexibly modulated by controlling its parameters such as derivative order, topological charge, and power order. Intriguingly, the evolution of such beams with different fractional topological charges is also investigated in detail by means of phase singularities distribution. In addition, from the perspective of transverse gradient force, the proposed beam is capable of efficiently protecting the trapped Rayleigh particles located at the beam center from the impact by surrounding particles. Furthermore, the beam width, orbital angular momentum (OAM) density and spiral spectrum are also compared and analyzed under different beam parameters. The proposed beams are expected to be useful for extending applications of optical vortices and autofocusing beam, especially for multi-regional particle gathering and central particle protecting.

According to the theory of electromagnetic field, the orbital angular momentum density formula of a general beam was deduced. From the electric field intensity of a Gauss Vortex Beam, the orbital angular momentum density calculation formula of a Gaussian vortex beam was also deduced. A MATLAB program was applied to simulate the optical field distributions and the orbital angular momentum density distributions of Gauss Vortex Beams, and found the size and the direction of orbital angular momentum were closely related to the order of a Gaussian vortex beam.

We derive new Lorentz invariance and equation of motion relations between twist-three generalized parton distributions (GPDs) and moments in the parton transverse momentum, ${k}_{T}$, of twist-two generalized transverse momentum-dependent distributions (GTMDs), as a function of the parton longitudinal momentum fraction $x$. Although GTMDs in principle define the observables for partonic orbital motion, experiments that can unambiguously detect them appear remote at present. The relations presented here provide a solution to this impasse in that, e.g., the orbital angular momentum density is connected to directly measurable twist-three GPDs. Out of 16 possible equation of motion relations that can be written in the $T$-even sector, we focus on three helicity configurations that can be detected analyzing specific spin asymmetries: two correspond to longitudinal proton polarization and are associated with quark orbital angular momentum and spin-orbit correlations; the third, obtained for transverse proton polarization, is a generalization of the relation obeyed by the ${g}_{2}$ structure function. We also exhibit an additional relation connecting the off-forward extension of the Sivers function to an off-forward Qiu-Sterman term.

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.

Perfect vortices have garnered significant attention due to their role as orbital angular momentum (OAM) beams with tunable ring-like intensity distributions. More recently, the non-separable combination of perfect vortices with opposite OAM and spin, known as perfect vector vortices, has extended their applicability in optical manipulation, high-resolution lithography, imaging, and telecommunications. The generation of perfect vector vortices with a size that remains constant regardless of the encoded topological charge typically requires both phase and amplitude modulation. In this study, we propose an efficient and innovative solution that leverages a multifocal approach encoded on phase-only silicon metalenses. A simultaneous control over dynamic and geometric phases was achieved through the careful design and fabrication of the individual meta-atoms comprising the metalens. This meta-atom engineering approach, modulating both phase components, enabled the generation and characterization of orbital angular momentum-independent perfect vector beams with an improved depth of focus. These devices represent a crucial step toward developing integrated optical architectures for information and communication technologies, with potential applications in both classical and quantum domains.

By using digital holograms, we present a simple technique for performing a complete azimuthal decomposition of an arbitrary laser mode. The match-filter, used to perform the azimuthal decomposition, is bounded by an annular ring, allowing us to conduct a scale-independent decomposition on our selected mode. This technique therefore requires no prior knowledge of the mode structure, the mode phases, or the amplitude distribution. A basis comprising of the angular harmonics is used to express the spatial distribution of the selected mode in terms of spatially dependant coefficients. We use this to infer directly from the measured weightings of the azimuthally decomposed modes and their phase-delay measurements, the intensity of the selected field, its phase, and its orbital angular momentum (OAM) density. We illustrate the concept by executing a full decomposition of two examples: a superposition of two Bessel beams, with relative phase differences, and an off-axis vortex mode. We show a reconstruction of the amplitude, phase and OAM density of these fields with a high degree of accuracy.

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.