Diffraction deep neural network-based classification for vector vortex beams

The vector vortex beam(VVB)has attracted significant attention due to its intrinsic diversity of information and has found great applications in both classical and quantum communications.However,a VVB is unavoidably affected by atmospheric turbulence(AT)when it propagates through the free-space optical communication environment,which results in detection errors at the receiver.In this paper,we propose a VVB classification scheme to detect VVBs with continuously changing polarization states under AT,where a diffractive deep neural network(DDNN)is designed and trained to classify the intensity distribution of the input distorted VVBs,and the horizontal direction of polarization of the input distorted beam is adopted as the feature for the classification through the DDNN.The numerical simulations and experimental results demonstrate that the proposed scheme has high accuracy in classification tasks.The energy distribution percentage remains above 95%from weak to medium AT,and the classification accuracy can remain above 95%for various strengths of turbulence.It has a faster convergence and better accuracy than that based on a convolutional neural network.

Tailoring electron vortex beams with customizable intensity patterns by electron diffraction holography

An electron vortex beam(EVB) carrying orbital angular momentum(OAM) plays a key role in a series of fundamental scientific researches, such as chiral energy-loss spectroscopy and magnetic dichroism spectroscopy. So far, almost all the experimentally created EVBs manifest isotropic doughnut intensity patterns. Here, based on the correlation between local divergence angle of electron beam and phase gradient along azimuthal direction, we show that free electrons can be tailored to EVBs with customizable intensity patterns independent of the carried OAM. As proof-of-concept, by using computer generated hologram and designing phase masks to shape the incident free electrons in the transmission electron microscope, three structured EVBs carrying identical OAM are tailored to exhibit completely different intensity patterns. Furthermore, through the modal decomposition, we quantitatively investigate their OAM spectral distributions and reveal that structured EVBs present a superposition of a series of different eigenstates induced by the locally varied geometries. These results not only generalize the concept of EVB, but also demonstrate an extra highly controllable degree of freedom for electron beam manipulation in addition to OAM.

Terahertz quasi-perfect vortex beam with integer-order and fractional-order generated by spiral spherical harmonic axicon

We propose a new method to generate terahertz perfect vortex beam with integer-order and fractional-order. A new optical diffractive element composed of the phase combination of a spherical harmonic axicon and a spiral phase plate is designed and called spiral spherical harmonic axicon. A terahertz Gaussian beam passes through the spiral spherical harmonic axicon to generate a terahertz vortex beam. When only the topological charge number carried by spiral spherical harmonic axicon increases, the ring radius of terahertz vortex beam increases slightly, so the beam is shaped into a terahertz quasi-perfect vortex beam. Importantly, the terahertz quasi-perfect vortex beam can carry not only integer-order topological charge number but also fractional-order topological charge number. This is the first time that vortex beam and quasi-perfect vortex beam with fractional-order have been successfully realized in terahertz domain and experiment.

Spatial quantum coherent modulation with perfect hybrid vector vortex beam based on atomic medium

The perfect hybrid vector vortex beam(PHVVB)with helical phase wavefront structure has aroused significant concern in recent years,as its beam waist does not expand with the topological charge(TC).In this work,we investigate the spatial quantum coherent modulation effect with PHVVB based on the atomic medium,and we observe the absorption characteristic of the PHVVB with different TCs under variant magnetic fields.We find that the transmission spectrum linewidth of PHVVB can be effectively maintained regardless of the TC.Still,the width of transmission peaks increases slightly as the beam size expands in hot atomic vapor.This distinctive quantum coherence phenomenon,demonstrated by the interaction of an atomic medium with a hybrid vector-structured beam,might be anticipated to open up new opportunities for quantum coherence modulation and accurate magnetic field measurement.

Optimization of extreme ultraviolet vortex beam based on high harmonic generation

In high harmonic generation(HHG),Laguerre–Gaussian(LG) beams are used to generate extreme ultraviolet(XUV)vortices with well-defined orbital angular momentum(OAM),which have potential applications in fields such as microscopy and spectroscopy.An experimental study on the HHG driven by vortex and Gaussian beams is conducted in this work.It is found that the intensity of vortex harmonics is positively correlated with the laser energy and gas pressure.The structure and intensity distribution of the vortex harmonics exhibit significant dependence on the relative position between the gas jet and the laser focus.The ring-like structures observed in the vortex harmonics,and the interference of quantum paths provide an explanation for the distinct structural characteristics.Moreover,by adjusting the relative position between the jet and laser focus,it is possible to discern the contributions from different quantum paths.The optimization of the HH vortex field is applicable to the XUV,which opens up a new way for exploiting the potential in optical spin or manipulating electrons by using the photon with tunable orbital angular momentum.

Asymmetrical spiral spectra and orbital angular momentum density of non-uniformly polarized vortex beams in uniaxial crystals

To explore the effect of non-uniform polarization on orbital angular momentum(OAM) in anisotropic medium, in this work investigated are the evolution of the spiral spectra and OAM densities of non-uniformly polarized vortex(NUPV)beams in uniaxial crystals propagating orthogonal to the optical axis, and also the case of uniformly polarized vortex(UPV)beams with left-handed elliptical polarization. In the input plane, the NUPV beams present their spiral spectra of m-mode concentrated at m = l ± 1 modes rather than m = l mode, and reveal the relation among topological charge l, mode of spiral spectra m and the power weight value Rmexpressed by l=∑^(∞)_(m)=-∞Rm. is still satisfied for UPV beams in uniaxially anisotropic crystals, whereas for NUPV beams their relations are no longer valid owing to non-uniform polarization. Furthermore, the analysis indicates that the asymmetrical distribution of power weight of spiral spectra and the non-zero value in the sum of longitudinal OAM densities originate from the initial non-uniform polarization and anisotropy in uniaxial crystals rather than topological charges. In addition, the relation between spiral spectrum and longitudinal OAM density is numerically discussed. This work may provide an avenue for OAM-based communications,optical metrology, and imaging by varying the initial non-uniform polarization.

Ultraviolet metalens and metalens array of focused vortex beams

The solar-blind ultraviolet(UV)wavelength is particularly interesting within the range of 200 nm–300 nm.Here,we propose a focusing metalens,focusing vortex beam(VB)metalens and metalens array that specifically work in the UV band to focus a beam or VB.Firstly,a high numerical aperture(NA)focusing metalens working at a wavelength of 214.2 nm was designed,and the NA reached 0.83.The corresponding conversion efficiency of the unit structure reached as high as 94%,and the full width at half maximum was only 117.2 nm.Metalenses with large NA can act as optical tweezers and can be applied to trap ultracold atoms and molecules.Secondly,a focused VB metalens in the wavelength range of200 nm–300 nm was also designed,which can convert polarized light into a VB and focus the VB simultaneously.Finally,a metalens array was developed to focus VBs with different topological charges on the same focal plane.This series of UV metalenses could be widely used in UV microscopy,photolithography,photonics communication,etc.

Spin splitting of vortex beams on the surface of natural biaxial hyperbolic materials

We investigated the spin splitting of vortex beam on the surface of biaxial natural hyperbolic materials(NHMs)rotated by an angle with respect to the incident plane. An obvious asymmetry of spatial shifts produced by the left-handed circularly(LCP) component and right-handed circularly polarized(RCP) component is exhibited. We derived the analytical expression for in-and out-of-plane spatial shifts for each spin component of the vortex beam. The orientation angle of the optical axis plays a key role in the spin splitting between the two spin components, which can be reflected in the simple expressions for spatial shifts without the rotation angle. Based on an α-MoO_(3) biaxial NHM, the spatial shifts of the two spin components with the topological charge were investigated. As the topological charge increases, the spatial shifts also increase;in addition, a tiny spatial shift close to zero can be obtained if we control the incident frequency or the polarization of the reflected beams. It can also be concluded that the maximum of the spin splitting results from the LCP component at p-incidence and the RCP component at s-incidence in the RB-Ⅱ hyperbolic frequency band. The effect of the incident angle and the thickness of the α-MoO_(3) film on spin splitting is also considered. These results can be used for manipulating infrared radiation and optical detection.

Generation of elliptical airy vortex beams based on all-dielectric metasurface

Elliptical airy vortex beams(EAVBs) can spontaneously form easily identifiable topological charge focal spots. They are used for topological charge detection of vortex beams because they have the abruptly autofocusing properties of circular airy vortex beams and exhibit unique propagation characteristics. We study the use of the dynamic phase and Pancharatnam–Berry phase principles for generation and modulation of EAVBs by designing complex-amplitude metasurface and phase-only metasurface, at an operating wavelength of 1500 nm. It is found that the focusing pattern of EAVBs in the autofocusing plane splits into |m| + 1 tilted bright spots from the original ring, and the tilted direction is related to the sign of the topological charge number m. Due to the advantages of ultra-thin, ultra-light, and small size of the metasurface, our designed metasurface device has potential applications in improving the channel capacity based on orbital angular momentum communication, information coding, and particle capture compared to spatial light modulation systems that generate EAVBs.

Propagation of Airy Gaussian vortex beams in uniaxial crystals

The propagation dynamics of the Airy Gaussian vortex beams in uniaxial crystals orthogonal to the optical axis has been investigated analytically and numerically. The propagation expression of the beams has been obtained. The propagation features of the Airy Gaussian vortex beams are shown with changes of the distribution factor and the ratio of the extraordinary refractive index to the ordinary refractive index. The correlations between the ratio and the maximum intensity value during the propagation, and its appearing distance have been investigated.

Tight focusing of axially symmetric polarized vortex beams

Tight focusing of axially symmetric polarized vortex beams is studied numerically based on vector diffraction theory. The mathematical expressions for the focused fields are derived. Simulation results show that the focused fields and phase distributions at focus are largely influenced by both the polarization order and topological charge of the incident beams. Moreover, focal spots with flat-topped or tightly-focused patterns can be flexibly achieved by carefully choosing the polar- ization order and the topological charge, which confirms the potential of such beams in wide applications, such as optical tweezers, laser printing, lithography, and material processing.

Experimental verification on tightly focused radially polarized vortex beams

The theoretical and experimental results of tightly focused radially polarized vortex beams are demonstrated. An auto-focus technology is introduced into the measurement system in order to enhance the measurement precision, and the radially polarized vortex beams are generated by a liquid-crystal polarization converter and a vortex phase plate. The focused fields of radially polarized vortex beams with different topological charges at numerical apertures （NAs） of 0.65 and 0.85 are measured respectively, and the results indicate that the total intensity distribution at focus is dependent not only on the NA of the focusing objective lens and polarization pattern of the beam but also on the topological charge l of the beam. Some unique focusing properties of radially polarized vortex beams with fractional topological charges are presented based on numerical calculations. The experimental verification paves the way for some practical applications of radially polarized vortex beams, such as in optical trapping, near-field microscopy, and material processing.

Tightly focused properties of a partially coherent radially polarized power-exponent-phase vortex beam

A partially coherent beam called a radially polarized multi-Gaussian Schell-model power-exponent-phase vortex beam is introduced. Both the analytical formula of the beam propagating through the high-numerical-aperture objective lens based on the vectorial diffraction theory, and the cross-spectral density matrix of the beam in the focal region are derived. Then,the tight focusing characteristics of the partially coherent radially polarized power-exponent-phase vortex beam are studied numerically, and the intensity distribution, degree of polarization and coherence of the beams in the focusing region with different topological charge, power order, beam index and coherence width are analyzed in detail. The results show that the contour of the spot becomes clearer and smoother with the increase in the beam index, and the focal fields of different structures that include the flattened beam can be obtained by changing the coherence width. In addition, by changing the topological charge and power order, the intensity can gather to a point along the ring. These unique properties will have potential applications in particle capture and manipulation, especially in the manipulation of irregular particles.

Paraxial propagation of cosh-Airy vortex beams in chiral medium

Propagation dynamics of the cosh-Airy vortex(CAiV) beams in a chiral medium is investigated analytically with Huygens–Fresnel diffraction integral formula. The results show that the CAiV beams are split into the left circularly polarized vortex(LCPV) beams and the right circularly polarized vortex(RCPV) beams with different propagation trajectories in the chiral medium. We mainly investigate the effect of the cosh parameter on the propagation process of the CAiV beams.The propagation characteristics, including intensity distribution, propagation trajectory, peak intensity, main lobe's intensity, Poynting vector, and angular momentum are discussed in detail. We find that the cosh parameter affects the intensity distribution of the CAiV beams but not its propagation trajectory. As the cosh parameter increases, the distribution areas of the LCPV and RCPV beams become wider, and the side lobe's intensity and peak intensity become larger. Besides, the main lobe's intensity of the LCPV and RCPV beams increase with the increase of the cosh parameter at a farther propagation distance, which is confirmed by the variation trend of the Poynting vector. It is significant that we can vary the cosh parameter to control the intensity distribution, main lobe's intensity, and peak intensity of the CAiV beams without changing the propagation trajectory. Our results may provide some support for applications of the CAiV beams in optical micromanipulation.

Propagation properties of chirped Airy vortex beams with x-polarization through uniaxial crystals

The propagation dynamics of a chirped Airy vortex（CAiV） beam with x-polarization in uniaxial crystals orthogonal to the optical axis is studied analytically and numerically. The effect of the ratio of extraordinary and ordinary refractive indices, the chirp parameter, as well as the propagation distance is analyzed, which shows that the focused position of the CAi V beams can be controlled through changing the ratio of the extraordinary and ordinary refractive indices. In addition,with the propagation distance increasing, the asymmetry of the intensity and the angular momentum of the CAi V beam during propagation becomes much more visible. The variation of the chirp parameters can change the attenuation velocity of the vortex as well.

Nonparaxial propagation properties of the chirped Airy Gaussian vortex beams in uniaxial crystals orthogonal to the optical axis

In this article, we investigate the nonparaxial propagation properties of the chirped Airy Gaussian vortex（CAiGV）beams in uniaxial crystals orthogonal to the optical axis analytically and numerically. We discuss how the linear chirp parameters, the quadratic chirp parameters, and the Gaussian factors influence the nonparaxial propagation dynamics of the CAiGV beams. The intensity, the energy flow, the beam center, and the angular momentum of the CAiGV beams are deeply investigated. It is shown that the Gaussian factors have a great effect on the intensity and the centroid positions of the CAiGV beams. With the Gaussian factors increasing, the intensity of CAiGV beams decreases rapidly. The main lobes of the transverse intensity distribution of the CAiGV beams are similar to triangles.

Tight focusing of partially polarized vortex beams by binary phase Fresnel zone plates

Based on vectorial Debye theory, the focusing properties of partially polarized vortex beam by high numerical aperture Fresnel zone plate are investigated. The effects of the numerical apertures of and the phase difference of binary phase Fresnel zone plates, the topological charge of vortex beam and the degree of polarization of incident beam on the intensity distribution and degree of coherence in the focal plane are investigated in detail. It is shown that elliptical light spots and the flat top beam can be obtained by selecting certain parameters. Studies of degree of coherence reveal that the degree of coherence between x and y components of the electric field, which is zero in the source plane, is improved in the focal plane for vortex beam, but it is hardly changed for the nonvortex beam. It is also proved that any two of the three electric field components Ex, Ey and Ez are completely coherent everywhere in the focal region if the incident light beam is linearly polarized.

Recent advances in generation of terahertz vortex beams andtheir applications

Last decade has witnessed a rapid development of the generation of terahertz(THz)vortex beams as well as their wide applications,mainly due to their unique combination characteristics of regular THz radiation and orbital angular momentum(OAM).Here we have reviewed the ways to generate THz vortex beams by two representative scenarios,i.e.,THz wavefront modulation via specific devices,and direct excitation of the helicity of THz vortex beams.The former is similar to those wavefront engineering devices in the optical and infrared(IR)domain,but just with suitable THz materials,while the latter is newly-developed in THz regime and some of the physical mechanisms still have not been explained explicitly enough though,which would provide both challenges and opportunities for THz vortex beam generation.As for their applications,thanks to the recent development of THz optics and singular optics,THz vortex beams have potentials to open doors towards a myriad of practice applications in many fields.Besides,some representative potential applications are evaluated such as THz wireless communication,THz super-resolution imaging,manipulating chiral matters,accelerating electron bunches,and detecting astrophysical sources.

Multiple off-axis acoustic vortices generated by dual coaxial vortex beams

As a kind of special acoustic field, the helical wavefront of an acoustic vortex（AV） beam is demonstrated to have a pressure zero with phase singularity at the center in the transverse plane. The orbital angular momentum of AVs can be applied to the field of particle manipulation, which attracts more and more attention in acoustic researches. In this paper,by using the simplified circular array of point sources, dual coaxial AV beams are excited by the even-and odd-numbered sources with the topological charges of l_E and l_O based on the phase-coded approach, and the composite acoustic field with an on-axis center-AV and multiple off-axis sub-AVs can be generated by the superimposition of the AV beams for｜l_E｜ ≠ ｜l_O｜. The generation of edge phase dislocation is theoretically derived and numerically analyzed for l_E=-l_O. The numbers and the topological charges as well as the locations of the center-AV and sub-AVs are demonstrated, which are proved to be determined by the topological charges of the coaxial AV beams. The proposed approach breaks through the limit of only one on-axis AV with a single topological charge along the beam axis, and also provides the feasibility of off-axis particle trapping with multiple AVs in object manipulation.

Properties of focused Laguerre–Gaussian beam propagating in anisotropic ocean turbulence

We analyze the properties of a focused Laguerre–Gaussian(LG)beam propagating through anisotropic ocean turbulence based on the Huygens–Fresnel principle.Under the Rytov approximation theory,we derive the analytical formula of the channel capacity of the focused LG beam in the anisotropic ocean turbulence,and analyze the relationship between the capacity and the light source parameters as well as the turbulent ocean parameters.It is found that the focusing mirror can greatly enhance the channel capacity of the system at the geometric focal plane in oceanic turbulence.The results also demonstrate that the communication link can obtain high channel capacity by adopting longer beam wavelength,greater initial beam waist radius,and larger number of transmission channels.Further,the capacity of the system increases with the decrease of the mean squared temperature dissipation rate,temperature-salinity contribution ratio and turbulence outer scale factor,and with the increase of the kinetic energy dissipation rate per unit mass of fluid,turbulence inner scale factor and anisotropy factor.Compared to a Hankel–Bessel beam with diffraction-free characteristics and unfocused LG beam,the focused LG beam shows superior anti-turbulence interference properties,which provide a theoretical reference for research and development of underwater optical communication links using focused LG beams.