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.

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.

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.

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.

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.

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.

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.

High efficiency and broad bandwidth terahertz vortex beam generation based on ultra-thin transmission Pancharatnam-Berry metasurfaces

The terahertz(THz)vortex beam generators are designed and theoretically investigated based on single-layer ultra-thin transmission metasurfaces.Noncontinuous phase changes of metasurfaces are obtained by utilizing Pancharatnam-Berry phase elements,which possess different rotation angles and are arranged on two concentric rings centered on the origin.The circularly polarized incident THz beam could be turned into a cross-polarization transmission wave,and the orbital angular momentum(OAM)varies in value by lh.The l values change from±1 to±5,and the maximal cross-polarization conversion efficiency that could be achieved is 23%,which nearly reaches the theoretical limit of a single-layer structure.The frequency range of the designed vortex generator is from 1.2 THz to 1.9 THz,and the generated THz vortex beam could keep a high fidelity in the operating bandwidth.The propagation behavior of the emerged THz vortex beam is analyzed in detail.Our work offers a novel way of designing ultra-thin and single-layer vortex beam generators,which have low process complexity,high conversion efficiency and broad bandwidth.

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.

Properties of off-axis hollow Gaussian–Schell model vortex beam propagating in turbulent atmosphere

The analytical expression of off-axis hollow Gaussian–Schell model vortex beam(HGSMVB)generated by anisotropic Gaussian–Schell model source is first introduced.The evolution properties of off-axis HGSMVB propagating in turbulent atmosphere are analyzed.The results show that the off-axis HGSMVB with smaller coherence length or propagating in stronger turbulent atmosphere will evolve from dark hollow beam into Gaussian-like beam with a larger beam spot faster.The beams with different values of integer order N or the position for hollow and vortex factor R will have almost the same Gaussian-like spot distribution at the longer propagation distance.

Broadband and high efficiency terahertz metasurfaces for anomalous refraction and vortex beam generation

The applications of metasurfaces are currently a highly active research field due to their extraordinary ability to manipulate electromagnetic waves. The ultra-thin characteristics of metasurfaces allow the miniaturization and integration of metasurface devices. However, these devices work typically under a low efficiency and narrow bandwidth condition. In this work, we design eight multilayered unit cells with similar amplitudes and a phase interval of π/4, which convert the polarization states of the terahertz(THz) waves between two orthogonal directions. The average cross-polarized transmission amplitudes of these cells are all around 0.9 in an ultra-broad frequency range from 0.5 THz to 1.4 THz. Furthermore,unit cells are used to construct both an ultra-thin anomalous refraction metalens and a vortex phase plate. Our simulation results show that the anomalous refraction for the transmitted linear polarization component is comparable to the theoretical prediction, and the maximum error is determined to be below 4.8%. The vortex phase plate can also generate an ideal terahertz vortex beam with a mode purity of 90% and more. The distributions of longitudinal electric field, intensity, and phase illustrate that the generated vortex beam has excellent propagation characteristics and a weak divergence. Simulations of the two types of metasurface devices, based on the eight unit cells, exhibit very high efficiencies in a wide bandwidth. Our research will assist in the improvement in the practical applications of metasurfaces. It also provides a reference for the design of high efficiency and broadband devices that are applied to other frequency ranges.

A crossed focused vortex beam with application to cold molecules

We report the generation of a crossed,focused,optical vortex beam by using a pair of hybrid holograms,which combine the vortex phase and lens phase onto a spatial light modulator.We study the intensity distributions of the vortex beam in free propagation space,and the relationship of its dark spot size with the incident Gaussian beam’s waist,the lens’s focal length,and its orbital angular momentum.Our results show that the crossed,focused,vortex beam’s dark spot size can be as small as 16.3μm and adjustable by the quantum number of the orbital angular momentum,and can be used to increase the density of trapped molecules.Furthermore,we calculate the optical potential of the blue-detuned,crossed vortex beam for MgF molecules.It is applicable to cool and trap neutral molecules by intensity-gradient-induced Sisyphus cooling,as the intensity gradient of such vortex beam is extremely high near the focal point.

Switchable vortex beam polarization state terahertz multi-layer metasurface

We propose a switchable vortex beam polarization state terahertz multi-layer metasurface,which consists of threelayer elliptical metal crosses,four-layer dielectrics,and two-layer hollow metal circles,which are alternately superimposed.Under the normal incidence of left-handed circularly polarized(LCP)wave and the right-handed circularly polarized(RCP)waves,the proposed structure realizes three independent control functions,i.e.,focused and vortex beam,vortex beam with different topological charges,and polarization states switching,and azimuth switching of two vortex beams with different polarization states.The results show that the proposed metasurface provides a new idea for investigating the multifunctional terahertz wave modulation devices.

Transmission characteristics of terahertz Bessel vortex beams through a multi-layered anisotropic magnetized plasma slab

The transmission of terahertz(THz)Bessel vortex beams through a multi-layered anisotropic magnetized plasma slab is investigated by using a hybrid method of cylindrical vector wave functions(CVWFs)and Fourier transform.On the basis of the electromagnetic boundary conditions on each interface,a cascade form of expansion coefficients of the reflected and transmitted fields is obtained.Taking a double Gaussian distribution of the plasma density as an example,the influences of the applied magnetic field,the incident angle and polarization mode of the incident beams on the magnitude,OAM mode and polarization of the transmitted beams are analyzed in detail.The results indicate that the applied magnetic field has a major effect upon the polarization state of the transmitted fields but not upon the transmitted OAM spectrum.The incident angle has a powerful influence upon both the amplitude profile and the OAM spectrum of the transmitted beam.Furthermore,for multiple coaxial vortex beams,an increase of the maximum value of the plasma density causes more remarkable distortion of both the profile and OAM spectrum of the transmitted beam.This research makes a stable foundation for the THz OAM multiplexing/demultiplexing technology in a magnetized plasma environment.

Electromagnetic field of a relativistic electron vortex beam

Electron vortex beams(EVBs)have potential applications in nanoscale magnetic probes of condensed matter and nanoparticle manipulation as well as radiation physics.Recently,a relativistic electron vortex beam(REVB)has been proposed[Phys.Rev.Lett.107174802(2011)].Compared with EVBs,except for orbital angular momentum,an REVB has intrinsic relativistic effect,i.e.,spin angular momentum and spin-orbit coupling.We study the electromagnetic field of an REVB analytically.We show that the electromagnetic field can be separated into two parts,one is only related to orbital quantum number,and the other is related to spin-orbit coupling effect.Exploiting this separation property,the difference between the electromagnetic fields of the REVB in spin-up and spin-down states can be used as a demonstration of the relativistic quantum effect.The linear momentum and angular momentum of the generated electromagnetic field have been further studied and it is shown that the linear momentum is weakly dependent on the spin state;while the angular momentum is evidently dependent on the spin state and linearly increases with the topological charge of electron vortex beam.The electromagnetic and mechanical properties of the REVB could be useful for studying the interaction between REVBs and materials.

Settled fast measurement of topological charge by direct extraction of plane wave from vortex beam

A method of measuring the vortex beam topological charge(TC)is proposed based on a device that can directly extract the plane wave form from the vortex beam in which the different propagation angles of the plane waves are uniquely related to the different TCs.Then the TC can be obtained by simply comparing the energy values perceived by two fixed sensors in the detection location with the help of twin omnidirectional energy absorbers(OEAs).Because the settled detection relies only on the simple quantitative value at two fixed positions,neither pattern recognition nor field analysis procedure is applied,thus allowing faster measurement.Some features of the methodology are investigated,and the numerical simulations verify the feasibility and robustness of the system.

Tunable Optical Rotation with an M-Type Atomic System Using Vortex Beam

We consider the optical rotation of the polarization of a linearly polarized probe field passing through an M-type atomic system by using the interaction between two vortex control fields and optical transitions. We investigate theoretically to generate the spatially dependent structured light with the atoms acting as a spatially varying circular birefringent medium. We show that the polarization and intensity distributions of the vector beam spatially vary by changing the orbital angular momentum (OAM) of the vortex control field.

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.