Orbital-Angular-Momentum Mode Selection by Rotationally Symmetric Superposition of Chiral States with Application to Electron Vortex Beams

Coherence vortices by binary pinholes

Singularity in a two-point complex coherence function, known as coherence vortices, represents zero visibility with a helical phase structure. In this paper, we introduce a novel technique to generate the coherence vortices of different topological charges by incoherent source transmittance with exotic structured binary pinholes. The binary pinhole structures have been realized by lithography, followed by wet etching methods. We control the transmittance from the incoherent source plane using these exotic apertures, which finally results in a coherence vortex spectrum that features multiple and pure orbital angular momentum modes. The generation of the coherence vortices is achieved within the two-point complex spatial coherence function. The spatial coherence function exhibits the helical phase profile in its phase part, and its absolute part shows a doughnut-shaped structure. A theoretical basis is developed and validated with simulation, and experimental results. The coherence vortex spectra with OAM modes superposed with opposite topological charges, known as photonic gears, are also generated with the proposed theory.

Inelastic two-wave mixing induced high-efficiency transfer of optical vortices

A scheme for high-efficiency transfer of optical vortices is proposed by an inelastic two-wave mixing (ITWM) process in an inverted-Y four-level atomic medium, which is originally prepared in a coherent superposition of two ground states. The orbital angular momentum (OAM) information in the incident vortex probe field can be transferred to the generated signal field through the ITWM process. Choosing reasonable experimentally realizable parameters, we find that the presence of the off-resonance control field can greatly improve the conversion efficiency of optical vortices, rather than in the absence of a control field. This is caused by the broken of the destructive interference between two one-photon excitation pathways. Furthermore, we also extend our model to an inelastic multi-wave mixing process and demonstrate that the transfer efficiency between multiple optical vortices strongly depends on the superposition of the ground states. Finally, we explore the composite vortex beam generated by collinear superposition of the incident vortex probe and signal fields. It is obvious that the intensity and phase profiles of the composite vortex can be effectively controlled via adjusting the intensity of the control field. Potential applications of our scheme may exist in OAM-based optical communications and optical information processing.

Longitudinal evolution of phase vortices generated by rotationally interleaved multi-spiral

Phase vortices exhibit significant applications and hold promising prospects across various scientific fields. However, while extensive attention has been devoted to the two-dimensional transverse plane of these vortices, their longitudinal properties have received comparatively limited exploration. Our study focuses on the longitudinal evolution of phase vortices, encompassing an investigation of variational topological charges and phase distributions. The investigation employs the rotationally interleaved multi-spiral, characterized by multiple identical spirals arranged in an azimuthally symmetric rotation, to modulate phase distributions by the variable spiral radius versus the azimuthal angle. Initially, we analyze the modulation effect theoretically, delving into propagation properties and vortex formations. Subsequently, through numerical simulations of vortices generated by both single and multi-spiral setups, we examine the longitudinal evolution of topological charges and phase distributions. The analyses reveal a step-wise reductant topological charges and a tortuous increasing spatial variations of phase singularities in transmission direction, with the dependency on both propagation distance and number of multi-spiral. The outcomes hold significant potential applications in optical communications and optical tweezers.

Generation of Perfect Electron Vortex Beam with a Customized Beam Size Independent of Orbital Angular Momentum

The electron vortex beam (EVB)-carrying quantized orbital angular momentum (OAM) plays an essential role in a series of fundamental research. However, the radius of the transverse intensity profile of a doughnut-shaped EVB strongly depends on the topological charge of the OAM, impeding its wide applications in electron microscopy. Inspired by the perfect vortex in optics, herein, we demonstrate a perfect electron vortex beam (PEVB), which completely unlocks the constraint between the beam size and the beam's OAM. We design nanoscale holograms to generate PEVBs carrying different quanta of OAM but exhibiting almost the same beam size. Furthermore, we show that the beam size of the PEVB can be readily controlled by only modifying the design parameters of the hologram. The generation of PEVB with a customized beam size independent of the OAM can promote various in situ applications of free electrons carrying OAM in electron microscopy.

Generation of spatiotemporal optical vortices in ultrashort laser pulses using rotationally interleaved multispirals

Ultrashort optical vortex pulses carrying spatiotemporal orbital angular momentum (OAM) have inspired versatile applications such as the micromachining of integrated quantum chips and discoveries such as optical toroidal structures and OAM-carrying X-waves. Generating high-quality ultrashort vortices with controllable topological charges remains a crucial issue. Thus, we propose a rotationally interleaved multispiral to generate such vortices. A multispiral comprises multiple identical spirals rotated around the center in the equal-azimuthal interval and interleaved in equal-radius increments; this structure overcomes the previous structural asymmetry of the single spiral and improves the vortex quality. Accordingly, we conducted theoretical analyses, numerical simulations, and experimental investigations that demonstrated the feasibility of multispirals in generating the ultrashort vortices with symmetric distributions and flexibly controlling the topological charges. The proposed study is significant for broader applications involving ultrashort vortices and extensive investigations in related areas such as research on electron vortices, plasmonic vortices, and other matter vortices.

Universal orbital angular momentum detection scheme for any vortex beam

Existing methods for probing the orbital angular momentum carried by vortex beams have many limitations and are generally only applicable to specific types of vortex beam. In this work, we present a concise and efficient universal method for probing the orbital angular momentum that is applicable for any type of vortex beam. The vortex beam could range from being fully to partially coherent, with different spatial modes including Gaussian vortex beam, Bessel-Gaussian beam, Laguerre-Gaussian beam, etc., of any wavelength including x rays, matter waves such as electron vortices, and with high topological charge. This protocol only requires a (commercial) angular gradient filter, making it very easy to implement. The feasibility of the proposed scheme is demonstrated both theoretically and experimentally.

Orbital Angular Momentum Multiplexing in Space-Time Thermoacoustic Metasurfaces

Multiplexing technology with increased information capacity plays a crucial role in the realm of acoustic communication. Different quantities of sound waves, including time, frequency, amplitude, phase, and orbital angular momentum (OAM), have been independently introduced as the physical multiplexing approach to allow for enhanced communication densities. An acoustic metasurface is decorated with carbon nanotube patches, which when electrically pumped and set to rotate, functions as a hybrid mode-frequency-division multiplexer with synthetic dimensions. Based on this spatiotemporal modulation, a superposition of vortex beams with orthogonal OAMs and symmetric harmonics are both numerically and experimentally demonstrated. Also, flexible combinations of OAM modes with diverse frequency shifts are obtained by transforming the azimuthal phase distributions, which inspires a mode-frequency-division multiplexing approach that significantly promotes the communication capacity.

Diffraction-limit focusing using a 60-nm-thick spiral slit

We demonstrate a technique for diffraction-limit focusing, on the basis of a spatial truncation of incident light using spirally structured slit motifs. The spiral pattern leads to a global phase domain where the diffractive wave vectors are distributed in phase. We fabricate such a spiral pattern on a 60-nm-thick metallic film, capable of converting an orbital-angular-momentum beam to a non-helical high-resolution diffractive focusing beam, resulting in a high numerical aperture of 0.89 in air, and of up to 1.07 in an oil-immersion scenario. The topological complementarity between the incident beam and the slit motifs generates broadband subwavelength focusing. The idea can be extended to large-scale scenarios with larger constituents. The presented technique is more accessible to low-cost fabrications as compared with metasurface-based focusing elements.

Modal properties of a beam carrying OAM generated by a circular array of multiple ring-resonator emitters

We investigate the modal properties of a beam carrying orbital angular momentum (OAM) generated by a circular array (ring) of multiple micro-ring emitters (rings) analytically and via simulation. In such a "ring-of-rings" structure, N emitters generate N optical vortex beams with the same OAM-order l₀ at the same wavelength. The output beam is a coherent combination of the N vortex beams located at different azimuthal positions, having the same radial displacement. We derive an analytical expression for the output optical field and calculate the OAM-order power spectrum of the generated beam. The analytical expression and simulation results show that (1) the OAM spectrum of the output beam composes equidistant OAM spectral components, symmetrically surrounding l₀ with a spacing equal to N; (2) the envelope of the OAM spectrum broadens with an increased radius of the circular array or the value of l₀; and (3) the OAM components of the generated beam could be tuned either by changing the value of l₀, corresponding to different spectrum envelopes, or by adding different linear phase delays to the micro-ring emitters, which does not affect the envelope of the OAM spectrum.

Orbital angular momentum multiplication in plasmonic vortex cavities

Orbital angular momentum of light is a core feature in photonics. Its confinement to surfaces using plasmonics has unlocked many phenomena and potential applications. Here, we introduce the reflection from structural boundaries as a new degree of freedom to generate and control plasmonic orbital angular momentum. We experimentally demonstrate plasmonic vortex cavities, generating a succession of vortex pulses with increasing topological charge as a function of time. We track the spatiotemporal dynamics of these angularly decelerating plasmon pulse train within the cavities for over 300 femtoseconds using time-resolved photoemission electron microscopy, showing that the angular momentum grows by multiples of the chiral order of the cavity. The introduction of this degree of freedom to tame orbital angular momentum delivered by plasmonic vortices could miniaturize pump probe-like quantum initialization schemes, increase the torque exerted by plasmonic tweezers, and potentially achieve vortex lattice cavities with dynamically evolving topology.

Synthesis of multiple longitudinal polarization vortex structures and its application in sorting chiral nanoparticles

As the essential properties of organisms, detection and characterization of chirality are of supreme importance in physiology and pharmacology. In this work, we propose an optical technique to sort chiral materials by use of longitudinal polarization vortex (LPV) structures, which is generated with tightly focusing Pancharatnam-Berry tailored Laguerre-Gaussian beam. The nonparaxial propagation of the focusing field leads to the creation of multiple pairs of dual LPV structures with arbitrary topological charge and location, which can be independently controlled by the spatial phase modulation applied on the illumination. More importantly, the opposite spin angular momentums carried by each pair of dual foci lead to different energy flow directions, making it suitable to sort nanoparticles by their handedness. In addition, the LPV structures would also bring different dynamic behaviors to the enantiomers, providing a feasible route toward all-optical enantiopure chemical syntheses and enantiomer separations in pharmaceuticals.

The role of tunable nonlinear dark resonances on vacuum Rabi splitting and optical bistability in an atom-cavity system

The phenomenon of “dark resonances” is a well-known concept in quantum optics and laser spectroscopy. As a general rule, interactions involving in such a “dark state” lead to multiple quantum superposition states that interact coherently and are undesirable. In this paper, two types nonlinear interaction in an atomic cavity, namely the nested and cascaded interactions, are theoretically analyzed how the dark resonances form the dark state peak to modulate the vacuum Rabi splitting (VRS) and optical bistability (OB) behavior. In both the zero- and high order modes, there are four VRS peaks generated in the nested interaction and three in the cascade interaction. Dark resonance can modulate not only the peak number of VRS, but also the OB thresholds. It is found that dark state can determine the asymmetric OB distribution of nested type and symmetric OB distribution of cascade type. Besides that, the distinctive OB thresholds in two kinds of interaction also be studied. The observations not only conceptually extend the conventional “dark resonances” phenomenon, but also opens the door for a variety of new applications in tunable all-optical switch and quantum communication.

Generation of an asymmetric optical vortex array with tunable singularity distribution

Light beams with multiple phase singularities, namely, optical vortex arrays (OVAs), can be generated via coherent superpositions of symmetric laser modes, e.g., the combination of a circular vortex beam and a Gaussian beam. Further, a non-trivial evolution of the singularity structure can be obtained when the system's symmetry is broken. In this paper, we propose an asymmetric OVA (AOVA) with a highly tunable structure. The AOVA is generated by the coaxial superposition of a vortex beam and an elliptical Gaussian beam in the waist plane. After the interference of the two beams, the original high-order phase singularity residing on the beam axis breaks up into multiple +1 and -1 order vortices. The vortices are located at discrete azimuthal angles and different distances from the beam center. Unlike previous OVAs with annular shapes, the AOVA can present various singularity structures devoid of rotational symmetry, which are decided by the radii of the elliptical Gaussian beam and the topological charge of the vortex beam. Furthermore, we theoretically show that the number, sign, and distribution of local singularities can be modulated by defining two azimuthal discriminant functions. Numerical simulations and visualizations are also carried out. This work provides a new perspective for designs of connected OVAs and may find potential applications, especially in particle manipulation, optical communication, and optical metrology.

Giant Helical Dichroism of Single Chiral Nanostructures with Photonic Orbital Angular Momentum

Optical activity, demonstrating the chiral light-matter interaction, has attracted tremendous attention in both fundamental theoretical research and advanced applications of high-efficiency enantioselective sensing and next-generation chiroptical spectroscopic techniques. However, conventional chiroptical responses are normally limited in large assemblies of chiral materials by circularly polarized light, exhibiting extremely weak chiroptical signals in a single chiral nanostructure. Here, we demonstrate that an alternative chiral freedom of light-orbital angular momentum-can be utilized for generating strong helical dichroism in single chiral nanostructures. The helical dichroism by monochromatic vortex beams can unambiguously distinguish the intrinsic chirality of nanostructures, in an excellent agreement with theoretical predictions. The single planar-chiral nanostructure can exhibit giant helical dichroism of ∼20% at the visible wavelength. The vortex-dependent helical dichroism, expanding to single nanostructures and two-dimensional space, has implications for high-efficiency chiroptical detection of planar-chiral nanostructures in chiral optics and nanophotonic systems.

Nonlinear optical induced lattice in atomic configurations

Traditional artificial lattice with untunable refractive index have been restricted to flexible applied to kinds of micro medium imaging. This study proposes a novel approach to quantifying lattice using nonlinear optically induced periodic lattice, which possesses a striking feature of tunable refractive index, to further broaden current knowledge of optical imaging equipment. We conduct self-dressed and dual-dressed nonlinear four-wave mixing (FWM) signal modulation in the atoms by using the dressing effect of standing waves, and then investigate the space amplitude modulation and synthetization (amplitude and phase) modulation of the electromagnetic induced lattice (EIL) of FWM signal at the atom surface. The EIL presented in the far-field diffraction region confirms that diffraction intensity of the FWM signal can be easily transformed from zero-order to higher-order based on the dispersion effects. The tunable EIL with ultra-fast diffraction energy change can contribute to a better understanding of nonlinear process and provides a further step toward developing two-dimensional nonlinear atomic higher-resolution.

Dynamics of rotating Laguerre-Gaussian soliton arrays

Trajectory control of spatial solitons is an important subject in optical transmission field. Here we investigate the propagation dynamics of Laguerre-Gaussian soliton arrays in nonlinear media with a strong nonlocality and introduce two parameters, which we refer to as initial tangential velocity and displacement, to control the propagation path. The general analytical expression for the evolution of the soliton array is derived and the propagation properties, such as the intensity distribution, the propagation trajectory, the center distance, and the angular velocity are analyzed. It is found that the initial tangential velocity and displacement make the solitons sinusoidally oscillate in the x and y directions, and each constituent soliton undergoes elliptically or circularly spiral trajectory during propagation. A series of numerical examples is exhibited to graphically illustrate these typical propagation properties. Our results may provide a new perspective and stimulate further active investigations of multisoliton interaction and may be applied in optical communication and particle control.

Variations of topological charge of vortex beam based on a diffraction plate with spiral transmission structures

The phenomenon of vortex beams passing through a diffraction plate with rotationally symmetric superposition of spiral pinholes array is investigated. The variations of the topological charges of vortex beams are theoretically analyzed, numerically simulated and experimentally observed. It proves that the obtained topological charge value (l) is a combination of that of incident beam (l₀) and the number of the spiral structures (m). The relationship is l = Mm-l₀, where M is an integer. With this study, we proved that spiral transmission structures can also achieve the variations of the topological charge of a vortex beam. And this method is simple and costless. With the advantages of this method, it might have important applications in optical communications and optical tweezers.

Interference-assisted kaleidoscopic meta-plexer for arbitrary spin-wavefront manipulation

Achieving simultaneous polarization and wavefront control, especially circular polarization with the auxiliary degree of freedom of light and spin angular momentum, is of fundamental importance in many optical applications. Interferences are typically undesirable in highly integrated photonic circuits and metasurfaces. Here, we propose an interference-assisted metasurface-multiplexer (meta-plexer) that counterintuitively exploits constructive and destructive interferences between hybrid meta-atoms and realizes independent spin-selective wavefront manipulation. Such kaleidoscopic meta-plexers are experimentally demonstrated via two types of single-layer spin-wavefront multiplexers that are composed of spatially rotated anisotropic meta-atoms. One type generates a spin-selective Bessel-beam wavefront for spin-down light and a low scattering cross-section for stealth for spin-up light. The other type demonstrates versatile control of the vortex wavefront, which is also characterized by the orbital angular momentum of light, with frequency-switchable numbers of beams under linearly polarized wave excitation. Our findings offer a distinct interference-assisted concept for realizing advanced multifunctional photonics with arbitrary and independent spin-wavefront features. A variety of applications can be readily anticipated in optical diodes, isolators, and spin-Hall meta-devices without cascading bulky optical elements.

Topological charge measurement of vortex beams by phase-shifting digital hologram technology

We propose a direct measurement method that is applicable to both integral and fractional vortex beams. In this approach, the phase distribution of the vortex beam is visualized via the phase-shifting digital holography technique. The least square method is initiatively employed to improve the measurement precision. The maximal error of the experimental results is below 4.8%.

Measuring topological charge of partially coherent elegant Laguerre-Gaussian beam

The partially coherent elegant Laguerre-Gaussian (ELG) beam is of importance and exhibits extraordinary characteristics in many fields, such as optical communications and optical trapping. Here, we show a method to measure the topological charge of a partially coherent ELG beam. We find that the number of ring dislocations in the far-field complex degree of coherence is equal to the topological charge |l| of a partially coherent ELG beam, and which is confirmed experimentally. Our results will be useful for applications using partially coherent ELG beams.

Mapping Twisted Light into and out of a Photonic Chip

Twisted light carrying orbital angular momentum (OAM) provides an additional degree of freedom for modern optics and an emerging resource for both classical and quantum information technologies. Its inherently infinite dimensions can potentially be exploited by using mode multiplexing to enhance data capacity for sustaining the unprecedented growth in big data and internet traffic and can be encoded to build large-scale quantum computing machines in high-dimensional Hilbert space. While the emission of twisted light from the surface of integrated devices to free space has been widely investigated, the transmission and processing inside a photonic chip remain to be addressed. Here, we present the first laser-direct-written waveguide being capable of supporting OAM modes and experimentally demonstrate a faithful mapping of twisted light into and out of a photonic chip. The states OAM_{0}, OAM_{-1}, OAM_{+1}, and their superpositions can transmit through the photonic chip with a total efficiency up to 60% with minimal crosstalk. In addition, we present the transmission of quantum twisted light states of single photons and measure the output states with single-photon imaging. Our results may add OAM as a new degree of freedom to be transmitted and manipulated in a photonic chip for high-capacity communication and high-dimensional quantum information processing.

Restriction on orbital angular momentum distribution: a role of media in vortex beams propagation

The vortex beam carrying single orbital angular momentum (OAM) propagating through a medium with a certain transmission function is investigated. We show that the OAM mode weights in the output OAM spectrum involve two factors: the radial distribution of output beam power and the proposed restriction-characterized function. Based on the restriction-characterized function, we show that the OAM mode weights can only vary in a limited range. We analyze the relationship between the radial distribution of the output beam power and the OAM mode weights in the output OAM spectrum. Finally, our theoretical analysis is illustrated numerically with the cases of eccentric circular aperture and atmospheric turbulence in a weak fluctuation regime. These results provide new insights into the characterization of the OAM spectrum and may find applications for fields involving OAM, such as an OAM-based optical communication link and object detection.

Interplay between topological phase and self-acceleration in a vortex symmetric Airy beam

Photons in an optical vortex usually carry orbital angular momentum, which boosts the application of the micro-rotation of absorbing particles and quantum information encoding. Such photons propagate along a straight line in free space or follow a curved trace once guided by an optical fiber. Teleportation of an optical vortex using a beam with non-diffraction and self-healing is quite challenging. We demonstrate the manipulation of the propagation trace of an optical vortex with a symmetric Airy beam (SAB) and found that the SAB experiences self-rotation with the implementation of a topological phase structure of coaxial vortex. Slight misalignment of the vortex and the SAB enables the guiding of the vortex into one of the self-accelerating channels. Multiple off-axis vortices embedded in SAB are also demonstrated to follow the trajectory of the major lobe for the SAB beam. The Poynting vector for the beams proves the direction of the energy flow corresponding to the intensity distribution. Hence, we anticipate that the proposed vortex symmetric Airy beam (VSAB) will provide new possibilities for optical manipulation and optical communication.