Close-packed optical vortex lattices with controllable structures

Archimedes spiral optical vortex array emitter

Optical vortex arrays (OVAs) are important for large-capacity optical communications, optical tweezers, and optical imaging. However, there is an urgent need to generate an optical vortex emitter to construct a specific OVA with a functional structure for the accurate transport of particles. To address this issue, we propose an Archimedes spiral OVA emitter that uses an Archimedes spiral parametric equation and coordinate localization techniques to dynamically regulate the position of each optical vortex. We discuss the phenomena of the location coordinates and Archimedes spiral from unclosed to closed on the OVA emitter. Furthermore, the propose of multiple OVA emitters demonstrates a chiral structure that has the potential for optical material processing. This study lays the foundation for generating OVAs with functional structures, which will facilitate advanced applications in the complex manipulation, separation, and transport of multiple particles.

Generation of arbitrarily structured optical vortex arrays based on the epicycle model

Optical vortex arrays (OVAs) are complex light fields with versatile structures that have been widely studied in large-capacity optical communications, optical tweezers, and optical measurements. However, generating OVAs with arbitrary structures without explicit analytical expressions remains a challenge. To address this issue, we propose an alternative scheme for customizing OVAs with arbitrary structures using an epicycle model and vortex localization techniques. This method can accurately generate an OVA with an arbitrary structure by pre-designing the positions of each vortex. The influence of the number and coordinates of the locating points on customized OVAs is discussed. Finally, the structures of the OVA and each vortex are individually shaped into specifically formed fractal shapes by combining cross-phase techniques. This unique OVA will open up novel potential applications, such as the complex manipulation of multiparticle systems and optical communication based on optical angular momentum.

Generation of discrete higher-order optical vortex lattice at focus

Higher-order vortices (HOVs) extend the dimensions of optical vortex regulation, which is of great significance in optical communication and optical tweezers. Herein, we demonstrate an alternative scheme to produce a HOV in the focus plane using multiple Laguerre-Gaussian (LG) beam interference, termed a discrete higher-order optical vortex lattice (DHOVL). The modulation depth of the DHOVL exceeds 2π. In this case, the topological charge (TC) of the DHOVL is determined by the difference of the phase period between the innermost and the outermost interference beams. Compared with a conventional HOV (CHOV), the vortex exists in a form of multiple unit singularities sharing a dark core. In addition, the average orbital angular momentum per photon of the DHOVL increases with increasing TC, surpassing that of the CHOV. This work provides a novel, to the best of our knowledge, scheme to produce a HOV, which will facilitate several advanced applications, including optical micromanipulation, optical sensing and imaging, and optical fabrication.

Generation of optical vortex lattices by in-line phase modulation with partially coherent light

Of late, generation of different kinds of optical vortex lattices has been gaining much attention due to various applications. Several methods have been reported for the generation of optical vortex lattices using a coherent light source involving interferometric, diffractive, and pinhole phase plate methods. Owing to cost effectiveness and ease in optical implementation, these days use of incoherent or partially coherent light beams is becoming popular. In this study, we demonstrate generation of different kinds of optical vortex lattices through in-line modulation of phase distributions employing the phase concatenation approach and a light-emitting diode as a light source. It is a non-interferometric and flexible technique for the selection of the parameters that characterize the optical vortices and their arrays. The proposed method allows generation of an array of optical vortices of different topological charges with zero and non-zero radial indices having different symmetries.

When optical vortex array meets cycloid

Optical vortex arrays (OVAs) have drawn widespread attention owing to their multiple optical vortices and higher dimensions. However, existing OVAs have not yet been utilized to exploit the synergy effect as an entire system, particularly for manipulating multiple particles. Thus, the functionality of OVA should be explored to respond to application requirements. Hence, this study proposes a functional OVA, called cycloid OVA (COVA), based on a combination of cycloid and phase-shift techniques. By modifying the cycloid equation, multiple structural parameters are designed to modulate the structure of the COVAs. Subsequently, versatile and functional COVAs are experimentally generated and modulated. In particular, COVA executes local dynamic modulation, whereas the entire structure remains unchanged. Further, the optical gears are first designed using two COVAs, which exhibit potential for transferring multiple particles. Essentially, OVA is endowed the characteristics and capacity of the cycloid when they meet. This work provides an alternative scheme to generate OVAs, which will open up advanced applications for the complex manipulation, arrangement and transfer of multiple particles.

Generation of optical vortex lattices by a coherent beam combining system

Owing to the unique features in intensity and phase structures, optical vortex lattices (OVLs) have attracted intensive attention and promoted various applications. However, the power scaling of OVLs always presents a critical challenge. Here we take advantage of the brightness enhancement of coherent beam combining (CBC) technology and propose an architecture for creating OVLs based on the CBC system. In the experiment, by utilizing the stochastic parallel gradient descent algorithm, the dynamic phase noises were compensated. The desired piston phase shifting of each element for tailoring the structured wavefront was implemented by the liquid crystal. When the system in a closed loop, hexagonal close-packed OVL consists of spatially distributed orbital angular momentum, beams can be generated in the far-field. This work is an important step toward future implementation of high-power structured light beams.

Goal-driven method for decoding the configuration of coherent wave groups required for the generation of arbitrary-order vortex lattices

Together, the number of waves, wave vectors, amplitudes, and additional phases constitute the coherent wave group configuration and determine the pattern of the interference field. Identifying an appropriate wave group configuration is key to generating vortex lattices via interferometry. Previous studies have approached this task by first assigning the four elements, then calibrating the vortex state of the interference field. However, this method has failed to progress beyond generating third-order vortex lattices, which are insufficient for some practical applications. Therefore, this study proposes a method for determining the proper wave group configurations corresponding to arbitrary-order vortex lattices. We adopt a goal-driven approach: First, we set a vortex lattice as the target field and model it, before decomposing the target field into a sum of multiple harmonics using Fourier transforms. These harmonics constitute the wave group required to generate the target vortex lattice. As vortex lattices of any order can be set as the target field, the proposed method is compatible with any mode order. Simulations and experiments were conducted for fourth- and fifth-order vortex lattices, thus demonstrating the effectiveness of the proposed method.

Tailoring a complex perfect optical vortex array with multiple selective degrees of freedom

Optical vortex arrays (OVAs) have successfully aroused substantial interest from researchers for their promising prospects ranging from classical to quantum physics. Previous reported OVAs still show a lack of controllable dimensions which may hamper their applications. Taking an isolated perfect optical vortex (POV) as an array element, whose diameter is independent of its topological charge (TC), this paper proposes combined phase-only holograms to produce sophisticated POV arrays. The contributed scheme enables dynamically controllable multi-ring, TC, eccentricity, size, and the number of optical vortices (OVs). Apart from traditional single ring POV element, we set up a β_g library to obtain optimized double ring POV element. With multiple selective degrees of freedom to be chosen, a series of POV arrays are generated which not only elucidate versatility of the method but also unravel analytical relationships between the set parameters and intensity patterns. More exotic structures are formed like the "Bear POV" to manifest the potential of this approach in tailoring customized structure beams. The experimental results show robust firmness with the theoretical simulations. As yet, these arrays make their public debut so far as we know, and will find miscellaneous applications especially in multi-microparticle trapping, large-capacity optical communications, novel pumping lasers and so on.

Anomalous ring-connected optical vortex array

In this study, an anomalous ring-connected optical vortex array (ARC-OVA) via the superposition of two grafted optical vortices (GOVs) with different topological charges (TCs) has been proposed. Compared with conventional OVAs, the signs and distribution of the OVs can be individually modulated, while the number of OVs remains unchanged. In particular, the positive and negative OVs simultaneously appear in the same intensity ring. Additionally, the size of the dark core occupied by the OV can be modulated, and the specific dark core is shared by a pair of plus-minus OVs. This work deepens our knowledge about connected OVAs and facilitates new potential applications, especially in particle manipulation and optical measurement.

Seeing infrared optical vortex arrays with a nonlinear spiral phase filter

We demonstrate a new method to detect infrared optical vortex arrays efficiently, which is based on simultaneous up-conversion imaging and spiral phase contrast via second-harmonic generation (SHG) in the Fourier domain. In our experiment, we use a spatial light modulator to prepare a variety of 1064 nm structured vortex arrays and employ a vortex phase plate of different topological charges to serve as the nonlinear orbital angular momentum (OAM) filter. The SHG is done by mixing the Fourier spectra of input-structured vortices with a single OAM beam in a type-II potassium titanyl phosphate crystal. Then we can convert the input invisible vortex arrays into the visible SHG light fields, and the vortex cores are mapped and seen by bright Gaussian spots, revealing both their positions and topological charges. Our work has potential in the field of infrared imaging and monitoring.

High-power vortex beam generation enabled by a phased beam array fed at the nonfocal-plane

High-power vortex beams have extensive applications in optical communication, nonlinear frequency conversion, and laser processing. To overcome a single beam's power limitation, generating vortex beams, based on a phased beam array, is an intuitive idea that requires locking each beamlet's phase to a specific different value. Conventionally, the intensity profiles of the focal plane (far field) are used for extracting the cost functions in active phase control systems. However, as for generating vortex beams, the cost function extraction method at the focal plane suffers because the same intensity profile of the beam array could correspond to different phase distributions in near field. Thus, the accurate phase control signals are difficult to obtain. In this paper, a new concept of extracting cost functions at the non-focal-plane is firstly presented and analyzed in detail by numerical simulation. This cost function extraction method is an efficient way of generating vortex beams with different topological charges, including second-order Bessel-Gaussian beams. The new concept could provide a valuable reference and contribute to the practical implementation of generating vortex beams by coherent beam combining technology.

Generation and probing of 3D helical lattices with tunable helix pitch and interface

We propose a method for generation of tunable three-dimensional (3D) helical lattices with varying helix pitch. In order to change only the lattice helix pitch, a periodically varying phase along the propagation direction is added to the central beam - one of the interference beams for lattice construction. The phase periodicity determines the helix pitch, which can be reconfigured at ease. Furthermore, a helical lattice structure with an interface (domain wall) is also achieved by changing the phase structure of the lateral beams, leading to opposite rotating direction (helicity) on different sides of the interface. When a Gaussian beam is used to probe the bulk lattice, it can evolve into a spiral beam with its helicity varying in accordance with that of the lattice. Probing along the interface with two dipole-like optical beams leads to unusual propagation dynamics, depending on the phase and size of the two beams. This approach could be further explored for studies of nonlinear interface solitons and topological interface states. In addition, the helical lattices may find applications in dynamical multi-beam optical tweezers.

Quadrant-separable multi-singularity vortices manipulation by coherent superposed mode with spatial-energy mismatch

We propose a new method of phase-singularities manipulation in optical vortices carrying orbital angular momentum (OAM), namely, quadrant-separable multi-singularity manipulation (QSMSM). In QSMSM, the positions of partial vortices in a quadrant region can be manipulated, while the singularities in other regions remain unchanged. The basic model of the multi-singularity OAM beam is obtained by the principle of coherent superposition of two Hermite-Gaussian modes with spatial mismatch. The actual multi-singularity beams are generated by external modulation with a spatial light modulator. The distribution of vortices trajectory can be controlled by the energy mismatch degree and the spatial mismatch degree. The vortices in a quadrant region can be independently manipulated by partially controlling the energy mismatch degree. The technology of partially tuning singularities in QSMSM improves the flexibility of vortices control and has great potential in applications of optical tweezers and optical modulators.

Propagation of Optical Coherence Vortex Lattices in Turbulent Atmosphere

Propagation properties in the turbulence atmosphere of the optical coherence vortex lattices (OCVLs) are explored by the recently developed convolution approach. The evolution of spectral density distribution, the normalized M 2 -factor, and the beam wander of the OCVLs propagating through the atmospheric turbulence with Tatarskii spectrum are illustrated numerically. Our results show that the OCVLs display interesting propagation properties, e.g., the initial Gaussian beam distribution will evolve into hollow array distribution on propagation and finally becomes a Gaussian beam spot again in the far field in turbulent atmosphere. Furthermore, the OCVLs with large topological charge, large beam array order, large relative distance, and small coherence length are less affected by the negative effects of turbulence. Our results are expected to be used in the complex system optical communications.