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Manipulating single emitter radiation is essential for quantum information science. Significant progress has been made in enhancing the radiation efficiency and directivity by coupling quantum emitters with microcavities and plasmonic antennas. However, there has been a great challenge to generate complex radiation patterns such as vortex beam from a single emitter. Here, we report a chiral plasmonic nanocavity, which provides a strong local chiral vacuum field at an exceptional point. We show that a single linear dipole emitter embedded in the nanocavity will radiate to vortex beam via anomalous spontaneous emission with a Purcell enhancement factor up to ∼1000. Our scheme provides a new field manipulation method for chiral quantum optics and vortex lasers at the nanoscale.

We analyze the propagation of hypergeometric beams with a parabolic initial wavefront in a homogeneous medium. While hypergeomentric beams have a central amplitude singularity in the initial plane and are of infinite energy, superposition of two such beams has no singularity and is of finite energy. A particular case of such a superposition we study in detail is a sinusoidal Gaussian beam with a unit topological charge. This beam belongs to the class of elegant laser beams since it is described by the same complex-argument function both in the initial plane and in the Fresnel diffraction zone. The diameter of the first light ring of the sinusoidal Gaussian beam is almost independent of the Gaussian beam waist radius.

An optical resonator with a spiral-phase defect is proposed for vortex laser generation. Theoretical models and calculations were conducted to predict the topological charge distribution of the emitted vortex laser. Utilizing a reflective spatial light modulator that creates a spiral-phase defect of variable radius and azimuthal phase modulation, vortex beams with controllable topological charges and intensity distributions were demonstrated experimentally.

The transverse spin and orbital-to-spin angular momentum conversion during strong focusing of light beams have attracted wide interest due to the novel physics behind and their broad potential applications. In this work, we study the effect of incident beam’s degree of polarization on the localized spin density of a tightly focused field. By modulating the correlation strength between two orthogonally polarized vortex modes of the incident beam, we find that the magnitude of the focal-plane transverse spin density component changes only slightly, while its spatial shape becomes an isotropic spin vortex with the decrease of the incident degree of polarization. Whereas, the longitudinal spin density, induced by the vortex phase, reduces its magnitude significantly with the decrease of incident beam’s degree of polarization. The behavior of the focal-plane spin density is interpreted with the two-dimensional degrees of polarization among the tightly focused field components. Furthermore, we explore the roles of the topological charge on enhancing the longitudinal spin density for unpolarized incident beam. Our results reveal the feasibility of spin-orbit interaction with partially polarized or even completely unpolarized light, such as the thermal light.

Modality is a generic concept of wave-optics at the basis of optical information and communications. One of the challenges of photonics technologies based on optical orbital angular momentum consists in the production of a modal content for both the azimuthal and radial degrees of freedom. This basically requires shaping the complex amplitude of an incident light beam, which is usually made up from adaptive spatial light modulators or bespoke devices. Here, we report on the experimental attempt of a recent theoretical proposal [Opt. Lett. 42, 1966 (2017)] toward the production of various optical vortex modes of the Laguerre–Gaussian type relying on the spin–orbit interaction of light. This is done in the visible domain from optical elements made out of silica glass. The idea consists in exploiting the combined effects of azimuthally-varying geometric phase with that of radially-varying propagation features. The proposed approach can be readily extended to any wavelength as well as to other families of optical modes, although some dynamic phase problems remain to be solved to make it a turnkey technology.

We discuss the sharp focusing of an initial hybrid vector light field of the n-th order that has n C-lines (lines along which the polarization is circular). Using a complex Stokes field, it is shown that the polarization singularity index of such a field is equal to n / 2. The initial field is shown to retain it singularity index in the focal plane. Analytical expressions are obtained for the intensity and Stokes vector components in the focal plane. It is shown theoretically and numerically that for an even-order field with n = 2p, the intensity pattern at the focus has symmetry and instead of C-lines, C-points are formed, with the axes of polarization ellipses rotating around them. For n = 4, there are C-points with singularity indices 1/2 and with a “lemon” topology. Around such points, a surface that is formed by the polarization ellipses in a three-dimensional space has a Möbius strip topology. For an odd-order initial field with n = 2p +1, the intensity pattern at the focus is shown to have no symmetry, with the field becoming pure vectorial (no elliptical polarization) and the linear polarization vectors rotating around V-points.

Gears and cogwheels are elemental components of machines. They restrain degrees of freedom and channel power into a specified motion. Building and powering small‐scale cogwheels are key steps toward feasible micro and nanomachinery. Assembly, energy injection, and control are, however, a challenge at the microscale. In contrast with passive gears, whose function is to transmit torques from one to another, interlocking and untethered active gears have the potential to unveil dynamics and functions untapped by externally driven mechanisms. Here, it is shown the assembly and control of a family of self‐spinning cogwheels with varying teeth numbers and study the interlocking of multiple cogwheels. The teeth are formed by colloidal microswimmers that power the structure. The cogwheels are autonomous and active, showing persistent rotation. Leveraging the angular momentum of optical vortices, we control the direction of rotation of the cogwheels. The pairs of interlocking and active cogwheels that roll over each other in a random walk and have curvature‐dependent mobility are studied. This behavior is leveraged to self‐position parts and program microbots, demonstrating the ability to pick up, direct, and release a load. The work constitutes a step toward autonomous machinery with external control as well as (re)programmable microbots and matter.

We have shown how the spin Hall effect is formed in a tight focus for two light fields with initial linear polarization. We have demonstrated that an even number of local subwavelength regions appear in which the sign of the longitudinal projection of the spin angular momentum (the third Stokes component) alternates. When an optical vortex with topological charge n and linear polarization passes through an ideal spherical lens, additional optical vortices with topological charges n + 2, n − 2, n + 1, and n − 1 with different amplitudes are formed in the converged beam. The first two of these vortices have left and right circular polarizations and the last two vortices have linear polarization. Since circularly polarized vortices have different amplitudes, their superposition will have elliptical polarization. The sign of this elliptical polarization (left or right) will change over the beam cross section with the change in the sign of the difference in the amplitudes of optical vortices with circular polarization. We also have shown that optical vortices with topological charges n + 2, n − 2 propagate in the opposite direction near the focal plane, and together with optical vortices with charges n + 1, n − 1, they form an azimuthal energy flow at the focus.

The highly localized and uneven spatial distribution of the subwavelength light field in metal metasurfaces provides a promising means for the generation of optical vortices (OVs) with arbitrary topological charges. In this paper, a simple and reliable way for generating multichannel OVs on gold nanoporous metasurfaces is reported. The instantaneous field of arbitrary-order OVs can be regulated and concentrated on the same focal surface by adapting photonic spin–orbit interaction (SOI) and geometric phase. The focal ring energy distribution of OVs along the conical propagation path is accurately calculated, and the double phase of units induced by spin rotation is confirmed. Based on the parameter optimization of the nanohole arrangement, the simultaneous amplitude and phase modulation of multichannel OVs has been realized. Furthermore, the average multichannel signal-to-noise ratio exceeds 15 dB, which meets the requirements of high resolution and low crosstalk. Our study obtains broadband and efficient OVs, which can contribute to improving the capacity storage and security of optical information and possess great application prospects in beam shaping, optical tweezers, and communication coding. [ABSTRACT FROM AUTHOR]

In optical computing machines, many parameters of light beams can be used as data carriers. If the data are carried by optical vortices, the information can be encoded by the vortex topological charge (TC). Thus, some optical mechanisms are needed for performing typical arithmetic operations with topological charges. Here, we investigate the superposition of a single-ringed (zero-radial-index) Laguerre–Gaussian (LG) beam with an off-axis Gaussian beam in the waist plane. Analytically, we derive at which polar angles intensity nulls can be located and define orders of the optical vortices born around these nulls. We also reveal which of the vortices contribute to the total TC of the superposition and which are compensated for by the opposite-sign vortices. If the LG beam has a TC of m, TC of the superposition is analytically shown to equal [m/2] or [m/2] + 1, where [] means an integer part of the fractional number. Thus, we show that the integer division of the TC by two can be done by superposing the LG beam with an off-axis Gaussian beam. Potential application areas are in optical computing machines and optical data transmission. [ABSTRACT FROM AUTHOR]

We introduce and investigate a novel Laguerre-Gaussian (LG) beam, different from the conventional modal LG beams, which conserve the transverse intensity structure (up to scale) on propagation. The proposed beam does not conserve its structure on free space propagation but possesses some interesting properties. This beam is Fourier-invariant, and it has an increased dark area both in the initial (waist) plane and in the far field. Thus, without changing the topological charge of the beam, varying the radial (lower) index of the associated Laguerre polynomial allows increasing or decreasing the effective diameter of the central dark spot in the intensity pattern. In addition, the beam is autofocusing, i.e., the intensity distribution at the Rayleigh distance from the waist has a shape of the light ring (at any value of the radial index) with the minimal diameter and with the maximal on-ring intensity. Such a beam can be adopted for microparticle manipulation. Increasing the dark area in the focus of a high-aperture spherical lens allows the simultaneous trapping of several absorbing microparticles into this dark area. [ABSTRACT FROM AUTHOR]

An optical resonator with a spiral-phase defect is proposed for vortex laser generation. Theoretical models and calculations were conducted to predict the topological charge distribution of the emitted vortex laser. Utilizing a reflective spatial light modulator that creates a spiral-phase defect of variable radius and azimuthal phase modulation, vortex beams with controllable topological charges and intensity distributions were demonstrated experimentally. [ABSTRACT FROM AUTHOR]

In this paper we investigate the self-reference interferometry of optical vortices using a Michelson interferometer. It is found that the detection of topological charge (TC) for optical vortices is constrained by some physical conditions. We present these conditions through theoretical analyses, numerical simulation and experimental results. The maximal detectable TCs are different for different parameters, which is helpful for the measurement of TC in practical applications. Within the range allowed by the constrained conditions, we also study the detection of TC using the interference pattern of a two-way optical vortex, by changing the inclined angle of one mirror of the Michelson interferometer. [ABSTRACT FROM AUTHOR]

Featured Application: Optical communication, Optical manipulation, Optical processing. An optical system consisting of a straight-line polarization grating (SPG) and two parabolic-line polarization gratings (PPGs) is presented for the characterization of optical vortices (OVs) with arbitrary states of polarization (SoPs). The PPG is capable of converting an OV with a specific SoP into a bright bar-like spot with 100% efficiency. The number of dark lines and their orientation respectively correspond to the magnitude and sign of topological charge (TC) of the incident OV, thereby enabling characterization of OVs with high efficiency. Furthermore, on combining an SPG with PPGs, the present system can characterize the TC of incident OVs regardless of their SoP. The feasibility of the system was demonstrated in experiments using gratings fabricated by applying the photoalignment method and employing films of a photo-crosslinkable polymer liquid crystal. The experimentally obtained efficiency is 70.2%. We furthermore demonstrate the system's capability to characterize polarization vortices. [ABSTRACT FROM AUTHOR]

An optical vortex possesses a ring-shaped spatial profile and orbital angular momentum (OAM) owing to its helical wavefront. This form of structured light has garnered significant attention in recent years, and it has enabled new investigations in fundamental physics and applications. One such exciting application is laser-based material transfer for nano-/micro-fabrication. In this work, we demonstrate the application of a single-pulse optical vortex laser beam for direct printing of ring-shaped structures composed of hexagonal close-packed, mono-/multi-layered nanoparticles which exhibit ‘structural color’. We compare and contrast the interaction of the vortex beam with both dielectric and metallic nanoparticles and offer physical insight into how the OAM of vortex beams interacts with matter. The demonstrated technique holds promise for not only photonic-based nano-/micro-fabrication, but also as a means of sorting particles on the nanoscale, a technology which we term ‘optical vortex nanoparticle sorting’.

Experimental results of the investigation of self-healing properties of terahertz Bessel beams with orbital angular momentum (OAM) with topological charges of l=3 and l=4 in free space after passing through a dispersive medium are presented.

It is theoretically and numerically shown that when tightly focusing an n-th order vector light field that has the central V-point (at which the linear polarization direction is undetermined), the polarization singularity index n, and a "flower"-shaped intensity pattern with 2(n-1) lobes it forms a transverse intensity distribution with 2(n-1) local maxima. At the same time, a vector light field with the polarization singularity index -n, which has the form of a "web" with 2(n+1) cells generates at the sharp focus a transverse intensity distribution with 2(n+1) local maxima. In the focal spot, either 2(n-1) or 2(n+1) V-point polarization singularities with alternating indices +1 or -1 are formed at the intensity zero.

It is shown theoretically and numerically that circularly and linearly polarized incident beams produce at the tight focus identical circularly symmetric distributions of an on-axis energy flux. It is also shown that the on-axis energy fluxes from radially and azimuthally polarized optical vortices with unit topological charge are equal to each other. An optical vortex with azimuthal polarization is found to generate the minimum focal spot measured for the intensity (all other parameters being equal). Slightly larger (by a fraction of a percent) is the spot size calculated for the energy flux for the circularly and linearly polarized light. The spot size in terms of intensity is of importance in light-matter interaction, whereas the spot size in terms of energy flux affects the resolution in optical microscopy.

In this paper, we summarize a remarkable result obtained by Soskin et al. in Phys Rev A 56, 4064 (1997). We show that for an on-axis superposition of two different-waist Laguerre-Gauss beams with numbers (0, n) and (0, m), the topological charge equals TC=m up to a plane where the waist radii become the same, given that the beam (0, m) has a greater waist radius, changing to TC=n after this plane. This occurs because in the initial plane the superposition has an on-axis op-tical vortex with TC=m and on different axis-centered circles there are (n – m) vortices with TC= +1 and (n – m) vortices with TC= –1. On approaching the above-specified plane, the vortices with TC= -1 "depart" to infinity with a higher-than-light speed, with the TC of the total beam becoming equal to TC=n. If, on the contrary, the beam (0, m) has a smaller waist, then the total TC equals n on a path from the initial plane up to a plane where the waist radii become the same, changing to TC=m after the said plane. This occurs because after the said plane, n–m vortices with TC= –1 "arrive" from infinity with a higher-than-light speed.

Optical vortices are getting attention in modern optical metrology. Because of their unique features, they can be used as precise position markers. In this paper, we show that an artificial neural network can be used to improve vortex localization. A deep neural network with several hidden layers was trained to find subpixel vortex positions on the spiral phase maps. Several thousand training samples, differing by spiral density, its orientation, and vortex position, were generated numerically for teaching purposes. As a result, Best Validation Performance of the order of 10��5 pixel has been reached. To verify the usefulness of the proposed method, a related experiment in the setup of an optical vortex scanning microscope has been reported. It is shown that the vortex can be localized with subpixel accuracy also on experimental phase maps.

Recently, orbital angular momentum (OAM) has been adopted to measure the shape of static objects and the translation motion of moving objects in optical remote sensing. Most of these studies rely on measuring the intensity variation of OAM beams. However, the OAM intensity does not change with the rotation of the spinning object, but its phase changes. The phase variation is proved to be proportional to the object’s angular velocity. Since a rotating object will cause the OAM phase dependent on time, the OAM phase needs to be measured instantaneously, to support the OAM-based angular velocity measurement. In this work, we report a scheme to measure the angular velocity of a spinning object using a photonic OAM phase spectrum. A phase-to-intensity strategy is implemented to enable the real-time multi-OAM phase measurement, in which the phase can be determined with the intensities of four focal spots in a two-dimensional array generated by a phase-only spatial light modulator. The experimental results show that the average error of the measured angular velocity could be under 2.45% by detecting the phase of two OAM modes. This OAM-based angular velocity detection method provides a complementary approach to characterize the rotational Doppler effect, especially for slow angular motion.

Over the past 30 years, physical optics has been enriched by the appearance of singular optics as a new branch approved in scientific classifiers. This review briefly outlines the main concepts of the singular optics, their role in physical research and applications, and prospects of further development. The wave singularities are considered as a sort of structured-light elements and analyzed based on the generic example of screw wavefront dislocation (optical vortex). Their specific topological and mechanical properties associated with the transverse energy circulation are discussed. Peculiar features of the non-linear optical phenomena with singular fields are exhibited, with the special attention to generation of multidimensional entangled quantum states of photons. Optical fields with multiple singularities, especially, the stochastic speckle fields, are discussed in the context of optical diagnostics of random scattering objects. The exact and approximate correspondences between characteristic parameters of the optical-field intensity and phase distributions are analyzed with the aim of recovering phase information from the intensity measurements (“phase problem” solution). Rational singularity-based approaches to informative measurements of the scattered-field distribution are discussed, as well as their employment for the objects’ diagnostics. In particular, the practical instruments are described for the high-precision rough-surface testing. Possible enhancements of the singular-optics ideas and concepts in a wider context, including the transformation optics, near-field optics (surface waves), partially-coherent fields, and wave fields of other physical nature, are briefly exposed.

It is an interesting and meaningful exploration to produce a new type of multi-dimensional spatiotemporal light field with non-diffraction and self-focusing properties. In this paper, a novel scheme is proposed to construct a tunable weak chirp dual Airy Bessel vortex (CdAiBV) spatiotemporal wave packet (WP), and the generation experimental setup is also demonstrated. Significantly, the generated higher-order wave packet carries optical vortices with a complex structure and presents propagation-invariant property within a fairly long distance. Dependence of the targeted wave packet’s non-diffraction properties and self-focusing effects on the topological charge n and phase mask’s control parameter β, and influence of the initial frequency chirp coefficients C1 and C2 on the acceleration and deceleration characteristics of the temporal Airy pulse and the spatiotemporal structure of the CdAiBV wave packet are investigated. Furthermore, evolution of the topological phase, energy flow, and orbital angular momentum (OAM) density of higher-order wave packets propagating in the time-space domain are considered. Results demonstrate that the generated spatiotemporal CdAiBV wave packet would undergo a process of spatial “autofocus to defocus” and temporal “deceleration and collapse” during propagation, and only a fairly weak chirp is needed in such a process. It is also noted that the optical vortex is well confined in the space-time domain, and preserves intact spiral wavefront structure and conserved topological charge. What’s more, the transverse energy flow rotates periodically, and the central irradiance increases continuously when increase the propagation distance. Our work realized the separation and combination of the intertwined time and space variables, and further revealed the propagation dynamics of spatiotemporal structured light fields.

Orbital angular momentum (OAM) beams, featured by the helical phase front and doughnut intensity profile, have been demonstrating great potential for various applications. Ring‐core optical fiber is also experimentally proven to be an effective waveguide for OAM mode. In general, managing the chromatic dispersion in the optical fiber is important for a wide range of applications. In this article, a highly dispersive germanium‐doped ring‐core fiber with dual selectable operating windows for OAM mode is proposed. The proposed fiber consists of three concentric high‐refractive‐index germanium‐doped rings with different mole fractions. The chromatic dispersion of the OAM1,1 mode in the ring fiber can be as low as −129 964 ps/(nm·km) at 1644.4 nm as the light launches into the fiber from the innermost ring and −270 017 ps/(nm·km) at 1651 nm as the light enters from the outermost ring. Furthermore, the effect of the geometrical and material parameters on chromatic dispersion for OAM1,1 mode is investigated. When the parameters of the innermost and outermost rings are varied separately, the corresponding operation windows are changed independently. An extremely negative dispersion for the OAM1,1 mode of −817 576 ps/(nm·km) can be achieved. This design can serve as a dispersive element in various OAM‐based optical fiber systems.

The angular lower bound does not correspond to the Robertson lower bound in the range of coordinate variable and the correlation form between the pair of uncertainties. In addition, the pair of angular uncertainties in a singular light beam is unevaluated. Moreover, these two uncertainties are independent of n-fold symmetry of azimuthal intensity that are with the two invariable types in a light beam. Herein, we report the smaller difference between mean OAM and the product of azimuthal phase-gradient of beam cross-section and ℏ, the larger azimuthal coordinate range of one periodic helical wavefront in a set of numerous singular light beams, each of which utilises the superposition comprising two fractional OAM light beams that have a difference of δ in the azimuthal phase-gradient. This is attributed to the angular uncertain principle as an uncertainty relation between the pair of periodically angular uncertainties that is defined with the sub-n-fold periodicity of a light beam by a constant bound between 0.184ℏ and 0.204ℏ. This periodically angular lower bound corresponds to the Robertson lower bound for the infinity range of the coordinate variable and the constant correlation between the pair of uncertainties; however, it is stronger by 2.45 times of magnitude at least. Moreover, we quantitatively estimated the unevaluated OAM uncertainty in a singular light beam by using the periodically angular relation. We demonstrate that the OAM uncertainty is a monotonic function of the azimuthal phase-gradient difference δ, 0 ≤ δ ≤ n, in this singular light with identically mean OAMs of 0 and nℏ/2.

We have shown that a reverse energy flow (negative projection of the Poynting vector onto the optical axis) at the sharp focus of an optical vortex with topological charge 2 and left-hand circular polarization arises because the axial spin flow has a negative projection onto the optical axis and is greater in magnitude than positive projection onto the optical axis of the orbital energy flow (canonical energy flow). Also, using the Richards-Wolf formulas, it is shown that when focusing a left-handed circularly polarized light, in the region of the on-axis reverse energy flow, the light is right-handed circularly polarized.

In optical data transmission with using vortex laser beams, data can be encoded by the topological charge, which is theoretically unlimited. However, the topological charge of a single separate vortex (screw dislocation) is limited by possibilities of its generating. Therefore, we investigate here three examples of multivortex Gaussian light fields (two beams are form-invariant and one beam is astigmatic) with an unbounded (countable) set of screw dislocations. As a result, such fields have an infinite topological charge. The first beam has the complex amplitude of the Gaussian beam, but multiplied by the cosine function with a squared vortex argument. Phase singularity points of such a beam reside in the waist plane on the Cartesian axes and their density grows with increasing distance from the optical axis. The transverse intensity distribution of such a beam has a shape of a four-pointed star. All the optical vortices in this beam has the same topological charge of +1. The second beam also has the complex amplitude of the Gaussian beam, multiplied by the vortex-argument cosine function, but the cosine is raised to an arbitrary power. This beam has a countable number of the optical vortices, which reside in the waist plane uniformly on one Cartesian axis and the topological charge of each vortex equals to power, to which the cosine function is raised. The transverse intensity distribution of such beam consists of two light spots residing on a straight line, orthogonal to a straight line with the optical vortices. Finally, the third beam is similar to the first one in many properties, but it is generated with a tilted cylindrical lens from a 1D parabolic-argument cosine grating.

In optical data transmission with using vortex laser beams, data can be encoded by the topo-logical charge, which is theoretically unlimited. However, the topological charge of a single sepa-rate vortex is limited by possibilities of its generating. Therefore, in this work, we analyze light beams with an unbounded (countable) set of optical vortices. The summary topological charge of such beams is infinite. Phase singularities (isolated intensity nulls) in such beams typically have a unit topological charge and reside equidistantly (or not equidistantly) on a straight line in the beam cross section. Such beams are form-invariant and, on propagation in space, change only in scale and rotate. Orbital angular momentum of such multivortex beams is finite, since only a finite number of optical vortices fall into the area, where the Gaussian beam has a notable intensity. Other phase singularities are located in the periphery (and at the infinity), where the intensity is almost zero.

Generally, an optical vortex lattice (OVL) is generated via the superposition of two specific vortex beams. Thus far, OVL has been successfully employed to trap atoms via the dark cores. The topological charge (TC) on each optical vortex (OV) in the lattice is only ±1. Consequently, the orbital angular momentum (OAM) on the lattice is ignored. To expand the potential applications, it is necessary to rediscover and exploit OAM. Here we propose a novel high-order OVL (HO-OVL) that combines the phase multiplication and the arbitrary mode-controllable techniques. TC on each OV in the lattice is up to 51, which generates sufficient OAM to manipulate microparticles. Thereafter, the entire lattice can be modulated to desirable arbitrary modes. Finally, yeast cells are trapped and rotated by the proposed HO-OVL. To the best of our knowledge, this is the first realization of the complex motion of microparticles via OVL. Thus, this work successfully exploits OAM on OVL, thereby revealing potential applications in particle manipulation and optical tweezers.

We theoretically show that an astigmatic transformation of an nth-order edge dislocation (a zero-intensity straight line) produces n optical elliptical vortices (spiral dislocations) with unit topological charge at the double focal distance from the cylindrical lens, located on a straight line perpendicular to the edge dislocation, at points whose coordinates are the roots of an nth-order Hermite polynomial. The orbital angular momentum of the edge dislocation is proportional to the order n.

If a vortex propagation-invariant beam is given by all its intensity nulls, then its topological charge (TC) can be defined easily: its TC is equal to the sum of topological charges of all optical vortices in these intensity nulls. If, however, a propagation-invariant beam is given as a superposition of several light fields, then determining its TC is a complicated task. Here, we derive the topological charges of four different types of propagation-invariant beams, represented as axial superpositions of Hermite–Gaussian beams with different amplitudes and different phase delays. In particular, topological charges are obtained for such beam families as the Hermite–Laguerre–Gaussian (HLG) beams and two-parametric vortex Hermite beams. We show that the TC is a quantity resistant to changing certain beam parameters. For instance, when the parameters θ and α of the HLG beams are altered, the beam intensity also changes significantly, but the TC remains unchanged.

We consider sharp focusing of an axial superposition of two optical vortices with identical topological charges, but different amplitudes and circular polarizations of different signs. The ratio of the amplitudes of the two beams is a parameter. When this parameter changes, the polarization state of the superposition changes from linear polarization to right-hand circular polarization. Based on the Richards–Wolf theory, exact expressions are obtained for the longitudinal components of the spin angular momentum (SAM) density and orbital angular momentum (OAM) density at the focus of the considered superposition. It follows from these expressions that the sum of the total longitudinal components of the SAM and OAM is conserved upon focusing, and also that, due to the spin-orbit conversion, the total longitudinal component of the SAM decreases during focusing, while the total longitudinal component of the OAM increases by the same amount. By changing the ratio of the amplitudes of the constituent beams from 1 to 0, one can change the value of the spin-orbit conversion from zero (for linear polarization) to a maximum (for circular polarization). Also, by changing this parameter, one can control the spin Hall effect at the focus, which takes place at the focus of the considered beam. This study can be applied for controlling the rotation velocity of microparticles trapped in the focus.

The dynamics of the topological charge of a vortex optical beam propagating in turbulent air while accounting for the cubic nonlinearity is theoretically considered. In a number of examples, we show that the optical beam, self-focusing, manifests itself ambiguously depending on the optical wave power. At near-critical values of beam power, self-focusing leads to enhanced spatial localization of optical vortices and substantial suppression of vortex walk-off relative to the beam axis caused by air turbulence. However, with increasing optical intensity, the modulation instability imposed by cubic nonlinearity becomes significant and contributes jointly with medium turbulence and leads to faster divergence of vortex beams.

In this paper, we focus on the study of the negative energy flow in the tight focusing of a radially polarized vortex beam. We know that, because of the coupling of the polarization state and the vortex charge, the on-axis energy flow in the focal region can be well modulated by changing the polarization order and the vortex charge of the incident vector beam. This shows that when the polarization order and the vortex charge satisfy the specific relation, the on-axis negative energy flow can be obtained in the focal region. Moreover, the initial phases of two polarization unit vectors also affect the evolution of the on-axis negative energy flow in the tight focusing of the radially polarized beam. The phase difference modulation of the two polarization unit vectors indicates two different modulations of the polarization state. Our work provides a more flexible modulation method for focal shaping and optical modulation.

Given that circular symmetric Airy vortex beam (CSAVB) was found to possess a stable central cavity and an opposing transport process to circular Airy vortex beam, it has been recognized as a potentially powerful tool for particle trapping and optical communication. In order to facilitate broader application scenarios, this paper presents a novel approach to the generation of multiple CASVBs based on a single metasurface. In the proposed method, three independent CSAVBs carrying different new kinds of power-exponent-phase vortices (NPEPVs) can be obtained under two orthogonal circularly polarized or an arbitrary linear polarized incident, respectively. Each of these vortex structures is characterized by a distinct orbital angular momentum, which is jointly determined by two parameters of the NPEPVs. This indicates that the CSAVB and the device have greater freedom than the canonical optical vortex beams and the previous vortex beam generators in controlling the optical vortex. These results have the potential to advance the development of vortex beams and enhance their applications in micromanipulation, optical communication and imaging. [ABSTRACT FROM AUTHOR]

In this paper, we have realized the high purity non-diffracting optical vortex arrays with a high topological charge using quasi-symmetrical plane waves for the first time. The triangular vortex arrays with l = ±2 can be generated by six quasi-symmetrical plane waves, and the square vortex arrays with l = ±3 can be generated by eight quasi-symmetrical plane waves. The adjacent vortex units have opposite topological charges. We have also obtained the relations between the periods of the field formed by the six/eight quasi-symmetrical plane waves and the periods of the field formed by the three/four symmetrical plane waves. The simulation and experimental results demonstrate the feasibility of this method. • The high purity non-diffracting triangular vortex arrays with l =±2 can be generated by six quasi symmetric plane waves. • The high purity non-diffracting square vortex arrays with l =±3 can be generated by eight quasi symmetric plane waves. • The relationship between the periods of the field formed by six quasi symmetric plane waves or three symmetric plane waves. • The relationship between the periods of the field formed by eight quasi symmetric plane waves or four symmetric plane waves. [ABSTRACT FROM AUTHOR]

The significance of abruptly autofocusing vortex beams with a unique helical phase structure lies in particle trapping and optical spanner applications. This paper presents a novel modulation of a circular Pearcey beam utilizing a multicyclic helical phase and a chirp factor. Both theoretical analyses and experimental results demonstrate that we have successfully designed a beam with tornado properties and optically chiral structure. This beam has multidimensionally tunable parameters, allowing not only different focusing intensities, focal lengths and focal spot shape distributions, but also controllable rotational propagation directions. Furthermore, it has the ability to produce two dual focusing modes with dissimilar focal spot distributions. We believe that such a beam holds potential applications in the realisation of optical spanners, multi-region trapping of particles and the fabrication of chiral metamaterials. • Multifocal tornado beam: This article introduces a novel multifocal chiral tornado beam (CTCPB), which features chiral structure capable of generating dual-focus modes with varying focal intensities, focal lengths, and focal spot distributions. • Transmission Characteristics: Through theoretical analysis and experimental validation, this article has demonstrated the design of the CTCPB and its propagation characteristics in free space. • Optical chirality and Rayleigh particle trapping: The theoretical analysis indicates that the CTCPB can enable multi-regional capture of Rayleigh particles and has potential for interactions with chiral materials. [ABSTRACT FROM AUTHOR]

In this work, using the Richards-Wolf formalism, we consider the sharp focusing of optical vortices with hybrid polarization, which combines the properties of azimuthal and circular polarizations. It is shown that these beams have a number of interesting properties: the intensity in such beams rotates with distance from the focal spot, and the longitudinal component of the spin angular momentum has an asymmetric appearance. [ABSTRACT FROM AUTHOR]

We derive a closed-form expression for the mutual coherence function (MCF) of a twisted spatiotemporal optical vortex (STOV) beam after propagating a distance z in a linear dispersive medium. A twisted STOV beam is a partially coherent optical field that possesses a coherent STOV and a stochastic twist coupling its space and time dimensions. These beams belong to a special class of space–time-coupled light fields that carry transverse (to the direction of propagation) orbital angular momentum, making them potentially useful in numerous applications including quantum optics, optical manipulation, and optical communications. After presenting the derivation, we validate our new general MCF by showing that it simplifies to the MCFs for two example beams from the literature. Lastly, we present and analyze space–time beam profiles and complex arguments (phases) of the MCF at multiple z and differing amounts of material dispersion, field correlation or coherence, and beam twist to gain insight into how twisted STOV beams evolve in dispersive media. We conclude with a brief summary. • We derive the MCF for a twisted STOV beam propagating in dispersive media. • A twisted STOV beam is a space–time-coupled (STC) field that carries transverse OAM. • We observe interesting propagation behaviors not predicted in prior works. • Our analysis will be useful in applying these STC beams in optical tweezing, optical communications, etc. [Display omitted] [ABSTRACT FROM AUTHOR]

The effect of light beams of various structures (TEM 00 , TEM 01 , annular, vortex) on films of the photochromic azobenzene-containing polymethacrylates is studied. To analyze induced anisotropy, the methods of polarization microscopy and aberrational self-action were used. The latter is convenient non-destructive method for determining induced phase profiles and the anisotropy sign. Under the influence of the polarized light in the visible range, initially amorphous polymer samples become optically anisotropic, the induced anisotropy obeys the dose law in a wide range of light powers and illumination times. The induced anisotropy can be rewritten upon re-exposure to light or erased by heating above the transition point to the isotropic state. The direction of the induced optical axis depends on the type of light polarization. By controlling the polarization and structure of a light beam, it is possible to obtain regions with a refractive index higher or lower than the original one, as well as complex distributions, including similar to those in phase converters for vortex generation. High photosensitivity in the UV and visible ranges, local response and rewritability make these materials promising for photopatterning and light-beam diagnostics. Light beams of various types induce optical anisotropy in initially amorphous polymer layer in accordance with beam polarization structure and intensity distribution. The modified regions acts as a phase converters and are visualized with polarization optical microscopy. [Display omitted] • PMDCN shows effective and local light-rewritable relief-free light-induced anisotropy. • Aberrational self-action is a convenient way to study induced anisotropy in polymers. • Light beams of various types record spatially inhomogeneous optical-phase structures. • Vortex beam can transfer anisotropy structure from converter into polymer. [ABSTRACT FROM AUTHOR]

A combined high-aperture metalens in a thin silicon nitride film that consists of two tilted sectored metalenses is considered. Each sector of the metalens consists of a set of binary subwavelength gratings. The diameter of the metalens is 14 μm. Using a time-domain finite difference method, we show that the metalens can simultaneously detect optical vortices with two topological charges −1 and −2, almost over the entire spectrum of visible wavelengths. The metalens can distinguish several wavelengths that are focused at different points in the focal plane due to a 1-nm change in wavelength resulting in a focal spot shift of about 4 nm. When the metalens is illuminated by a Gaussian beam with left-handed circular polarization, two optical vortices with topological charges 1 and 2 are simultaneously formed 6-μm apart at the focal distance of 6 μm. [ABSTRACT FROM AUTHOR]

In optical communications, it is desirable to know some quantities describing a light field, which are conserved on propagation or resistant to some distortions. Typically, optical vortex beams are characterized by their orbital angular momentum (OAM) and/or topological charge (TC). Here, we show analytically that the OAM of a single rotationally symmetric optical vortex is not affected by an arbitrary-shape aperture or by other amplitude perturbations. For a superposition of two or several optical vortices (with different TCs), we studied what happens to its OAM when it is distorted by a hard-edge sector aperture. We discovered several cases when such perturbation does not violate the OAM of the whole superposition. The first case is when the incident beam consists of two vortices of the same power. The second case is when the aperture half-angle equals π multiplied by an integer number and divided by the difference between the topological charges. For more than two incident beams, this angle equals π multiplied by an integer number and divided by the greatest common divisor of all possible differences between the topological charges. We also show that such a sector aperture also conserves the orthogonality between the complex amplitudes of the constituent vortex beams. For two incident vortex beams with real-valued radial envelopes of the complex amplitudes, the OAM is also conserved, when there is a ±π/2 phase delay between the beams. When two beams with the same power pass through a binary radial grating, their total OAM is also conserved. We hope that these findings could be useful for optical communications since they allow for the identification of incoming optical signals by their OAM by registering only part of the light field within a sector aperture, thus reducing the cost of the receiving devices. [ABSTRACT FROM AUTHOR]

The rotational Doppler effect (RDE), as a counterpart of the conventional well-known linear Doppler effect in the rotating frame, has attracted increasing attention in recent years for rotating object detection. However, the effect of the beam size on the RDE is still an open question. In this article, we investigated the influence of the size of the probe light; i.e., the size of the ring-shaped orbital angular momentum (OAM)-carrying optical vortex (OV), on the RDE. Both the light coaxial and noncoaxial incident conditions were considered in our work. We analyzed the mechanism of the influence on the RDE under the light coaxial, lateral misalignment, and oblique incidence conditions based on the small-scatterer model. A proof-of-concept experiment was performed to verify the theoretical predictions. It was shown that both the signal-to-noise ratio and the frequency spectrum width were related to the OV size. The larger the beam size, the stronger the RDE signal observed in the practical detection. Especially in the lateral misalignment condition, the large OV size effectively reduced the signal spreading and enhanced the signal strength. These findings may be useful for practical application of the optical RDE in remote sensing and metrology. [ABSTRACT FROM AUTHOR]

Blood coagulation is a complicated dynamic process that maintains the blood's fluid state and prevents uncontrollable bleeding. The real-time monitoring of coagulation dynamics is critical for blood transfusion guidance, emergency management of trauma-induced coagulopathy, perioperative bleeding, and targeted hemostatic therapy. Here, we utilize optical vortex dynamics to detect the blood coagulation dynamic process in a rapid and non-contact manner. To characterize the temporal changes in viscoelastic properties of blood during coagulation, we track the stochastic motion of optical vortices in the time-varying speckles reflected from 100 blood samples with varied coagulation profiles. The mean square displacement (MSD) of the vortices increases nonlinearly with time lag during blood coagulation reminiscent of the particles in viscoelastic fluids. The MSD curves with coagulation time are similar to the tracings of thromboelastography (TEG) during the blood coagulation. The retrieved coagulation parameters, such as reaction time and activated clotting time measured using the optical vortex method, exhibit a close correlation to those parameters acquired from TEG. These results demonstrate the feasibility of the optical vortex method for monitoring blood coagulation at the point of care. Our method is also applicable to measuring the viscoelasticity of complex fluids and turbid soft matters. [ABSTRACT FROM AUTHOR]

Circular airy vortex beams (CAVBs) have attracted much attention due to their "abruptly autofocusing" effect, phase singularity, and their potential applications in optical micromanipulation, communication, etc. In this paper, we numerically investigated the propagation properties of circular airy beams (CABs) imposed with different optical vortices (OVs) along the optical axis of a uniaxial crystal for the first time. Like other common beams, a left-hand circular polarized (LHCP) CAVB, propagating along the optical axis in a uniaxial crystal, can excite a right-hand circular polarized (RHCP) component superimposed with an on-axis vortex of topological charge (TC) number of 2. When the incident beam is an LHCP CAB imposed with an on-axis vortex of TC number of l = 1, both of the two components have an axisymmetric intensity distribution during propagation and form hollow beams near the focal plane because of the phase singularity. The phase pattern shows that the LHCP component carries an on-axis vortex of TC number of l = 1, while the RHCP component carries an on-axis vortex of TC number of l = 3. With a larger TC number (l = 3), the RHCP component has a larger hollow region in the focal plane compared to the LHCP component. We also studied cases of CABs imposed with one and two off-axis OVs. The off-axis OV makes the CAVB's profile remain asymmetric throughout the propagation. As the propagation distance increases, the off-axis OVs move near the center of the beam and overlap, resulting in a special intensity and phase distribution near the focal plane. [ABSTRACT FROM AUTHOR]

The diffraction of elegant vortex hypergeometric (HyG) laser beams with a parabolic initial wavefront in a homogeneous medium is considered. While HyG beams have a central amplitude singularity in the initial plane and are of infinite energy, the superposition of two such beams has no singularity and is of finite energy. A particular case of this superposition, i.e., a sinusoidal Gaussian beam with a unit topological charge, is studied in detail. This beam belongs to the class of elegant laser beams since it is described by the same complex-argument function both in the initial plane and in the Fresnel diffraction zone. [ABSTRACT FROM AUTHOR]

A method allowing one to extract an information signal in a beam whose distortions result in the appearance of additional optical vortices in it is developed. The information is also transmitted with the use of a vortex. The investigation is carried out based on numerical experiments. All dislocations in the corresponding model are introduced into the wavefront in the plane of the source aperture and then the radiation propagates under conditions of free diffraction. The optical scheme of the experiment approximately corresponded to an optical communication line in which radiation undergoes considerable distortions in a thin medium layer located near the exit aperture of the laser generator. In this paper, two methods of extracting an information signal on the background of noises are considered and the possibility of using one of them in real communication lines is demonstrated. [ABSTRACT FROM AUTHOR]

We study coaxial superpositions of Gaussian optical vortices described by a geometric progression. The topological charge (TC) is obtained for all variants of such superpositions. The TC can be either integer or half-integer in the initial plane. However, it always remains integer when the light field propagates in free space. In the general case, the geometric progression of optical vortices (GPOV) has three integer parameters and one real parameter, values which define its TC. The GPOV does not conserve its intensity structure during propagation in free space. However, the beam can have the intensity lobes whose number is equal to one of the family parameters. If the real GPOV parameter is equal to one, then all angular harmonics in the superposition are of the same energy. In this case, the TC of the superposition is equal to the order of the average angular harmonic in the progression. Thus, if the first angular harmonic in the progression has the TC of k and the last harmonic has the TC of n, then the TC of the entire superposition in the initial plane is equal to (n + k)/2, but the TC is equal to n during propagation. The experimental results on generating of the GPOVs by a spatial light modulator are in a good agreement with the simulation results. [ABSTRACT FROM AUTHOR]