Bessel Beam: Significance and Applications-A Progressive Review

Performance evaluation and comparative research of underwater wireless optical communication system by using different structured beams

Structured beams have attracted increasing interest in free-space and fiber-based optical communications. Underwater wireless optical communication (UWOC) is becoming a prospective technique in marine exploration. We investigated UWOC performance using different representative structured beams. The transmission performances of the Gaussian, Bessel-Gaussian (BG), Ince-Gaussian (IG), and radially polarized Gaussian (RPG) beams were experimentally demonstrated and evaluated in underwater channels subjected to thermal gradient. The experimental results show that the BG, IG, and RPG perform better against the thermal gradient. Compared with the Gaussian beams, the beam wanders of BG, IG, and RPG beams under the thermal gradient have been reduced by 56.9%, 8.2%, and 59%, the scintillation indices have been decreased by 12.8%, 17.3%, and 28.9%, and the BER performance of the BG, IG, and RPG beams have been improved by ∼5.5, ∼3.7, and ∼5.2d B at the forward error correction threshold (FEC threshold). Based on the above results, the RPG beam is a more promising light source for UWOC. The experimental results provide a promising beam choice for UWOC.

Depth of focus and intensity distribution of a lensacon illuminated by a partially coherent Gaussian Schell vortex beam

Using the extended Huygens-Fresnel principle, a cross-spectral density formula was developed for a Gaussian Schell model vortex (PCGSMV) beam diffracted through a lensacon (lens with an axicon). The intensity and depth of focus (DOF) shaped by the lensacon were calculated. Our numerical results show the relationship between the intensity distribution and depth of focus with the beam waist width as well as the spatial correlation of the coherence length. Furthermore, the relationship between the beam spot size and propagation distance was investigated. In the case of the lensacon tandem, the maximum intensity was greater than that attained by the axicon alone for the same beam parameters, and the DOF was smaller than that of the axicon alone. The vortex structure canceled out the low value of the spatial degree of coherence length. Our numerical model exhibited high-intensity values and high-quality Bessel rings along the DOF, which are critical for various applications.

Extending the Depth of Focus of an Infrared Microscope Using a Binary Axicon Fabricated on Barium Fluoride

Axial resolution is one of the most important characteristics of a microscope. In all microscopes, a high axial resolution is desired in order to discriminate information efficiently along the longitudinal direction. However, when studying thick samples that do not contain laterally overlapping information, a low axial resolution is desirable, as information from multiple planes can be recorded simultaneously from a single camera shot instead of plane-by-plane mechanical refocusing. In this study, we increased the focal depth of an infrared microscope non-invasively by introducing a binary axicon fabricated on a barium fluoride substrate close to the sample. Preliminary results of imaging the thick and sparse silk fibers showed an improved focal depth with a slight decrease in lateral resolution and an increase in background noise.

Analysis of centroiding algorithms for non-diffracting structured and hollow structured laser beams

This paper explores the potential of optical-based systems, specifically pseudo-non-diffractive beams, as an alternative for alignment. The study focuses on structured laser beams and hollow structured laser beams, which exhibit lower divergence and enhanced detection capabilities. The research objective is to analyze and compare centroiding algorithms in terms of accuracy and robustness to noise. The study compares the gamma-corrected and threshold-corrected center of gravity and correlation template matching. It also introduces a polarization-based algorithm.

Micro-Ring Resonator-Based Tunable Vortex Beam Emitter

Light beams bearing orbital angular momentum (OAM) are used in various scientific and engineering applications, such as microscopy, laser material processing, and optical tweezers. Precise topological charge control is crucial for efficiently using vortex beams in different fields, such as information encoding in optical communications and sensor systems. This work presents a novel method for optimizing an emitting micro-ring resonator (MRR) for emitting vortex beams with variable orders of OAM. The MRR consists of a ring waveguide with periodic structures side-coupled to a bus waveguide. The resonator is tunable due to the phase change material Sb2Se3 deposited on the ring. This material can change from amorphous to crystalline while changing its refractive index. In the amorphous phase, it is 3.285 + 0i, while in the transition to the crystalline phase, it reaches 4.050 + 0i at emission wavelength 1550 nm. We used this property to control the vortex beam topological charge. In our study, we optimized the distance between the bus waveguide and the ring waveguide, the bending angle, and the width of the bus waveguide. The optimality criterion was chosen to maximize the flux density of the radiated energy emitted by the resonator. The numerical simulation results proved our method. The proposed approach can be used to optimize optical beam emitters carrying OAM for various applications.

Variation of structured laser beam pattern and optimization for an alignment reference line creation

The alignment of particle accelerators demands a dedicated measurement system based on a straight-line reference. This straight line can be provided by a laser beam. The alignment then involves accurately measuring the offset of accelerator components with respect to this light path. In order to be efficient, the laser beam needs to serve as a stable and straight reference for distances of several hundreds of meters. The attainable accuracy depends, among other parameters, on the laser spot size, which should ideally change very little over the distances at which the alignment system needs to operate. Due to the significant divergence of Gaussian laser beams, we propose using a structured laser beam (SLB) for alignment. Its transversal intensity profile is similar to a Bessel beam and consists of an intense inner core (IC) and concentric rings. The divergence of the IC, i.e., the growth of its size with distance, can be limited to 10μrad using a favorable generator configuration. Thus an SLB may be suitable as a straight-line reference for long-distance alignment applications. However, the SLB is distorted if obstructions cover parts of the outermost ring (OR) of the beam within, which should therefore also be small. In this paper, we investigate the relationship between the size of the IC and OR depending on the design parameters of the SLB generator. We use numerical simulations and experiments with different generators over distances up to 50 m to analyze the transversal intensity profile and wavefronts of different SLBs. The results indicate the general suitability of an SLB as a reference line for long-distance alignment but also expose tradeoffs between small IC and small OR. The findings outlined in the paper help to describe the optimal SLB parameters for given conditions.

Power transfer efficiency for obstructed wireless links using Bessel beams

The power transfer efficiency of a partially obstructed wireless link operating in the Fresnel region is studied in this work. The wireless link consists of two equal apertures, axially aligned, radiating weakly-diffractive beams (truncated Bessel beams). A metallic obstacle is considered along the propagation path of the radiated beam to analyze its impact on the power transfer efficiency with respect to a clear line of sight link. The power transfer efficiency in the obstructed case is derived by resorting to a scattered field formulation. In the proposed approach, the distance between the apertures is considered larger than their radius, which is also bigger than the operating wavelength. A paraxial approximation is then applied to the formulation. Numerical results validate the proposed approach. It appears that the transverse propagation constant of the Bessel Beam and resulting non-diffractive range strongly affects the distance of operation of the wireless link in both the clear and obstructed cases. In addition, we observe how the self-healing property of Bessel beams preserves the efficiency of the partially obstructed link by establishing a resilient link under defined conditions for the propagating beam and size of the obstruction.

Bessel Beams in Ophthalmology: A Review

The achievable resolution of a conventional imaging system is inevitably limited due to diffraction. Dealing with precise imaging in scattering media, such as in the case of biomedical imaging, is even more difficult owing to the weak signal-to-noise ratios. Recent developments in non-diffractive beams such as Bessel beams, Airy beams, vortex beams, and Mathieu beams have paved the way to tackle some of these challenges. This review specifically focuses on non-diffractive Bessel beams for ophthalmological applications. The theoretical foundation of the non-diffractive Bessel beam is discussed first followed by a review of various ophthalmological applications utilizing Bessel beams. The advantages and disadvantages of these techniques in comparison to those of existing state-of-the-art ophthalmological systems are discussed. The review concludes with an overview of the current developments and the future perspectives of non-diffractive beams in ophthalmology.

Variable Bessel Beam Profiles Generated through Refraction by Liquid Media

Various methods have been employed to produce Bessel beams (BBs), with axicon-based techniques remaining the most efficient. Among the limitations of axicons are manufacturing defects such as oblate tips and difficulty in tuning the generated BBs. In this work, we combine the effect of a blunt-tip axicon with refraction using various combinations of liquid media to generate variable BB intensity profiles. The output BBs from the axicon are made to pass through a custom-built fluid chamber and magnified using a telescope system. When traversing an empty chamber, the Bessel beam core diameter is measured to be 773.8 µm at propagation distance z' = 30 cm. The core diameter increases as the beam passes through a chamber containing different liquids as a result of an effective axicon-telescope distance produced by the indices of refraction of the pertinent fluids. Bessel beams modified by the fluid chamber maintain the properties of non-diffraction and self-healing.

Average intensity of Bessel-Gauss beams propagating through Kolmogorov turbulence with the quadratic structure function

It is well known that in free space propagations, Bessel-Gauss (BG) beams are non-diffractive, in the sense that over a finite distance the beam mainlobe does not spread. Non-diffraction beams have been found to offer advantages over diffractive beams, for example, in terms of power delivery. However, in random media, such as a turbulent atmosphere, the performance of BG beams is still an active area of research. For example, applying the extended Huygens-Fresnel (EHF) principle results in an intractable expression for the optical field and the average intensity. This work is concerned with finding a closed-form expression for the average intensity of BG beam propagating through weak and strong Kolmogorov turbulence under the quadratic structure function (QSF) assumption. This is achieved by considering the average intensity convolution integral of the free space intensity with the point spread function (PSF). This convolution integral is reduced to a one-dimensional integral that can be easily evaluated in closed form and plotted. Moreover, the beam root mean square (rms) width is also given in terms of one-dimensional integrals. The work presented can be used for assessing the utility of a BG beam for applications in emerging communication systems such as optical wireless communications (OWC).

Abruptly Autofocusing Vortex Beams for Rapid Controllable Femtosecond Two-Photon Polymerization

Micro-fabrication based on structured-beam-assisted Two-Photon Polymerization (2 PP) provides a rapid and flexible method for the manufacture of microstructures with complex morphologies. The tunable Abruptly Autofocusing Vortex (AAFV) beams were designed theoretically and generated experimentally based on a single-phase-only Spatial Light Modulator (SLM). Their specific spatial intensity distributions were further utilized to assist the fabrication of a bowl-shaped Three-Dimensional (3D) micro-trap array via 2 PP with a one-step exposure technique. Finally, the fabricated microstructures act as a novel tool for the trapping and spatial positioning of micro-particles with different diameters, which shows potential applications in fiber optics and cell study.

Propagation of intense electromagnetic pulse with a small conical phase shift induced by Axicon optics

The conical phase shift induced by the axicon generates a non-diffracting Bessel beam. In this paper, we examine the propagation property of an electromagnetic wave focused by a thin lens and axicon waveplate combination, which induces a small amount of conical phase shift less than one wavelength. A general expression describing the focused field distribution has been derived under the paraxial approximation. The conical phase shift breaks the axial symmetry of intensity and shows a focal spot-shaping capability by controlling the central intensity profile within a certain range near focus. The focal spot-shaping capability can be applied to form a concave or flattened intensity profile, which can be used to control the concavity of a double-sided relativistic flying mirror or to generate the spatially uniform and energetic laser-driven proton/ion beams for hadron therapy.

Composite Diffraction-Free Beam Formation Based on Iteratively Calculated Primitives

To form a diffraction-free beam with a complex structure, we propose to use a set of primitives calculated iteratively for the ring spatial spectrum. We also optimized the complex transmission function of the diffractive optical elements (DOEs), which form some primitive diffraction-free distributions (for example, a square or/and a triangle). The superposition of such DOEs supplemented with deflecting phases (a multi-order optical element) provides to generate a diffraction-free beam with a more complex transverse intensity distribution corresponding to the composition of these primitives. The proposed approach has two advantages. The first is the rapid (for the first few iterations) achievements of an acceptable error in the calculation of an optical element that forms a primitive distribution compared to a complex one. The second advantage is the convenience of reconfiguration. Since a complex distribution is assembled from primitive parts, it can be reconfigured quickly or dynamically by using a spatial light modulator (SLM) by moving and rotating these components. Numerical results were confirmed experimentally.

Flow Cytometry with Anti-Diffraction Light Sheet (ADLS) by Spatial Light Modulation

Flow cytometry is a widespread and powerful technique whose resolution is determined by its capacity to accurately distinguish fluorescently positive populations from negative ones. However, most informative results are discarded while performing the measurements of conventional flow cytometry, e.g., the cell size, shape, morphology, and distribution or location of labeled exosomes within the unpurified biological samples. Herein, we propose a novel approach using an anti-diffraction light sheet with anisotroic feature to excite fluorescent tags. Constituted by an anti-diffraction Bessel-Gaussian beam array, the light sheet is 12 μm wide, 12 μm high, and has a thickness of ~0.8 μm. The intensity profile of the excited fluorescent signal can, therefore, reflect the size and allow samples in the range from O (100 nm) to 10 μm (e.g., blood cells) to be transported via hydrodynamic focusing in a microfluidic chip. The sampling rate is 500 kHz, which provides a capability of high throughput without sacrificing the spatial resolution. Consequently, the proposed anti-diffraction light sheet flow cytometry (ADLSFC) can obtain more informative results than the conventional methodologies, and is able to provide multiple characteristics (e.g., the size and distribution of fluorescent signal) helping to distinguish the target samples from the complex backgrounds.

Flat variable liquid crystal diffractive spiral axicon enabling perfect vortex beams generation

A transparent variable diffractive spiral axicon (DSA) based on a single LC cell is presented. The manufactured DSA can be switched between 24 different configurations, 12 convergent and 12 divergent, where the output angle is varied as a function of the applied topological charge. The active area of the device is created using a direct laser writing technique in indium-tin oxide coated glass substrates. Liquid crystal is used to modulate the phase of the incoming beam generating the different DSA configurations. The DSA consists in 24 individually driven transparent spiral shaped electrodes, each introducing a specific phase retardation. In this article, the manufacture and characterization of the tunable DSA is presented and the performance of the DSA is experimentally demonstrated and compared to the corresponding simulations.

Multilevel Spiral Axicon for High-Order Bessel-Gauss Beams Generation

This paper presents an efficient method to generate high-order Bessel-Gauss beams carrying orbital angular momentum (OAM) by using a thin and compact optical element such as a multilevel spiral axicon. This approach represents an excellent alternative for diffraction-free OAM beam generation instead of complex methods based on a doublet formed by a physical spiral phase plate and zero-order axicon, phase holograms loaded on spatial light modulators (SLMs), or the interferometric method. Here, we present the fabrication process for axicons with 16 and 32 levels, characterized by high mode conversion efficiency and good transmission for visible light (λ = 633 nm wavelength). The Bessel vortex states generated with the proposed diffractive optical elements (DOEs) can be exploited as a very useful resource for optical and quantum communication in free-space channels or in optical fibers.

Environmental Monitoring: A Comprehensive Review on Optical Waveguide and Fiber-Based Sensors

Globally, there is active development of photonic sensors incorporating multidisciplinary research. The ultimate objective is to develop small, low-cost, sensitive, selective, quick, durable, remote-controllable sensors that are resistant to electromagnetic interference. Different photonic sensor designs and advances in photonic frameworks have shown the possibility to realize these capabilities. In this review paper, the latest developments in the field of optical waveguide and fiber-based sensors which can serve for environmental monitoring are discussed. Several important topics such as toxic gas, water quality, indoor environment, and natural disaster monitoring are reviewed.

Simulating multilevel diffractive optical elements on a spatial light modulator

Multilevel diffractive optical elements (DOEs) offer a solution to approximate complex diffractive phase profiles in a stepwise manner. However, while much attention has focused on efficiency, the impact on modal content in the context of structured light has, to our best knowledge, remained unexplored. Here, we outline a simple theory that accounts for efficiency and modal purity in arbitrary structured light produced by multilevel DOEs. We make use of a phase-only spatial light modulator as a "testbed" to experimentally implement various multileveled diffractive profiles, including orbital angular momentum beams, Bessel beams, and Airy beams, outlining the subsequent efficiency and purity both theoretically and experimentally, confirming that a low number of multilevel steps can produce modes of high fidelity. Our work will be useful to those wishing to digitally evaluate modal effects from DOEs prior to physical fabrication.

Quadraxial metamaterial

We study the dispersion of electromagnetic waves in a spatially dispersive metamaterial with Lorentz-like dependence of principal permittivity tensor components on the respective components of the wave vector performing the analysis of isofrequency contours. The considered permittivity tensor describes a triple non-connected wire medium. It is demonstrated that the metamaterial has four optic axes in the frequency range below the artificial plasma frequency. The directions of the optical axes do not depend on frequency and coincide with the diagonals of quadrants. The conical refraction effect is observed for all four optic axes.

Flexible method for generating needle-shaped beams and its application in optical coherence tomography

Needle-shaped beams (NBs) featuring a long depth-of-focus (DOF) can drastically improve the resolution of microscopy systems. However, thus far, the implementation of a specific NB has been onerous due to the lack of a common, flexible generation method. Here we develop a spatially multiplexed phase pattern that creates many axially closely spaced foci as a universal platform for customizing various NBs, allowing flexible manipulations of beam length and diameter, uniform axial intensity, and sub-diffraction-limit beams. NBs designed via this method successfully extended the DOF of our optical coherence tomography (OCT) system. It revealed clear individual epidermal cells of the entire human epidermis, fine structures of human dermal-epidermal junction in a large depth range, and a high-resolution dynamic heartbeat of alive Drosophila larvae.

Tuning Axial Resolution Independent of Lateral Resolution in a Computational Imaging System Using Bessel Speckles

Speckle patterns are formed by random interferences of mutually coherent beams. While speckles are often considered as unwanted noise in many areas, they also formed the foundation for the development of numerous speckle-based imaging, holography, and sensing technologies. In the recent years, artificial speckle patterns have been generated with spatially incoherent sources using static and dynamic optical modulators for advanced imaging applications. In this report, a basic study has been carried out with Bessel distribution as the fundamental building block of the speckle pattern (i.e., speckle patterns formed by randomly interfering Bessel beams). In general, Bessel beams have a long focal depth, which in this scenario is counteracted by the increase in randomness enabling tunability of the axial resolution. As a direct imaging method could not be applied when there is more than one Bessel beam, an indirect computational imaging framework has been applied to study the imaging characteristics. This computational imaging process consists of three steps. In the first step, the point spread function (PSF) is calculated, which is the speckle pattern formed by the random interferences of Bessel beams. In the next step, the intensity distribution for an object is obtained by a convolution between the PSF and object function. The object information is reconstructed by processing the PSF and the object intensity distribution using non-linear reconstruction. In the computational imaging framework, the lateral resolution remained a constant, while the axial resolution improved when the randomness in the system was increased. Three-dimensional computational imaging with statistical averaging for different cases of randomness has been synthetically demonstrated for two test objects located at two different distances. The presented study will lead to a new generation of incoherent imaging technologies.

Demonstration of speckle resistance using space-time light sheets

The capacity of self-healing fields to reconstruct after passing through scattering media may prove useful in reducing speckle formation. Here, we study the speckle response of the space-time (ST) light sheet compared to a Gaussian wave packet, Airy beam, and Bessel Gauss beam. We find that the Pearson's correlation coefficient for the ST light sheet is 50%, 48% and 40% larger than that of the Gaussian, Airy beam and Bessel Gauss beams, respectively, demonstrating a strong correlation to an input beam that has not been speckled. These results suggest that the ST light sheet exhibits considerable resistance to speckle generation. We also investigate the speckle response of the ST light sheet at its second-harmonic frequency and observe a mean Pearson's correlation coefficient close to 0.6, comparable to the second-harmonic Bessel Gauss beam, and 2.8 × the value obtained for the second-harmonic Gaussian beam. Our results lend themselves to a variety of applications including bioimaging, communications, and optical tweezers.

Lightsheet Microscopy

In this paper, we review lightsheet (selective plane illumination) microscopy for mouse developmental biologists. There are different means of forming the illumination sheet, and we discuss these. We explain how we introduced the lightsheet microscope economically into our core facility and present our results on fixed and living samples. We also describe methods of clearing fixed samples for three-dimensional imaging and discuss the various means of preparing samples with particular reference to mouse cilia, adipose spheroids, and cochleae. © 2022 The Authors. Current Protocols published by Wiley Periodicals LLC.

Optical Computing: Status and Perspectives

For many years, optics has been employed in computing, although the major focus has been and remains to be on connecting parts of computers, for communications, or more fundamentally in systems that have some optical function or element (optical pattern recognition, etc.). Optical digital computers are still evolving; however, a variety of components that can eventually lead to true optical computers, such as optical logic gates, optical switches, neural networks, and spatial light modulators have previously been developed and are discussed in this paper. High-performance off-the-shelf computers can accurately simulate and construct more complicated photonic devices and systems. These advancements have developed under unusual circumstances: photonics is an emerging tool for the next generation of computing hardware, while recent advances in digital computers have empowered the design, modeling, and creation of a new class of photonic devices and systems with unparalleled challenges. Thus, the review of the status and perspectives shows that optical technology offers incredible developments in computational efficiency; however, only separately implemented optical operations are known so far, and the launch of the world's first commercial optical processing system was only recently announced. Most likely, the optical computer has not been put into mass production because there are still no good solutions for optical transistors, optical memory, and much more that acceptance to break the huge inertia of many proven technologies in electronics.

Picosecond Bessel Beam Fabricated Pure, Gold-Coated Silver Nanostructures for Trace-Level Sensing of Multiple Explosives and Hazardous Molecules

A zeroth-order, non-diffracting Bessel beam, generated by picosecond laser pulses (1064 nm, 10 Hz, 30 ps) through an axicon, was utilized to perform pulse energy-dependent (12 mJ, 16 mJ, 20 mJ, 24 mJ) laser ablation of silver (Ag) substrates in air. The fabrication resulted in finger-like Ag nanostructures (NSs) in the sub-200 nm domain and obtained structures were characterized using the FESEM and AFM techniques. Subsequently, we employed those Ag NSs in surface-enhanced Raman spectroscopy (SERS) studies achieving promising sensing results towards trace-level detection of six different hazardous materials (explosive molecules of picric acid (PA) and ammonium nitrate (AN), a pesticide thiram (TH) and the dye molecules of Methylene Blue (MB), Malachite Green (MG), and Nile Blue (NB)) along with a biomolecule (hen egg white lysozyme (HEWL)). The remarkably superior plasmonic behaviour exhibited by the AgNS corresponding to 16 mJ pulse ablation energy was further explored. To accomplish a real-time application-oriented understanding, time-dependent studies were performed utilizing the AgNS prepared with 16 mJ and TH molecule by collecting the SERS data periodically for up to 120 days. The coated AgNSs were prepared with optimized gold (Au) deposition, accomplishing a much lower trace detection in the case of thiram (~50 pM compared to ~50 nM achieved prior to the coating) as well as superior EF up to ~10⁸ (~10⁶ before Au coating). Additionally, these substrates have demonstrated superior stability compared to those obtained before Au coating.

Bessel beam with a micrometer-size central spot and interferometry for small volume bioliquid refractive index measurement

This work demonstrates an interferometric technique to measure the refractive index (RI) of microliter volume of biosample solutions with the help of an optical fiber negative axicon and Bessel beam with the micrometer-size central spot. The RI measuring device consists of a broadband superluminescent diode (SLD) source along with an optical circulator and spectrometer. The axicon optical fiber probe packaged with a glass slide is connected to a broadband SLD source through an optical circulator, and a drop of microliter bioliquid sample is placed on the packaged probe's head. The reflected light from the glass-liquid interface couples back to the axicon probe and interferes with the reference beam generated at the air-glass interface of the axicon. The interference spectrum is further analyzed by applying the fast Fourier transform to calculate power from the respective interface and solve the Fresnel equation for the RI measurement. The RI of small sample volume ∼2µl of glucose solutions and bovine serum albumin protein solutions are reported as an application of the proposed method. This sensing platform shows promising applications in biomedicine for monitoring small volume various biosample concentrations. We also demonstrate RI measurement of flowing liquid sample using the developed setup in case the design can be considered for microfluidic channel research.

Modern Types of Axicons: New Functions and Applications

Axicon is a versatile optical element for forming a zero-order Bessel beam, including high-power laser radiation schemes. Nevertheless, it has drawbacks such as the produced beam's parameters being dependent on a particular element, the output beam's intensity distribution being dependent on the quality of element manufacturing, and uneven axial intensity distribution. To address these issues, extensive research has been undertaken to develop nondiffracting beams using a variety of advanced techniques. We looked at four different and special approaches for creating nondiffracting beams in this article. Diffractive axicons, meta-axicons-flat optics, spatial light modulators, and photonic integrated circuit-based axicons are among these approaches. Lately, there has been noteworthy curiosity in reducing the thickness and weight of axicons by exploiting diffraction. Meta-axicons, which are ultrathin flat optical elements made up of metasurfaces built up of arrays of subwavelength optical antennas, are one way to address such needs. In addition, when compared to their traditional refractive and diffractive equivalents, meta-axicons have a number of distinguishing advantages, including aberration correction, active tunability, and semi-transparency. This paper is not intended to be a critique of any method. We have outlined the most recent advancements in this field and let readers determine which approach best meets their needs based on the ease of fabrication and utilization. Moreover, one section is devoted to applications of axicons utilized as sensors of optical properties of devices and elements as well as singular beams states and wavefront features.

Generation of Complex Transverse Energy Flow Distributions with Autofocusing Optical Vortex Beams

Optical vortex (OV) beams are widely used for the generation of light fields with transverse energy flow inducing orbital motion of the nano- and microparticles in the transverse plane. Here, we present some new modifications of OV beams with autofocusing properties for shaping complex transverse energy flow distributions varying in space. The angular component of the complex amplitude of these beams is defined by the superpositions of OV beams with different topological charges. The proposed approach provides a convenient method to control the three-dimensional structure of the generated autofocusing OV beams. The control of the transverse distribution of an autofocusing beam provides a wide variety of generated fields with both rotating and periodic properties, which can be used in the field of laser manipulation and laser material processing. Thus, the obtained numerical results predict different types of motion of the trapped particles for the designed OV autofocusing beams. The experimental results agree with modeling results and demonstrate the principal possibility to shape such laser beams using spatial light modulators.

Spiral Caustics of Vortex Beams

We discuss the nonparaxial focusing of laser light into a three-dimensional (3D) spiral distribution. For calculating the tangential and normal components of the electromagnetic field on a preset curved surface we propose an asymptotic method, using which we derive equations for calculating stationary points and asymptotic relations for the electromagnetic field components in the form of one-dimensional (1D) integrals over a radial component. The results obtained through the asymptotic approach and the direct calculation of the Kirchhoff integral are identical. For a particular case of focusing into a ring, an analytical relation for stationary points is derived. Based on the electromagnetic theory, we design and numerically model the performance of diffractive optical elements (DOEs) to generate field distributions shaped as two-dimensional (2D) and 3D light spirals with the variable angular momentum. We reveal that under certain conditions, there is an effect of splitting the longitudinal electromagnetic field component. Experimental results obtained with the use of a spatial light modulator are in good agreement with the modeling results.