Generating and measuring non-diffracting vector Bessel beams

The advent of wireless communications technology, human connection and collaborations now span countries, continents, and even planets. Despite these advances, however, today's wireless technology still experiences limitations. In the past two decades, terahertz (THz) communications have been researched in depth, and it has become clear that THz communications will be part of expanding the capabilities of wireless technology. Although there was once a substantial gap in knowledge as well as transmission and reception capabilities at THz frequencies, this gap has been steadily closing. Some challenges, still remain; namely, the need to characterize and design for near-field propagation as well as the ability to take advantage of spatial diversity despite the primarily line-of-sight channel. In this proposal, these challenges begin to be addressed. The sub-THz MIMO channel is characterized using a novel channel-sounding implementation, and then a practical physical layer implementation to take advantage of the spatial diversity of the MIMO channel is presented. Then, a research roadmap for enabling broadband, mobile THz communications in the near-field followed by experimental results that characterize the near-field propagation characteristics with both Gaussian and non-diffracting Bessel beams. The performance of Bessel beams are further explored for sub-THz communications in the presence of blockage and shown to be a viable option for broadband, near-field communications. Other wavefront engineering techniques to enable line-of-sight MIMO using orbital angular momentum are discussed from a physical-layer-security perspective, and a novel successive-interference-cancellation eavesdropping attack is proposed along with a potential counter measure. Finally, concluding remarks are given. --Author's abstract

This work innovatively designs an all-dielectric metasurface fabricated using 3D printing technology with alumina as the substrate material. This metasurface successfully generates vectorial non-diffracting Bessel beams at a specific frequency of 0.1THz. Initially, through comprehensive simulation analysis of the interaction between the metasurface and the incident beam, it was discovered that the metasurface can precisely manipulate the properties of the transmitted beam based on the polarization state of the incident beam. Specifically, when illuminated by a left-handed circularly polarized (LCP) Gaussian beam, the transmitted beam manifests as a radially polarized Bessel beam. Conversely, under right-handed circularly polarized (RCP) Gaussian beam illumination, the transmitted light transforms into an azimuthally polarized Bessel beam. Building upon the theoretical simulations and considering experimental constraints, further experimental validation was conducted using linearly polarized light, confirming the effectiveness and feasibility of the proposed design. Experimental results demonstrate that the presented all-dielectric alumina metasurface, fabricated via 3D printing, successfully achieves the generation of vector nondiffracting Bessel beams. On one hand, the combination of alumina material and 3D printing technology significantly reduces manufacturing costs, laying a foundation for large scale application. On the other hand, leveraging the high precision of 3D printing ensures the accurate fabrication of the metasurface structure, thereby guaranteeing the high quality and stability of the generated vector beams. This work provides a novel approach for the efficient generation of Bessel beams and is expected to have profound implications in the field of terahertz technology.

We propose to generate vortex high harmonics in the extreme ultraviolet (XUV) with a controllable spatial profile by using a Bessel-Gaussian (BG) beam carrying a nonzero orbital angular momentum (OAM). Such BG beam has quite a different intensity profile at the focus compared to the generally used BG beam without carrying the OAM. We show that the BG beam is capable of generating single-ring structured high harmonics, which is quite different from an Laguerre-Gaussian (LG) beam with a similar intensity distribution at the laser focus. We reveal that favorable phase-matching conditions can be achieved off-axis and away from the laser focus because a single-atom intrinsic phase due to the short electron trajectory can be well compensated by a geometric phase of the BG beam. We thus give a general rule that vortex high harmonics with a single annular profile can be efficiently generated when a gas medium is located at 1.5zred to 2.0zred before or after the laser focus of the BG beam, here zred is a reduced length. We also show the validity of this rule when the BG beam carries a higher OAM. This work is expected to be useful for synthesizing attosecond vortex pulses.

In this study, we have generated a femtosecond (fs), non-diffracting Bessel beam (800 nm, 1 kHz, 50 fs) of zeroth order through an axicon (IR range, 100, AR coated). We have performed laser ablation of a bimetallic alloy (50% gold, 50 % silver) in the air engaging the generated fs Bessel beam. The high-intensity Bessel beam-matter interaction resulted in the fabrication of exotic bimetallic nanostructures. Extensive field emission scanning electron microscope and atomic force microscopy characterizations were undertaken to study the nanoscale topographical formations. The fs Bessel beam-induced ablation on the alloy target, involving the beam profile imprint on a single surface spot, followed by overlapping two ablation zones, has been meticulously explored. The central lobe ablated area, along with concentric rings-ablated exotic patterns, were thoroughly investigated in the topographical characterization. In the case of the complete raster scan ablation, ladder-like periodic surface structures (with sub ~20 nm growths on the ladder steps) were observed. Energy-dispersive X-ray mapping was performed to confirm the elemental distribution in the nanostructured areas. Subsequently, these plasmonic nanostructures were utilized as surface-enhanced Raman scattering (SERS) platforms to detect traces of real-time explosives, ammonium nitrate (AN), and Tetryl (TL). The SERS spectra of AN depicted a signature Raman peak at 1043 cm^-1, whereas TL exhibited a signature peak near 1353 cm^-1. The lowest possible detected traces were 10 μM and 5 μM, for AN and TL, respectively.

In this report we theoretically calculate and experimentally measure the OAM density of a coherent superposition of both symmetric and non-symmetric non-diffracting Bessel beams. Although the intensity pattern of the superimposed field rotates at a fixed angular velocity (which is due to the differing wave-vectors of the component fields), we show that the magnitude and direction of the OAM is dependent on the radial position within the field. We outline a simple approach using only a spatial light modulator to measure the OAM density for a superposition of non-diffracting Bessel beams. Our quantitative measurements are in good agreement with predicted values.

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.

In this paper, we have performed experimental, analytical, and numerical studies of beams with topological charges of $\ifmmode\pm\else\textpm\fi{}1$ and $\ifmmode\pm\else\textpm\fi{}2$ formed by silicon binary phase axicons (BPAs) with spiral zone structures. The axicons were illuminated with the Novosibirsk free electron laser radiation (a continuous stream of 100-ps pulses at $f=5.6$ MHz). The cw power of the beams produced reached 30 W and can by doubled via antireflection coating of the axicons. The intensity distribution in the beam cross sections was in good agreement with the Bessel functions and was kept constant within a distance of about $L/r\ensuremath{\approx}190$ and 100, where the first ring radii of the beams r were 0.9 and 1.5 mm for the Bessel beams of the first and second orders, respectively. Although the characteristics of the beams (Bessel cross section, ``diffraction-free'' propagation, self-recovery after passing obstacles, and randomly inhomogeneous media) corresponded to the properties of ideal Bessel beams, their spatial Fourier spectrum (the image in the focal plane of the lens) was, instead of an ideal ring, intertwined segments of arcs with phases shifted by $\ensuremath{\pi}$, the number of which was equal to the double value of the topological charge. This feature can be used, for example, in a demultiplexing unit of a free vortex-wave communication system or for identification of beam topological charge. We also revisited Young's double-slit diffraction and rotation of beams obstructed by a half-plane, previously applied to Laguerre-Gaussian beam characterization, in the case of the Bessel beams. The Young diffraction pattern demonstrated in this case a complicated intensity-phase distribution. It was shown that the Bessel beams formed by BPAs have two important advantages, which can be used in applications, in comparison with other methods of generation, e.g., a combination of an axicon lens with a spiral phase plate. Although the phase jumps of the axicons are designed for a determined wavelength (141 $\ensuremath{\mu}\mathrm{m}$ in our case), the BPAs can form the beams at incident radiation with any wavelength, albeit with a reduced diffraction efficiency, and their cross section is the same for any wavelength.

We experimentally generated superpositions of higher-order Bessel beams that possess no global orbital angular momentum (OAM), yet exhibit an angular rotation in their intensity profile as the field propagates. The digital holograms encoded on a spatial light modulator (SLM), used for generating such fields, consist of two annular rings of unequal radial wave-vectors where each ring is encoded with an azimuthal mode of equal order but opposite charge. We present experimentally measured angular rotation rates for some example superposition fields, which are shown to be in good agreement with that predicted theoretically. Introducing a second SLM and a Fourier transforming lens, we demonstrate a simple approach to perform an azimuthal decomposition of our generated optical fields. Bounding the match-filter to an annular ring, of varying radius, we are able to perform a scale-independent azimuthal decomposition of our initial field. From the measured weightings of the azimuthally decomposed modes we show reconstruction of the cross-sectional intensity profile and OAM density of our initial field.

Optical vortices (OVs) are known as light waves with helical wavefronts, which are characterized by their azimuthal mode indices (topological charges) corresponding to orbital angular momenta (OAMs). Recently, mode division multiplexing (MDM) based on mode orthogonality is expected to enhance transmission capacity in telecommunications remarkably. The key technology for such OAM-based MDM is the mode decomposition with respect to topological charges, namely OAM mode sorting. Among various kinds of candidates, the OAM sorter based on log-polar transformation in optics [1] , [2] attracts great attentions since its insertion loss is low enough to support the decomposition on single photon level, and it also supports an inverse transformation. However, the log-polar transformation method has the serious disadvantage of non-negligible crosstalks among the neighboring modes. In order to overcome this problem, a beam copying technique by using specially-designed diffractive elements was demonstrated [3] . Although this novel technique can greatly reduce the crosstalks, but it spoils the advantage of the low-loss inverse transformation.

A new interpretation of the non-diffracting Bessel beams is given as a superposition of two fields described by Hankel functions. Within our picture, supported by the Sommerfeld radiation condition, we find that Bessel beams must be of finite transverse extension. Our approach also easily explains propagation characteristics of Bessel-Gauss beams and, in general, the propagation of amplitude modulated Bessel beams. Consequences are discussed and contrasted with the classic theory of Bessel beams.

The Bessel beam has become significant in optical research due to its properties such as a long focal depth, self-healing, and non-diffraction. However, conventional methods for generating Bessel beams have drawbacks such as limited flexibility and tunability and the use of bulky optics. These factors lead to the complexity of the optical systems. This paper presents what we believe is a novel approach to generating Bessel beams by utilizing a fully phase-modulated all-dielectric metasurface. The proposed method enables the arbitrary and independent manipulation of cross-polarized and co-polarized components, allowing the creation of Bessel beams featuring multiple polarization conversions when subjected to left-handed circularly polarized (LCP) incidence. To demonstrate the versatility and effectiveness of the method, three metasurfaces with distinct characteristics are designed. The simulated generated Bessel beams exhibit qualities including long focal depth, non-diffraction behavior, self-healing capabilities, and polarization conversion, which align with the theoretical predictions. This work presents novel possibilities for effectively generating and multi-functional application of Bessel beams.

Conventional vortex beams carrying orbital angular momentum (OAM) suffer from the limitation of beam divergence in wireless communications applications. This article proposes novel 3-dimensional (3-D) printed discrete dielectric lenses (DDLs) for generation of nondiffractive OAM beams operating at 300 GHz. By virtue of its arbitrary aperture phase control capability, a terahertz (THz) DDL combining the functionalities of three conventional bulky refractive hyperbolic, spiral phase plane, and aixcon lenses is proposed to generate nondiffractive Bessel vortex beam carrying OAM. An aperture field analysis method is also developed to evaluate the radiation performance of the DDL antennas. Furthermore, to cover the OAM signal in an intended longitudinal region, two DDL synthesis methods are explored to generate extended higher order Bessel beams carrying OAM. The first approach is based on geometric optics, while the second uses the alternating projection method (APM) to optimize the aperture phase distribution of the DDL. Two THz DDLs are conveniently fabricated by 3-D printing technology. Measured results demonstrate that THz nondiffractive OAM beams can be successfully generated by the designed DDLs. The generated THz OAM beam with attractive nondiffractive characteristic may open new opportunities for next-generation ultra-high-speed wireless communications.

We introduce a compact method for generating guide stars to enable direct wavefront sensing in Bessel two-photon microscopy. By sequentially modulating an axicon phase and a thin lens phase using a spatial light modulator (SLM), our approach achieves seamless switching between Bessel and Gaussian illumination beams without requiring mechanical movement or additional optical components. The Bessel beam provides an expanded field of view for imaging, while the Gaussian beam serves as a point-like guide star for wavefront sensing. Experimental validation in a Bessel two-photon light sheet microscope demonstrates that wavefront correction based on our method enhances the signal-to-noise ratio (SNR) by 7.3 times and improves axial resolution by 4.4 times.

In this paper, the self-reconstruction property of astigmatic Bessel beam is studied experimentally and theoretically. Based on the Fresnel diffraction integral theory and Babinet principle, the general expression of the intensity distribution of astigmatic Bessel beams passing through a circular obstacle is derived. The cross-section light intensity at transmission distance of, 10, 30, and 80 mm after astigmatism of the astigmatic Bessel beam are occluded by circular obstacles. The self-reconstruction process of the light field is observed and verified by using an specially designed experimental setup. In the experiment, we choose He-Ne laser as a light source, collimate and expand the beam through a telescope system, and a zero-order astigmatic Bessel beam is generated by a beam vertically incident on the tilted axicon after the diaphragm. A circular obstacle with a radius of 0.2 mm is placed at a distance of 200 mm behind the axicon. Finally, the cross-section intensities at different distances are observed and recorded by a microscope. The experimental phenomena are in good agreement with the theoretical prediction. The results show that the reconstruction of the zero-order astigmatic Bessel beams will occur after passing through the on-axis and off-axis obstacles. And as the transmission distance increases, the outer contour size of the astigmatic Bessel beam becomes larger, and the number of central spot arrays increases, and the complete beam is gradually reconstructed. Particularly, this feature is different from the behavior of the non-diffracting Bessel beam, which maintains the light field unchanged during transmission and has a single central spot. It is expected to be applied to multi-layer multi-particle control. And a new optical property is discovered in the experiments: the reconstruction speed of the beam in the horizontal and vertical direction are not consistent in the reconstruction process, and there is a certain speed difference. Further, we add a spiral phase plate between the diaphragm and the axicon to produce a high-order astigmatic Bessel beam. And it is verified that the high-order astigmatism Bessel beam has the same self-reconstruction characteristics after being shielded by obstacles. Compared with the zero-order aperture system, the high-order beam can not only expand the operating range, but also use the orbital angular momentum carried by the beam to achieve light rotation, which makes the particle manipulation more flexible. The research proves the self-reconstruction characteristics of astigmatic Bessel beams theoretically and experimentally, and broadens the research range of astigmatic Bessel beams. The research results have practical significance and application value in the field of optical micro-manipulation.

We introduce a new class of nondiffracting fractional vortex beams that connect Bessel beams of successive order in a smooth transition. The new fractional-order beams preserve the same nondiffracting feature of Bessel beams of integer order, and their orbital angular momentum per photon can take any value in a continuous range. The propagation of the more physically realizable fractional-order Bessel–Gauss beams, i.e. fractional Bessel beams apodized by a Gaussian transmittance, through general ABCD optical systems is studied in detail and is complemented by the experimental generation of several instances of fractional beams which in turn confirms our theoretical predictions.