Zero-order Bessel Beam Research Articles

Femtosecond Bessel laser beam induced concentric rings on SiC for circular symmetry wide-viewing angle structural color

The laser-induced structural coloring technique holds significant potential for various applications due to its precision, controllability, and versatility across different materials. However, laser-induced structural colors face the problems of durability, homogeneity and indistinguishability, which are not conducive to their application as large-scale identifiable markers. In this paper, an innovative approach has been developed to achieve a circular-symmetric structural color display on durable SiC surfaces by fabricating periodic concentric ring structure arrays using the sidelobe light field of a femtosecond zero-order Bessel beam. The research involved a systematic study of the effects of laser power and pulse number on SiC, along with a detailed analysis of the micro-nanostructures evolving on the SiC surface after laser scanning. Additionally, an examination of the characteristics of circular-symmetric structural color displays and their wide viewing angles in periodic circular structures was conducted. Finally, a comparison was made between the structural color display effects of a concentric ring structure generated by a single pulse and the Laser-Induced Periodic Surface Structures (LIPSS) generated by three pulses. This comparison underscores the potential application of alternating between the high saturation color of the concentric ring structure and the low saturation dark light of the LIPSS for anti-counterfeit coding purposes. The findings of this research present promising opportunities for low-cost mass manufacturing in anti-counterfeit labeling and the advanced processing of photonic devices using SiC.

Theoretical design of a single-mode fiber-based bi-order Bessel beam for a STED system

Stimulated emission depletion (STED) microscopy has attracted great research attention due to its applications to breaking diffraction limits for imaging and lithography. However, its implementation based on single-mode fibers often encounters challenges such as complex structural integration, costly fabrication processes, and the need for specific fiber designs. Herein, a low-cost bi-order Bessel beam based on one single-mode fiber integrated with a structurally simple wavelength-scale microstructure (WSM) on fiber end was proposed for STED system. Through simulation study for full-scale WSM optimization, we have successfully developed a bicolor laser beam (BLB) consisting of a zero-order Bessel beam at a wavelength of 405 nm and a donuts high-order Bessel beam at a wavelength of 532 nm. This fiber-based configuration allows us to achieve a diffraction-limited spot size with a working distance of 0.67λpump and a minimum FWHM of 0.395λpump. By combining wavelength division multiplexing technology with power modulation of the donuts beam, this work provides a promising way for achieving super-resolution imaging or lithography with only one single-mode fiber.

Scattering properties of dual Bessel beams on chiral layered particle

The paper investigates the scattering analytical solution of arbitrary direction double zero-order Bessel beams (ZOBBs) incident on a non-uniform layered chiral sphere. Using the generalized Lorenz-Mie theory (GLMT), the electromagnetic field expansion expression of the double ZOBBs is obtained through the vector superposition of the spherical vector wave functions (SVWFs). Analytical solutions of the scattering on chiral layered particles by dual Bessel beams are derived based on the boundary condition. The iterative coefficient equations are constructed to obtain the expansion coefficients of the SVWFs in each region of the multi-layer chiral sphere. The variation of radar cross section (RCS) with angular distribution is numerically simulated, and the scattering results of layered chiral spheres degenerated into isotropic layered spheres are compared with the literature, which verifies the correctness of the theory and program. The effects of incident angle, polarization angle, cone angle and chiral parameters on the scattering characteristics of far region and internal field of the layered chiral particle are analyzed in detail. The theory and results can offer significant assistance in studying the optical properties of non-uniform chiral particles and complex biological cells irradiated by multiple beams and may also provide important practical value in the micromanipulation of multi-layered biological structures.

Nanosecond Laser Fabrication of Dammann Grating-like Structure on Glass for Bessel-Beam Array Generation

The generation of optical beam arrays with prospective uses within the realms of microscopy, photonics, non-linear optics, and material processing often requires Dammann gratings. Here, we report the direct fabrication of one- and two-dimensional Dammann grating-like structures on soda lime glass using a nanosecond pulsed laser beam with a 1064 nm wavelength. Using the fabricated grating, an axicon lens, and an optical magnification system, we propose a scheme of generation of a diverging array of zero-order Bessel beams with a sub-micron-size central core, extending longitudinally over several hundred microns. Two different grating fabrication strategies are also proposed to control the number of Bessel beams in an array. It was demonstrated that Bessel beams of 12 degrees conical half-angle in an array of up to [5 × 5] dimensions can be generated using a suitable combination of Dammann grating, axicon lens and focusing optics.

Multi-dimensional tunable arbitrary shape beams with engineered axial profile

Bessel beams, as one type of special light field, would significantly do benefit to several applications such as light-sheet microscopy, particle manipulation and free-space optical communications. In this paper, we investigate the generation of multi-dimensional tunable arbitrary shape beams with engineered axial profile based on the superposition of zero-order Bessel beams by designing the angular spectrum, providing a universal method to manipulate arbitrary shape beams in terms of longitudinal intensity, transverse wavevector distribution and transverse field shape. Through angular spectral analysis, we demonstrate the shape-invariant axial engineering of circle, ellipse, parabolic, and epicycloid-shaped beams, as well as shape-variant axial engineering such as self-acceleration, self-rotation, and self-mode conversion, from both theoretical and experimental perspectives. Our work provides a deep insight into the fundamental properties of arbitrary shape light with engineered axial profile and paves new way toward exploiting more dimensions for its future applications.

Iterative suppression of Kerr-induced instabilities in Bessel beams using on-axis intensity shaping

Kerr-induced instabilities in zeroth-order Bessel beams with low focusing angle prevent the formation of longitudinally uniform plasma rods in the filamentation regime. These instabilities lead to the oscillation of the beam on-axis intensity via the generation of new spatial frequencies by a first stage of spectral broadening followed by a second stage of four-wave mixing. Here, we numerically demonstrate an efficient approach to drastically reduce the instabilities due to the second stage. It is based on shaping the longitudinal intensity profile with spatio-spectral components in opposition of phase to the Kerr-generated ones via an iterative approach. Zeroth-order Bessel beams with a longitudinal flat intensity plateau can be generated in a few iterations in the nonlinear regime. This is performed in both monochromatic and pulsed femtosecond regimes.

Extended Projection Distance and Sidelobe Suppression of THz Bessel Beam With Combined Axicons

Extended Projection Distance and Sidelobe Suppression of THz Bessel Beam With Combined Axicons

Optical pulling force on a uniaxial anisotropic sphere by a high-order Bessel (vortex) beam.

Based on the generalized Lorenz-Mie theory (GLMT) and the scattering theory of uniaxial spheres, a theoretical approach is introduced to study the axial radiation force (AOF) exerted on a uniaxial anisotropic sphere illuminated by an on-axis high-order Bessel (vortex) beams (HOBVBs). Applying Maxwell's stress tensor, an analytical expression of the AOF on a uniaxial anisotropic sphere by the on-axis HOBVB is derived. The correctness of the theoretical and numerical results is verified by comparing the AOF on an isotropic sphere by a zero-order Bessel beam (ZOBB) with those results by a plane wave, Gaussian beam, and ZOBB. The focus of this study is to determine some conditions of the tractor beam, so as to realize the inverse motion of an anisotropic sphere through a Bessel beam. The range of optical pulling force (OPF) that can pull particles in reverse motion generated by zero-order and first-order Bessel beams is extended from isotropic spherical particles to anisotropic spherical particles. The effects of the sphere radius, conical angle, and especially electromagnetic anisotropy parameters on the OPF in water or a vacuum environment are discussed in detail. Moreover, the OPF exerted on the uniaxial anisotropic sphere illuminated by a HOBVB with l=2, 3, and 4 is also exhibited. It indicates that the HOBVB with l=2, 3 is also a good tractor beam for the uniaxial anisotropic sphere. The OPF generated by Bessel beams on uniaxial anisotropic spherical particles is not only affected by the conical angle and radius but is also significantly influenced by anisotropic parameters and topological charges. These properties of the OPF are different from those on an isotropic sphere. The theory and results are hopeful to provide an effective theoretical basis for the study of optical micromanipulation of biological and anisotropic complex particles by optical tractor (vortex) beams.

Rapid, high-contrast, and steady volumetric imaging with Bessel-beam-based two-photon fluorescence microscopy.

Two-photon fluorescence microscopy (TPFM) excited by Gaussian beams requires axial tomographic scanning for three-dimensional (3D) volumetric imaging, which is a time-consuming process, and the slow imaging speed hinders its application for in vivo brain imaging. The Bessel focus, characterized by an extended depth of focus and constant resolution, facilitates the projection of a 3D volume onto a two-dimensional image, which significantly enhances the speed of volumetric imaging. We aimed to demonstrate the ability of a TPFM with a sidelobe-free Bessel beam to provide a promising tool for research in live biological specimens. Comparative in vivo imaging was conducted in live mouse brains and transgenic zebrafish to evaluate the performance of TPFM and Bessel-beam-based TPFM. Additionally, an image-difference method utilizing zeroth-order and third-order Bessel beams was introduced to effectively suppress background interference introduced by sidelobes. In comparison with traditional TPFM, the Bessel-beams-based TPFM demonstrated a 30-fold increase in imaging throughput and speed. Furthermore, the effectiveness of the image-difference method was validated in live biological specimens, resulting in a substantial enhancement of image contrast. Importantly, our TPFM with a sidelobe-free Bessel beam exhibited robustness against axial displacements, a feature of considerable value for in vivo experiments. We achieved rapid, high-contrast, and robust volumetric imaging of the vasculature in live mouse brains and transgenic zebrafish using our TPFM with a sidelobe-free Bessel beam.

Tunable Bessel beam generator based on a 3D-printed helical axicon on a fiber tip.

We demonstrate a tunable and fully enclosed fiber-based Bessel beam generator that has the potential for applications in a tough environment. This generator consists of a few-mode fiber (FMF), a short section of graded index fiber (GIF), and a 3D-printed helical axicon. The FMF provides tunable modes that carry an orbital angular momentum (OAM). The GIF was fused to the FMF to expand and collimate the generated modes. The helical axicon was 3D-printed on the GIF tip without any holes or gaps, which reshapes the OAM modes into Bessel modes and adds an additional helical phase structure to them, resulting in the generation of zeroth-order, first-order, and second-order Bessel beams. The fully enclosed structure provides high mechanical strength and optical stability, which enable the generator to be suitable for imaging or particle manipulation in a complex liquid or air environment.

Diffraction-free distance enhancement of Bessel beams based on spatial domain phase modulation

Bessel beams have garnered significant interest due to their unique diffraction-free properties and extensive potential applications. In this work, we propose a spatial domain phase modulation theory to achieve diffraction-free distance enhancement of Bessel beams, overcoming the limitation of the traditional methods due to the inability to infinitely decrease the wave vector angle. The traditional formula for non-diffraction distance is also modified. Simulation results demonstrate that our proposed scheme can significantly increase the maximum diffraction-free distance of zero-order and higher-order Bessel beams by more than two times, while ensuring the self-healing property of Bessel beams. Furthermore, our proposed scheme is not restricted to specific systems or limited to the optical wavelength range. This implies that the results have great applicative potential in long-distance free-space optical communication and wireless energy transmission.

Terahertz Bessel beam generator.

The Bessel beam has broad application prospects in wireless energy transmission and high-speed communications. The traditional Bessel beam generation method has the problems of large volume, low efficiency, and complex manufacturing. To solve the above problems, we present a terahertz Bessel beam generator based on the reflective metasurface, which is composed of a metal pattern, dielectric layer, and bottom metal plate. Under the incidence of right circularly polarized (RCP) wave, the zero-order Bessel beam and zero-order symmetric double Bessel beam are generated. It can be found that the bottom angle of the axicon of the first-order Bessel beam is inversely proportional to the propagation distance of the Bessel beam. Comparing the electric field intensity distribution, phase distribution, and mode purity of the second-order Bessel beam and the second-order vortex beam in different observation planes, it can be seen that the energy of the higher-order Bessel beam is more concentrated and the field distribution is more stable than those of the ordinary vortex beam. The reflective terahertz Bessel beam generator has potential application value in terahertz wireless communications, measurement, radar detection, and imaging.

Transverse Particle Trapping Using Finite Bessel Beams Based on Acoustic Metamaterials

We investigate the transverse trapping force acting on a small particle on or off the central axis of zero-order finite Bessel beams. Combining the simulated fields with the Gorkov force potential, the transverse trapping behaviors for small objects are analyzed, and the reversal of the trapping behaviors is recovered when varying the paraxiality parameter of the Bessel beam. The results prove the possibility of using axisymmetric Bessel beams to trap both dense and stiff particles as well as light and soft ones. The particles can be trapped at the maximum central pressure in the main lobe and also the maximum pressure of the other transverse locations. A lossy acoustic metastructure with the ability to decouple the phase and amplitude modulations is used to generate the desired sound field, which is used to trap a foam ball as an example. Our research opens a promising avenue to the design and development of simplified acoustic tweezers.

Submillimeter-Wave Cornea Phantom Sensing Over an Extended Depth of Field With an Axicon-Generated Bessel Beam

The feasibility of a 220–330 GHz zero-order axicon-generated Bessel beam for corneal water content was explored. Simulation and experimental data from the 25° cone angle hyperbolic-axicon lens illuminating metallic spherical targets demonstrate a monotonically decreasing, band integrated, backscatter intensity for increasing radius of curvature from 7–11 mm, when lens reflector and optical axis are aligned. Furthermore, for radii > = 9.5 mm, maximum signal was obtained with a 1-mm transverse displacement between lens and reflector optical axes arising from spatial correlation between main lobe and out-of-phase sidelobes. Thickness and permittivity parameter estimation experiments were performed on an 8-mm radius of curvature, 1-mm-thick fused quartz dome over a 10-mm axial span. Extracted thickness and permittivity varied by less than ∼25 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">μ</i> m and 0.2, respectively, after correction for superluminal velocity. Estimated water permittivity and thickness of water backed gelatin phantoms showed significantly more variation due to a time varying radius of curvature. To the best of our knowledge, this is the first work that describes axicon-generated Bessel beam measurements of layered spheres with varying radii of curvature, in the submillimeter range.

Light scattering of a uniform uniaxial anisotropic sphere by an on-axis high-order Bessel vortex beam.

Analytical solutions to the scattering of a uniform uniaxial anisotropic sphere illuminated by an on-axis high-order Bessel vortex beam (HOBVB) are investigated. Using the vector wave theory, the expansion coefficients of the incident HOBVB in terms of the spherical vector wave functions (SVWFs) are obtained. According to the orthogonality of the associated Legendre function and exponential function, more concise expressions of the expansion coefficients are derived. It can reinterpret the incident HOBVB faster compared with the expansion coefficients of double integral forms. The internal fields of a uniform uniaxial anisotropic sphere are proposed in the integrating form of the SVWFs by introducing the Fourier transform. The differences of scattering characteristics of a uniaxial anisotropic sphere illuminated by a zero-order Bessel beam, Gaussian beam, and HOBVB are exhibited. Influences of the topological charge, conical angle, and particle size parameters on the angle distributions of the radar cross section are analyzed in detail. The scattering and extinction efficiencies varied with the particle radius, conical angle, permeability, and dielectric anisotropy are also discussed. The results provide insights into the scattering and light-matter interactions and may find important applications in optical propagation and optical micromanipulation of biological and anisotropic complex particles.

Moiré meta-device for flexibly controlled Bessel beam generation

High-order Bessel beams are of great interest for most stable long-range optical quantum communications due to their unique nondiffraction, self-healing, and orbital angular-momentum-carrying capabilities. Until now, metasurfaces based on Bessel beam generators are mostly static and focused on generating zero-order Bessel beams. A moiré meta-device made of two cascaded metasurfaces is a simple, effective strategy to dynamically manipulate the wavefront of electromagnetic (EM) waves by mutual rotation between the two metasurfaces. Here, an all-dielectric moiré meta-device integrated with the functions of an axicon and a spiral phase plate to generate terahertz Bessel beams is designed. Not only the order, but also the nondiffraction length of the generated Bessel beam can be continuously tuned. As a proof of concept of the feasibility of the platform, the case of tuning order is experimentally demonstrated. The experimental results are in good agreement with the theoretical expectations. In addition, we also numerically proved that the nondiffraction length of the Bessel beam can be adjusted with the same approach. The moiré meta-device platform is powerful in dynamically manipulating the wavefront of EM waves and provides an effective strategy for continuously controlling the properties of the Bessel beam, which may find applications in optical communications, particle manipulation, and super-resolution imaging.

Nondestructive evaluation (NDE) of multilayered attenuative structures using ultrasonic Bessel beams

In this article Nondestructive Evaluation (NDE) of structures with attenuative coating or a layer of thermal protection system is presented utilizing various designs of acoustic axicons. Generation of ultrasonic Bessel beam in single-layered and multi-layered structures to overcome the ultrasonic attenuation is discussed. The possible modulation and the effective increase of the acoustic energy inside the attenuative layer are investigated using axicons, which are proposed to be an ad-hoc element to the existing ultrasonic transducers. Upon confirming the existence and generation of the ultrasonic Bessel beam in an arbitrary host media the spatial intensity distribution of the zeroth-order Bessel beam is studied. Further, we show how the generated Bessels beams propagate and penetrate deep inside the multi-layered structures comprising of different material properties. It is shown that the intensity of the Bessel beams and their possible deep penetration capabilities are altered when the geometrical properties of the axicon and material properties of the media are changed. We also report the numerical characterization of the different degrees of Bessel beams with a unique multi-annular shaped axicon. Modulating the axicon angles and the geometry, the long-distance propagation of the Bessel beam is ensured. Such beam can correspond to the field of Nondestructive Evaluation (NDE) for investigating materials with attenuative layers.

Analysis of radiation force on a uniaxial anisotropic sphere by dual zero-order Bessel beams

Based on the generalized Lorenz–Mie theory (GLMT), a theoretical approach is introduced to study the radiation force exerted on a uniaxial anisotropic sphere illuminated by dual zero-order Bessel beams (ZOBBs). The beams propagate with arbitrary direction, and are expanded in terms of the spherical vector wave functions (SVWFs) in the particle coordinate system using the coordinate rotation theorem. The total expansion coefficients of the incident fields are derived by superposition of the vector fields. Applying the Maxwell’s stress tensor, the analytical expressions of the radiation forces on a homogeneous absorbing uniaxial anisotropic sphere are derived. Comparing the radiation forces of dual ZOBBs with those results of dual ZOBBs simplified into single ZOBBs and dual plane waves, the accuracy and correctness of the theory are verified. In order to study the equilibrium state, the effects of beam parameters, particle size parameters, and anisotropy parameters on the radiation forces are discussed in detail. Comparing with the isotropic particle, the equilibrium status is sensitive to the anisotropic parameters. Moreover, the properties of optical force on a uniaxial anisotropic sphere in single ZOBB trap and zero-order Bessel standing wave trap are compared. The theory and results of this paper are hopeful to provide an effective theoretical basis for the study of optical micromanipulation of biological and anisotropic complex particles by multi-beams.

Tunable Bessel Beam Shaping for Robust Atmospheric Optical Communication

As a powerful supplement to the existing wireless communication technology, free-space optical communication helps to achieve ultra-high-speed wireless communication in many important applications such as redundant link, disaster recovery and secure link. However, beam distortion and intensity scintillation caused by atmospheric turbulence severely limits its communication performance through optical links, and there are still many problems in existing turbulent suppression schemes. Here, we propose an easy-implemented anti-turbulence free-space optical communication scheme based on the tunable zero-order Bessel beam, which is able to provide 2 dB to 3 dB power compensation in comparison with the ones employing traditional Gaussian beams. For the worse link environment with water fog, our scheme can still ensure the stability of the communication link when the Gaussian beam link is cut off. In addition, to generate tunable Bessel beams, we propose a method based on non-uniform Fourier transform to achieve accurate and fast light field simulation.

Design of a Trench-Assisted Optical Fiber for Generating Bessel Beams With Different Shapes

We have designed a trench-assisted optical fiber that can generate Bessel beams with different shapes in the fundamental mode. The trench-assisted structure is nested by rings with different refractive indexes on the cross-section. The fundamental mode field properties of the trench-assisted fiber are analyzed by using the finite element method. For the wavelengths from 400 nm to 2500 nm, the fundamental modes appear as Bessel beams with different shapes. The zero-order Bessel beams exhibit at the longer wavelength region, and the higher-order Bessel beams show at the shorter wavelength region. The Bessel beams’ shape can also be adjusted by tuning the structure parameters on the cross-section of the designed trench-assisted fiber.