Nondiffracting Beams Research Articles

Propagation properties of elegant modified Bessel Gaussian beams.

A kind of optical beam with a radially parabolic propagating manner and intensity decay inversely proportional to propagating distance in the far field is investigated. The initial complex amplitudes of this kind of beam have the form of a Gaussian function multiplied by a m/2-order modified Bessel function and a helical phase factor with topological charge m. The arguments for Bessel and Gauss parts in the propagating solutions of these beams are complex and symmetric as elegant Laguerre and Hermite Gaussian beams. As a result, the beams can be referred to as elegant modified Bessel Gauss (EMBG) beams. Similar to non-diffractive beams such as Bessel and Airy beams, the EMBG beams also carry infinite power due to a transversely slowly decaying tail of complex amplitude. The EMBG beams demonstrate intermediate propagating properties between non-diffractive and finite-power beams. Unlike non-diffractive beams that never spread their power and finite-power beams that always diverge in a linear manner and spread their power by inversely square law in the far field, the EMBG beams demonstrate a far-field parabolic propagating manner and decay their power by inversely linear law. In addition, the EMBG beams have total Gouy phase, which is only half of that of elegant Laguerre Gauss beams with the same topological charge, and have far-field intensity distributions regardless of the beam waist radius in the initial plane. The propagating and focusing properties of EMBG beams represent an intermediate status between the non-diffractive and finite-power beams.

Laser beam shaping using a photoinduced azopolymer droplet-based mask.

The dewetting of an azopolymer droplet, followed by the photostructuration of the evaporated droplet, is employed to create an amplitude mask. This straightforward process yields a large area featuring periodic micro- and nanostructures. The resulting pattern is utilized to generate a nondiffracting beam. Starting with a Gaussian beam illuminating the amplitude mask, the critical aspect is the production of a bright, ring-shaped beam with a high radius-to-width ratio and symmetric central laser spots, each with the same intensity. This alternative approach to shaping a laser beam is demonstrated as a rapid and cost-effective fabrication technique.

An optical needle with elongated transversal profile created using Airy beams for laser processing of glasses

In recent decades, significant progress has been made in the field of laser beam shaping, driven by the growing demands in both scientific research and industrial applications. Notably, a class of beams known as nondiffracting beams, which exhibit such characteristics as self-healing and resistance to diffraction, has found practical utility in communication, imaging, and laser microprocessing. Although Bessel beams have become commonplace for various optical applications, further advances in beam engineering remain a need. One of the key requirements is the ability to control the elongation of the transverse profile of an optical needle, which is highly sought after for specific applications. In this study, we propose to achieve this control by utilizing nondiffracting Airy beams. The elongation of the optical needle’s transverse profile is achieved through the implementation of a binary phase mask. We evaluate the performance of this method through both numerical simulations and experimental assessments, employing various metrics, such as the major-to-minor axis ratio, the length of the optical needle, and its stability. We present a specific case where a flat optical element is created using geometrical phase induced by nanogratings inscribed within the element’s volume by means of a femtosecond laser. We validate the performance of this geometrical phase element through laser microprocessing of transparent glasses and report the results obtained from these experiments.

Quantitative Mapping of Transient Thermodynamic States in Ultrafast Laser Nanostructuring of Quartz

Understanding material structural reaction to light is of utmost importance to advance processing resolution in ultrafast laser volume structuring into the nanoscale. Selective thermodynamic pathways are required to quench energy transport in the most rapid manner and to confine the process to nanometer lengths, bypassing optical resolution. Quantifying material dynamics under confinement, with in situ access to transient local temperature and density parameters, thus becomes key in understanding the process. We report in situ reconstruction of thermodynamic states over the entire matter relaxation path in bulk α -quartz irradiated by ultrafast nondiffractive laser beams using time-resolved qualitative and quantitative optical phase microscopy. Thermooptic dynamics indicate rapid spatially confined crystalline-to-amorphous transition to a hot dense fused silica form. Densification exceeds 20% and the matrix temperature rises to more than 2,000 K in the first nanosecond. This structural state relaxes in hundreds of nanoseconds. The dispersion and time design of the optical beam to picosecond durations increases the spatial confinement and triggers an extreme nanostructuring process based on nanocavitation that occurs within the amorphizing material, where the low-viscosity phase lowers the mechanical requirements for the process. Processing feature scales of less than a tenth of the optical wavelength are obtained in the volume. This allows for structural and morphological nanoscale material features under 3D confinement that can engineer optical materials.

Intelligent Beam Optimization for Light-Sheet Fluorescence Microscopy through Deep Learning.

Light-sheet fluorescence microscopy (LSFM) provides the benefit of optical sectioning coupled with rapid acquisition times, enabling high-resolution 3-dimensional imaging of large tissue-cleared samples. Inherent to LSFM, the quality of the imaging heavily relies on the characteristics of the illumination beam, which only illuminates a thin section of the sample. Therefore, substantial efforts are dedicated to identifying slender, nondiffracting beam profiles that yield uniform and high-contrast images. An ongoing debate concerns the identification of optimal illumination beams for different samples: Gaussian, Bessel, Airy patterns, and/or others. However, comparisons among different beam profiles are challenging as their optimization objectives are often different. Given that our large imaging datasets (approximately 0.5 TB of images per sample) are already analyzed using deep learning models, we envisioned a different approach to the problem by designing an illumination beam tailored to boost the performance of the deep learning model. We hypothesized that integrating the physical LSFM illumination model (after passing it through a variable phase mask) into the training of a cell detection network would achieve this goal. Here, we report that joint optimization continuously updates the phase mask and results in improved image quality for better cell detection. The efficacy of our method is demonstrated through both simulations and experiments that reveal substantial enhancements in imaging quality compared to the traditional Gaussian light sheet. We discuss how designing microscopy systems through a computational approach provides novel insights for advancing optical design that relies on deep learning models for the analysis of imaging datasets.

Full-Space Wavefront Shaping of Broadband Vortex Beam with Switchable Terahertz Metasurface Based on Vanadium Dioxide

Currently, vortex beams are extensively utilized in the information transmission and storage of communication systems due to their additional degree of freedom. However, traditional terahertz metasurfaces only focus on the generation of narrowband vortex beams in reflection or transmission mode, which is unbeneficial for practical applications. Here, we propose and design terahertz metasurface unit cells composed of anisotropic Z-shaped metal structures, two dielectric layers, and a VO2 film layer. By utilizing the Pancharatnam–Berry phase theory, independent control of a full 2π phase over a wide frequency range can be achieved by rotating the unit cell. Moreover, the full-space mode (transmission and reflection) can also be implemented by utilizing the phase transition of VO2 film. Based on the convolution operation, three different terahertz metasurfaces are created to generate vortex beams with different wavefronts in full-space, such as deflected vortex beams, focused vortex beams, and non-diffraction vortex beams. Additionally, the divergences of these vortex beams are also analyzed. Therefore, our designed metasurfaces are capable of efficiently shaping the wavefronts of broadband vortex beams in full-space, making them promising applications for long-distance transmission, high integration, and large capacity in 6G terahertz communications.

Liquid crystal anisotropic axicon for the generation of non-diffracting Bessel beams with longitudinally varying polarization

In this work we demonstrate a tunable liquid–crystal element of linear phase profile along the radial coordinate. In combination with a regular refractive axicon, it behaves as an anisotropic axicon, generating the collinear superposition of two orthogonally polarized Bessel beams with different propagation constant. This superposition results in a Bessel beam where the state of polarization (SOP) varies periodically along propagation. Experimental results probe the voltage control of the SOP oscillating period, which agree well with theory. This compound axicon is a very compact and efficient way of generating Bessel beams with polarization modulation, thus representing a significant advantage over other methods reported in the literature that require bulk optical systems based on spatial light modulators.

Arbitrary orthogonal polarization-dependent directional launching of Bessel-like surface plasmon polariton beams

Nondiffracting Bessel-like SPP beams, with the unique features of effectively suppressing the diffraction of the beam, have great application prospects in the fields of on-chip interconnection circuit, optical tweezers, and micromanipulation. In practical applications, active manipulation of nondiffracting Bessel-like SPP beams is essential. Here, we proposed two kinds of nondiffracting Bessel-like SPP beam unidirectional devices controlled by arbitrarily orthogonally polarized incidence light, which can generate and manipulate zeroth-order or first-order Bessel-like SPP beams, respectively. The results show that, by changing the distance between two pairs of slit couplers with different resonance responses, the nondiffracting Bessel-like SPP beams can be directionally excited at arbitrarily polarized incidence, and the excitation direction of the nondiffracting Bessel-like SPP beams will reverse under the corresponding orthogonally polarized incidence. The proposed devices provide promising opportunities for constructing polarization-based dynamic manipulation plasmonic devices of nondiffracting SPP beams and have potential applications in on-chip interconnection circuits.

Spatial–temporal engineering of light using Frozen Waves and Airy pulses

In this paper we combine two important theoretical methodologies, one related to the Frozen Wave beams (also referred to as Longitudinally Structured Light), which are non-diffracting beams whose longitudinal intensity pattern can be chosen a priori in a medium (absorbing or not), and the other related to the Airy-Type pulses, which are pulses resistant to dispersion effects in dispersive materials. As a result, a new method emerges capable of providing pulsed-beams resistant to three concomitant effects, i.e.: diffraction, dispersion, and attenuation; while concurrently the spatial variation of the wave along its axis of propagation can be engineered “at will”. The new approach can be seen as a generalization of the Localized Waves Theory in the paraxial regime and the new pulses can have potential applications in different fields such as optical communications, nonlinear optics, optical micromanipulations, optical microfabrication, and so on.

Generating broadband nondiffracting perfect vortex beams in the visible regime

Generating broadband nondiffracting perfect vortex beams in the visible regime

Non-Diffraction Self-Acceleration Beams With Customized Transverse Intensity Profiles Based on 3-D-Printed Meta-Structure

In this article, two 3-D-printed all-dielectric meta-structures that can produce diffraction-free self-acceleration beams with different transverse intensity profiles are proposed in the microwave frequency band. The first single-layer meta-structure, combining the Fourier lens phase and cubic phase distributions, is engineered to generate Airy beams with highly asymmetric transverse intensity profiles. In order to flexibly customize the propagation trajectory and transverse spot shape, Bessel-like beams with symmetric transverse profiles along arbitrary trajectories are realized by the second compact meta-structure based on phase synthesis. Calculating the phase mask of the metasurface is the most critical part. In this work, phase-modulated meta-structures can map the phase information to height distribution of the cube elements that can be precisely controlled. To verify the validity, two prototypes are printed and measured. From the beam intensities at different cross sections along the propagation trajectory, the oscillating multilobe intensity pattern of the 2-D Airy beam and the symmetric non-spreading central main lobe of the Bessel-like beam can be observed in simulation and measurement. Besides that, two kinds of beams have transverse acceleration behavior and self-reconstruction property. Therefore, the proposed meta-structures have great potential in numerous challenging fields, like microwave power transmission, secure communication, imaging, and detection.

Terahertz Bessel metalens with an extended non-diffractive length and a high efficiency.

In this paper, we propose a reflective terahertz (THz) Bessel metalens that utilizes polarization-insensitive sub-wavelength metal resonator-dielectric-metal structures. The Bessel metalens is configured with the superposition of hyperboloidal and conical phase profiles, resulting in a high-efficiency and long non-diffractive length Bessel beam. Our experimental results demonstrate that the proposed Bessel metalens has a focusing efficiency of 72.1% and a non-diffractive length of 239λ. This device has promising aspects in the fields of THz imaging systems and other miniaturized and integrated scenes that require non-diffractive Bessel beams.

On‐Demand Subwavelength‐Scale Light Sculpting Using Nanometric Holograms

AbstractSpatially or temporally structured light has attracted considerable attention for its intriguing beam characteristics, which have found extensive applications in classical and quantum optics. Extending structured light from macroscale and microscale to nanometricscale brings more prospects both for fundamental and applied science. However, sculpting light at the subwavelength scale remains a challenge since its transverse structure is fragile in the nanometric scale. Here a novelholography for arbitrary light sculpting at the subwavelength scale is demonstrated. A wave phenomenon of diffractive focusing from an amplitude‐only nanometric (50‐nm‐thick) film is introduced, and use of the induced high‐spatial‐frequency waves as carriers to encode information of an object is considered. Using this technique, nanometric holograms are designed and fabricated for generating the well‐defined eigen modes including the zero‐order Bessel beam, vortex beam, vector beam, Airy beam, as well as an arbitrary light pattern, with feature sizes on the deep‐subwavelength scale. The broadband performance of the hologram is examined, and a white‐light nondiffracting beam at the deep‐subwavelength scale is realized. This demonstration paves a way toward on‐demand light sculpting at the nanometric scale, which may find applications such as optical super‐resolution imaging, nanoparticle manipulation, and precise measurements.

A Systematic Summary and Comparison of Scalar Diffraction Theories for Structured Light Beams

Structured light beams have recently attracted enormous research interest for their unique properties and potential applications in optical communications, imaging, sensing, etc. Since most of these applications involve the propagation of structured light beams, which is accompanied by the phenomenon of diffraction, it is very necessary to employ diffraction theories to analyze the obstacle effects on structured light beams during propagation. The aim of this work is to provide a systematic summary and comparison of the scalar diffraction theories for structured light beams. We first present the scalar fields of typical structured light beams in the source plane, including the fundamental Gaussian beams, higher-order Hermite–Gaussian beams, Laguerre–Gaussian vortex beams, non-diffracting Bessel beams, and self-accelerating Airy beams. Then, we summarize and compare the main scalar diffraction theories of structured light beams, including the Fresnel diffraction integral, Collins formula, angular spectrum representation, and Rayleigh–Sommerfeld diffraction integral. Finally, based on these theories, we derive in detail the analytical propagation expressions of typical structured light beams under different conditions. In addition, the propagation of typical structured light beams is simulated. We hope this work can be helpful for the efficient study of the propagation of structured light beams.

Dual-Functional Tunable Metasurface for Meta-Axicon with a Variable Depth of Focus and Continuous-Zoom Metalens.

Optical metasurfaces have been widely investigated for their versatile ability to manipulate wavefront and miniaturize traditional optical components into ultrathin planar devices. The integration of metasurfaces with multifunctionality and tunability has fundamentally transformed optics with unprecedented control over light propagation and manipulation. This study introduces a pioneering framework for the development of tunable metasurfaces with multifunctionality, and an example of a tunable metasurface of dual functionalities is proposed and numerically verified as one of the tunable meta-axicon for generating Bessel beams with a variable depth of focus (DOF) and a continuous-zoom metalens. Specifically, this design achieves dual-functional phase modulation by helicity-multiplexing from the combination of the geometric phase as well as the propagation phase and realizes tunability for both functionalities through rotational actuation between double metasurface layers. As a result, dual functionalities with continuous tunability of the proposed TiO2 metasurface are enabled independently for the left and right circularly polarized (LCP and RCP) incidences at 532 nm. Specifically, LCP light triggers the metasurface to function as a tunable axicon, generating non-diffracting Bessel beams with variable numerical apertures (NA) and DOFs. Conversely, the RCP incidence induces it to operate as a continuous-zoom metalens and generates variable spherical wavefront focusing on diverse focal lengths. This study not only initially implements the design of tunable meta-axicon, but also achieves the integration of such a tunable meta-axicon and continuous-zoom metalens within a single metasurface configuration. The proposed device could find potential applications in biological imaging, microscopic measurement, laser fabrication, optical manipulation, multi-plane imaging, depth estimation, optical data storage, etc.

Ultrasonic imaging based on pulsed Airy beams.

In ultrasonic imaging, high impedance obstacles in tissues may lead to artifacts behind them, making the examination of the target area difficult. Acoustical Airy beams possess the characteristics of self-bending and self-healing within a specific range. They are limited-diffracting when generated from finite aperture sources and are expected to have great potential in medical imaging and therapy. In this paper, pulsed Airy (pAiry) beams are employed for ultrasonic imaging at megahertz frequency, and the protocol is demonstrated via both simulations and experiments. Firstly, the generation of pAiry beams using a linear array is simulated, and the pulsed beams inherit some characteristics of continuous wave Airy beams, such as propagating along curved paths and self-healing. In experiments where obstacles are present at the beam paths, the image quality in pAiry-based imaging is superior to that in classical iso-depth imaging. The results demonstrate the feasibility and benefits of ultrasonic imaging based on pAiry beams and provide an important basis for developing imaging techniques employing non-diffracting acoustic beams.

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.

Bessel Beam Dielectrics Cutting with Femtosecond Laser in GHz-Burst Mode.

We report, for the first time to the best of our knowledge, Bessel beam dielectrics cutting with a femtosecond laser in GHz-burst mode. The non-diffractive beam shaping is based on the use of an axicon and allows for cutting glasses up to 1 mm thickness with an excellent cutting quality. Moreover, we present a comparison of the cutting results with the state-of-the-art method, consisting of short MHz-bursts of femtosecond pulses. We further illustrate the influence of the laser beam parameters such as the burst energy and the pitch between consecutive Bessel beams on the machining quality of the cutting plane and provide process windows for both regimes.

Theoretical and experimental study of optical diffractometry based on Fresnel diffraction from a transmission phase step.

We present experiments to study the optical diffractometry of Fresnel diffraction from transmission phase steps under illuminating sources with distinct spatial profiles. The experimental results are extended analytically with the Fresnel Gaussian shape invariant introduced in previous publications to calculate the propagation of a coherent illuminating source through optical setups. We use a narrow coherent illuminating source to permit extending the applicability of the method for clinical purposes and perform calculations with illuminating sources with different spatial profiles, including a non-diffracting Airy beam, to allow for the establishment of general sensitivity formulae within the paraxial region.

Generating scalar and vector modes of Bessel beams utilizing holographic axicon phase with spatial light modulator

This paper presents an efficient method for the generation of scalar as well as vector modes of Bessel–Gaussian (BG) beams by utilizing a computer generated phase-only mask encoded using the spatial light modulator (SLM). A phase-only hologram corresponding to the transmission function of axicon combined with a spatial phase plate (SPP) is used. The SPP converts a Gaussian field into a phase singular beam of order l associated with an azimuthally varying spiral wavefront structure and the axicon helps achieve non-diffracting BG beams. A compact experimental setup is proposed for the experimental realization of BG fields possessing both homogeneous as well as spatially varying polarization distributions across the transverse plane. Scalar BG beams are generated through the modulation of the combined phase patterns of axicon and SPP with the SLM. Vector BG beams are generated in two special cases: azimuthally and radially polarized inhomogeneous distributions through dual-passes from the SLM. A non-interferometric technique of dual-pass modulation, from the phase patterns displayed on a single SLM, which is divided into two halves, has been utilized. Here, scalar BG beams with orthogonal phase structure are encoded into orthogonal components of incoming light for vector BG beam generation.