Non-diffracting Airy Research Articles

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.

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.

Improving longitudinal resolution of Airy beams two-photon volume imaging with fluorescence lifetime imaging

The non-diffracting Airy beams have been reported to increase acquisition speed by projecting the axially significantly elongated information to a two-dimensional (2D) image. Due to the elongated focal length, an Airy volumetric image can cover information as much as stack images with multiple Gaussian images at different imaging depths, which significantly increases the volumetric imaging rate. However, the projection of three-dimensional (3D) structures on a 2D plane is usually indistinguishable, especially those that overlap along the axis. Therefore, we proposed an axially resolved volume imaging technique based on a two-photon fluorescence lifetime microscopy imaging (FLIM) by using Airy beams.

Terahertz structured light: nonparaxial Airy imaging using silicon diffractive optics

Structured light – electromagnetic waves with a strong spatial inhomogeneity of amplitude, phase, and polarization – has occupied far-reaching positions in both optical research and applications. Terahertz (THz) waves, due to recent innovations in photonics and nanotechnology, became so robust that it was not only implemented in a wide variety of applications such as communications, spectroscopic analysis, and non-destructive imaging, but also served as a low-cost and easily implementable experimental platform for novel concept illustration. In this work, we show that structured nonparaxial THz light in the form of Airy, Bessel, and Gaussian beams can be generated in a compact way using exclusively silicon diffractive optics prepared by femtosecond laser ablation technology. The accelerating nature of the generated structured light is demonstrated via THz imaging of objects partially obscured by an opaque beam block. Unlike conventional paraxial approaches, when a combination of a lens and a cubic phase (or amplitude) mask creates a nondiffracting Airy beam, we demonstrate simultaneous lensless nonparaxial THz Airy beam generation and its application in imaging system. Images of single objects, imaging with a controllable placed obstacle, and imaging of stacked graphene layers are presented, revealing hence potential of the approach to inspect quality of 2D materials. Structured nonparaxial THz illumination is investigated both theoretically and experimentally with appropriate extensive benchmarks. The structured THz illumination consistently outperforms the conventional one in resolution and contrast, thus opening new frontiers of structured light applications in imaging and inverse scattering problems, as it enables sophisticated estimates of optical properties of the investigated structures.

Optical resonance and rainbow scattering of an electromagnetic Airy light-sheet by a dielectric sphere of arbitrary size

The selection of the type of the structured beam is great importance in the study of optical and first-order rainbow scattering by a particle. The Airy light-sheet is a specific type of limited-diffracting beam (in 2D), which has been used in investigations related to radiation forces and torque. Equally important and of practical significance is the study of the electromagnetic/optical resonance and first-order rainbow scattering by a dielectric sphere. The purpose of this paper is to calculate the electromagnetic resonance scattering, energy efficiencies and far-field scattered intensity of a lossless homogeneous dielectric spherical particle of arbitrary size, illuminated by a linearly-polarized non-diffracting electromagnetic Airy light-sheet. A rigorous parametric study is undertaken here to investigate the effect of varying the light-sheet parameters γ, kw0, and its polarization state as well as the size parameter ka of the lossless dielectric sphere on the scattering efficiencies and intensity. The analysis is extended to examine the first-order rainbow scattering phenomenon in the context of Airy light-sheets with different polarizations. Numerical results show that kw0, γ, ka and the state of polarization affect the amplitude and scattering directivity patterns of the efficiencies and intensity. Rainbow scattering arises along the polar scattering angle θ=143°, and is minimally influenced by the different values of the parameters kw0, γ, polarization, and ka. The results are of some practical significance in optical resonance scattering and related applications in optical tweezers, super-resolution imaging, particle characterization, and the measurement of temperature, velocity and size of a liquid jet to name a few applications.

Generation of Millimeter-Wave Nondiffracting Airy OAM Beam Using a Single-Layer Hexagonal Lattice Reflectarray

In this letter, a millimeter-wave (mm-wave) nondiffracting Airy orbital angular momentum (OAM) beam is experimentally demonstrated by using a single-layer hexagonal lattice reflectarray based on an Airy-OAM-phase modulation method. To reduce the design time, a near-field synthesis technique is used to theoretically analyze the nondiffracting characteristics of the Airy OAM beam. A hexagonal dual-resonance element, composed of a hexagon ring around a square patch, is employed in the reflectarray to provide a linear phase range of 360 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> . The proposed reflectarray with a diameter of 45 cm is designed at 47 GHz, which can reshape the incident wave according to the superposition phase of the desired Airy beam and OAM beam. To validate our design, a prototype is fabricated and measured. The measured results agree well with the theoretical and simulated ones. The experimental results show that an Airy OAM beam with the mode of $+$1 is successfully generated from 44 to 49 GHz. The nondiffracting propagation distance is greater than 2.5 m (392λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> ). Moreover, the measured results validate the autofocusing and self-healing properties of the Airy OAM beam.

Deep Penetration Microscopic Imaging with Non-Diffracting Airy Beams.

We report a deep penetration microscopic imaging method with a non-diffracting Airy beam. The direct mapping of volume imaging in free space shows that the axial imaging range of the Airy beam is approximately 4 times that of the traditional Gaussian beam along the axial direction while maintaining a narrow lateral width. Benefiting from its non-diffracting property, the microscopic imaging with Airy beam illumination can acquire image structures through turbid medium and capture a volumetric image in a single frame. We demonstrate the penetration ability of the Airy microscopic imaging through a strongly scattering environment with 633 nm and 780 nm lasers. The performances of the volumetric imaging method were evaluated using HeLa cells and isolated mouse kidney tissue. The thick sample was scanned layer by layer in the Gaussian mode, however, in the Airy mode, the three-dimensional (3D) structure information was projected onto a two-dimensional (2D) image, which vastly increased the volume imaging speed. To show the characteristics of the Airy microscope, we performed dynamic volumetric imaging on the isolated mouse kidney tissue with two-photon.

Nondiffracting gravitational waves

It is proved that accelerating nondiffracting gravitational Airy wave-packets are solutions of linearized gravity. It is also showed that Airy functions are exact solutions to Einstein equations for non-accelerating nondiffracting gravitational wave-packets.

Fresnel Gaussian shape invariant applied to optical diffraction grating calculation

We present numerical results on the diffraction produced by optical gratings in the Raman–Nath, Bragg and intermediate regimes calculated by means of the Fresnel Gaussian Shape Invariant. We describe how this numerical method based on a superposition of Gaussian wavelets, allows propagating, in an iterative manner within the grating, the illuminating beams, providing accurate calculations of the diffractive orders. We also include results due to a truncated, non-diffractive Airy illuminating beam.

Multiplexed Nondiffracting Nonlinear Metasurfaces

AbstractMetasurfaces and planar photonic nanostructures have drawn great interest from the optical scientific community due to their diverse abilities of manipulating electromagnetic waves and high integration. Most metasurfaces launch diffracting waves, and thus suffer from divergence, short working distance, and instability. Although much effort has been devoted to researching nondiffracting metasurfaces which can launch electromagnetic waves with constant transverse intensity profiles in free‐space propagation, the number of working channels is inherently limited as these meta‐devices are implemented in the linear optical regime. Here, the multiplexed nondiffracting nonlinear metasurfaces are theoretically proposed and experimentally realized, which can generate the representative nondiffracting Bessel beam and Airy beam. Three Bessel beams with different numerical apertures and topological charges and three Airy beams with different propagation curves and focal lengths can be generated by a combination of different spins and wavelengths. The complex properties of the nondiffracting beams can be designed and detected in a more comprehensive and concise way with Fourier analysis. This proof‐of‐concept represents a new strategy for realizing multiplexed nondiffracting metasurfaces with advantages of ultracompactness, high‐pixelation, and easy integration and paves the way for multi‐channel optical communication and manipulation.

Volumetric two-photon microscopy with a non-diffracting Airy beam.

We demonstrate a volumetric two-photon microscopy (TPM) using the non-diffracting Airy beam as illumination. Direct mapping of the imaging trajectory shows that the Airy beam extends the axial imaging range around six times longer than a traditional Gaussian beam does along the propagation direction, while maintaining a comparable lateral width. Benefiting from its non-diffracting nature, the TPM with Airy beam illumination is able not only to capture a volumetric image within a single frame, but also to acquire image structures behind a strongly scattered medium. The volumetric specimen is mapped layer by layer under Gaussian mode, while the three-dimensional structure is projected to a single two-dimensional image under Airy mode, leading to a significantly increased acquisition speed. The performance of the TPM is evaluated employing a phantom of agarose gel imbedding fluorescent beads as well as a mouse brain slice. Finally, we showcase the penetration ability of the developed Airy TPM by imaging through a scattering environment.

Millimeter-Wave Nondiffracting Circular Airy OAM Beams

We demonstrate using theoretical analysis and full-wave numerical simulations nondiffracting circular Airy beams modulated with different orbital angular momenta (OAM) at millimeter wavelengths. It is shown that applying an azimuthal spiral phase component to the circular Airy beam results in a circular Airy OAM beam. These beams are radially symmetric with a null at the center and experience an inward radial shift within a certain propagation distance. Such propagation dynamics are contrary to that of a conventional OAM beam where the vortex radius increases, and the beam intensity decreases as the beam propagates due to diffraction effects. Thus, the circular Airy OAM beam can be nondiffracting over an appreciable distance of few tens of meters (i.e., few thousand wavelengths) and open the door for high data-rate communications. Phase only spatial wave modulators of aperture 20 cm $\times20$ cm with $40 \times 40$ pixels are designed for generating the circular Airy OAM beams with OAM of order 0, 1, and 2. These spatial wave modulators when illuminated with Gaussian beams generate the corresponding circular Airy OAM beam. Full-wave numerical simulation results showing the generation and propagation of circular Airy OAM beams at millimeter wavelengths that are nondiffracting up to 50 m are presented.

Conventional volume holography for unconventional Airy beam shapes.

Utilizing multiplexed volume holography, a single optical element, enabling to shape structural variants of non-diffracting Airy wavefronts, from one-dimensional Airy mode to unconventional Airy modes such as vortex Airy and quad Airy modes, has been experimentally realized. Here, beam shaped angularly multiplexed volume holographic gratings (AMVHGs) are recorded in PQ: PMMA photopolymer, where five different spatial wavefronts of Airy beams have been sequentially recorded, for simultaneous reconstruction of different Airy modes, by a conventional Gaussian beam. Spatial and spectral mode selective properties of AMVHGs are demonstrated by narrow-band as well as by broadband light source. In addition, through wavelength degeneracy property, the maximum sensitivity wavelength of blue (488 nm) is used for recording in PQ: PMMA, but the AMVHGs are operated at a broad wavelength band of interest, all the way to longer wavelength in near infrared (850 nm). The K-sphere representation is used to explain the spectral properties of AMVHGs.

Anomalous Reflection of Acoustic Waves in Air with Metasurfaces at Low Frequency

An acoustic metasurface made of a composite structure of cavity and membrane is proposed and numerically investigated. The target frequency is in the low frequency regime (570 Hz). The unit cells, which provide precise local phase modulation, are rather thin with thickness in the order around 1/5 of the working wavelength. The numerical simulations show that the designed metasurface can steer the reflected waves at will. By taking the advantage of this metasurface, an ultrathin planar acoustic axicon, acoustic lens, and acoustic nondiffracting Airy beam generator are realized. Our design method provides a new approach for the revolution of future acoustic devices.

Multiwavelength Metasurfaces Based on Single‐Layer Dual‐Wavelength Meta‐Atoms: Toward Complete Phase and Amplitude Modulations at Two Wavelengths

Since its invention, metasurface has been widely utilized to achieve nearly arbitrary wavefront control based on phase only modulation at single wavelength. To achieve better performance or exotic functions, it is desirable to demonstrate metasurfaces capable of realizing both phase and amplitude modulations. Meanwhile, the wavelength‐dependent behavior of the metasurface is one of the critical limitations in existing metasurface structures. Specifically, single‐layer metasurfaces with the capability to tailor both phase and amplitude at multiple wavelengths have not been reported so far. In this paper, a single‐layer meta‐atom is proposed which can realize ultrathin metasurfaces with complete phase and amplitude modulations at two THz wavelengths. Several dual‐wavelength metalenses and a nondiffractive Airy beam generator operating at two THz wavelengths are numerically demonstrated, the simulated results of which are consistent with the theoretical calculations and design goals. The presented dual‐wavelength meta‐atom can provide a powerful building block in multiwavelength metasurface designs for controlling electromagnetic waves, including focusing, beam steering, beam generations, hologram, etc.

Complete solutions of finite Airy beams in free space and graded index media with fourier analysis

In order to analyze the far-field propagation characteristics of the new non-diffractive Airy beams theoretically and deeply on the condition of finite energy, the Fourier analysis method was utilized. The analytical solution to paraxial wave equation which described one-dimensional Airy beams’ propagation dynamics in free space was given. Furthermore, a new analytical solution to the modified paraxial wave equation which described one-dimensional Airy beams’ linear propagation dynamics in graded index media was also given, which was different from the known one. The far-field propagation characteristics of one-dimensional and two-dimensional Airy beams in free space were studied by utilizing the acquired analytical solution. In addition, the influence of different parameters on non-diffractive propagation and transverse acceleration characteristics of Airy beams were studied in detail. The non-diffractive propagation distances would become longer if the decay factor became smaller when the arbitrary transverse scale kept invariant. Moreover, the Airy beams would accelerate faster if the arbitrary transverse scale became smaller when the decay factor kept invariant. The linear propagation characteristics of one-dimensional Airy beams in the graded index media was also analyzed. Interesting phenomena were observed,and it was found the trajectory of the Airy beams could be modulated arbitrarily if the parameters of the media were selected properly.

Lossless Airy Surface Polaritons in a Metamaterial via Active Raman Gain.

We propose a scheme to realize a lossless propagation of linear and nonlinear Airy surface polaritons (SPs) via active Raman gain (ARG). The system we suggest is a planar interface superposed by a negative index metamaterial (NIMM) and a dielectric, where three-level quantum emitters are doped. By using the ARG from the quantum emitters and the destructive interference effect between the electric and magnetic responses from the NIMM, we show that not only the Ohmic loss of the NIMM but also the light absorption of the quantum emitters can be completely eliminated. As a result, non-diffractive Airy SPs may propagate for very long distance without attenuation. We also show that the Kerr nonlinearity of the system can be largely enhanced due to the introduction of the quantum emitters and hence lossless Airy surface polaritonic solitons with very low power can be generated in the system.

Graphene Plasmonic Metasurfaces to Steer Infrared Light.

Metasurfaces utilizing engineered metallic nanostructures have recently emerged as an important means to manipulate the propagation of light waves in a prescribed manner. However, conventional metallic metasurfaces mainly efficiently work in the visible and near-infrared regime, and lack sufficient tunability. In this work, combining the pronounced plasmonic resonance of patterned graphene structures with a subwavelength-thick optical cavity, we propose and demonstrate novel graphene metasurfaces that manifest the potential to dynamically control the phase and amplitude of infrared light with very high efficiency. It is shown that the phase of the infrared light reflected from a simple graphene ribbon metasurface can span over almost the entire 2π range by changing the width of the graphene ribbons, while the amplitude of the reflection can be maintained at high values without significant variations. We successfully realize anomalous reflection, reflective focusing lenses, and non-diffracting Airy beams based on graphene metasurfaces. Our results open up a new paradigm of highly integrated photonic platforms for dynamic beam shaping and adaptive optics in the crucial infrared wavelength range.

Acoustic non-diffracting Airy beam

The acoustic non-diffracting Airy beam as its optical counterpart has unique features of self-bending and self-healing. The complexity of most current designs handicaps its applications. A simple design of an acoustic source capable of generating multi-frequency and broad-band acoustic Airy beam has been theoretically demonstrated by numerical simulations. In the design, a piston transducer is corrugated to induce spatial phase variation for transducing the Airy function. The piston's surface is grooved in a pattern that the width of each groove corresponds to the half wavelength of Airy function. The resulted frequency characteristics and its dependence on the size of the piston source are also discussed. This simple design may promote the wide applications of acoustic Airy beam particularly in the field of medical ultrasound.

Coupled Airy breathers.

The dynamics of two component-coupled vectorial Airy beams is investigated. In the linear propagation regime, a complete analytic solution describes the breather-like propagation of two components that feature nondiffracting self-accelerating Airy behavior. The superposition of two beams with different input properties opens the possibility of designing more complex nondiffracting propagation scenarios. In the strongly nonlinear regime, the dynamics remain qualitatively robust as is revealed by direct numerical simulations. Because of the Kerr effect, the two beams emit solitonic breathers whose coupling period is compatible with the remaining Airy-like beams. The results of this study are relevant for the description of photonic and plasmonic beams that propagate in coupled planar waveguides, as well as for birefrigent or multiwavelength beams.