Nondiffracting Beams Research Articles

High-efficiency generation of long-distance, tunable, high-order nondiffracting beams

Nondiffracting beams (NDBs) have presented significant utility across various fields for their unique properties of self-healing, anti-diffraction, and high-localized intensity distribution. We present a versatile and flexible method for generating high-order nondiffracting beams predicated on the Fourier transformation of polymorphic beams produced by the free lenses with tunable shapes. Based on the tunability of the digital free lenses, we demonstrate the experimental generation of various long-distance nondiffracting beams, including Bessel beams, polymorphic generalized nondiffracting beams, tilted nondiffracting beams, asymmetric nondiffracting beams, and specially structured beams generated by the superposition of Bessel beams. Our method achieves efficiency of up to about seven times compared with complex beam shaping methods. The generated NDBs exhibit characteristics of extended propagation distance and high-quality intensity profiles consistent with the theoretical predictions. The proposed method is anticipated to find applications in laser processing, optical manipulation, and other fields.

Generating optical vortex needle beams with a flat diffractive lens

We present a novel method for generating optical vortex needle beams (focused optical vortices with extended depth-of-focus) using a compact flat multilevel diffractive lens (MDL). Our experiments demonstrate that the MDL can produce focused optical vortices (FOVs) with topological charges l=1−4 (extendable to other l values), maintaining focus over distances significantly longer than conventional optical vortices. Specifically, FOVs exhibit non-diffracting behavior with a depth-of-focus (DOF) extended beyond 5 cm, compared to conventional optical vortices, which show continuous size increase due to diffraction. When the MDL is illuminated by an optical vortex of 3 mm diameter, it achieves a transmission efficiency of approximately 90% and extends the DOF several times beyond that of traditional lenses. Increasing the size of the input optical vortex further extends the DOF but introduces additional rings, with their number increasing proportionally to the value of l. Our approach, validated by both experimental results and numerical simulations, proves effective for beams such as optical vortex and Hermite-Gaussian modes and holds potential applications in high-resolution imaging, material processing, optical coherence tomography, and three-dimensional optical tweezers, offering a simple and efficient solution for generating non-diffracting beams.

Transition from Ince-Gaussian beams to nondiffractive Mathieu beams.

We show that under the appropriate conditions, the Ince-Gaussian modes (IGBs) of stable resonators display a behavior very similar to that of the Mathieu beams (MBs), exhibiting nondiffracting propagation and self-healing properties. We show that the high-order IGB propagates in a quasi-nondiffractive manner within the same conical region as any nondiffractive beam, even when their profiles do not match exactly. Our results indicate new, to our knowledge, methods to generate a quasi-nondiffractive MB from spherical resonators and provide more efficient ways to generate them in the Fourier space. These high-order IGBs are an excellent option for applications where a quasi-nondiffractive, but not exact, behavior is required.

Multi-mode non-diffraction vortex beams enabled by polarization-frequency multiplexing transmissive terahertz metasurfaces

In terahertz (THz) wireless communication systems, non-diffraction vortex beams carrying an orbital angular momentum (OAM) have attracted extensive attention due to their ability to transmit information over long distances with high capacity. However, existing metasurfaces can only generate a single OAM mode non-diffracting vortex beam at reflection space for circular polarization (CP) incidence, limiting practical applications. To address this issue, we propose and design a polarization-frequency multiplexing transmissive THz metasurface to realize multi-mode non-diffracting vortex beams at linear polarization (LP) incidence. The meta-atom of this metasurface is composed of three anisotropic rectangular metallic structures embedded in vanadium dioxide (VO2) square rings, two circular aperture metallic grid layers, and four dielectric layers. By reasonably designing the size of the metal patch and the state of VO2, the designed metasurface can achieve polarization multiplexing and frequency multiplexing for LP incidence. Based on the phase response of the proposed meta-atoms, the transmissive metasurface can implement not only multi-mode non-diffraction vortex beams but also their space separation at two frequency ranges of 0.80–0.90 THz and 1.50–1.80 THz by changing the state of VO2. Therefore, the proposed multiple multiplexing metasurfaces can effectively shape the wavefront of non-diffraction vortex beams, which have broad application prospects in 6G THz communication.

Diffraction of quasi-nondiffracting Bessel beam by an impedance disc in an anisotropic plasma

The diffraction of the so-called nondiffracting Bessel beam by an impedance disc immersed in an anisotropic medium is examined. The external uniform magnetic field, which makes the plasma anisotropic, is taken to be rotational as opposed to being parallel to the edge of the problem geometries in the literature. Thus, the appropriate dielectric matrix that models the anisotropic region under the rotational dc external magnetic field is derived for the first time, to the best of our knowledge. Upon considering the geometric optics waves, the total scattered waves are obtained with the diffracted waves by using the definition of high-frequency asymptotic expressions associated with the scattered waves at the transition regions. The results are expressed in terms of the Fresnel functions so that the wave behaviors in the transition regions are uniform. The solutions are compared numerically with existing studies in the literature, including limit values.

Robustness of highly complex radial carpet beams in turbulent atmospheres

In this study, we report observations of propagating radial carpet beams (RCBs) through a turbulent atmosphere at ground level with a 120 m path length. RCBs are a class of nondiffracting, accelerating, self-healing, and self-amplifying beams, and generated in the diffraction of a plane wave from amplitude/phase radial gratings having different spoke numbers. Observations were made at different times of the day. The intensity profile of an RCB becomes complicated when the number of grating spokes used to generate the beam is large, and includes high intensity spots, called main intensity spots (MISs), which are symmetrically placed at the central area around the beam axis and whose number is equal to (twice) the number of spokes of the amplitude (phase) grating used to generate the beam. With the aid of a telescope and a CCD camera, successive frames of the intensity pattern of the RCBs having different levels of structural complexity are recorded at the end of the path. For the data recorded at different times of the day, we calculate the variance of displacements of MISs along the radial direction. We observe that displacements of the MISs increase with increasing mean temperature of the air; on the other hand, as the complexity of the beam intensity pattern increases, the displacements of the MISs decrease. In order to compare the resilience of different RCBs and a well-known structured beam against atmospheric turbulence, we investigate deformation of the intensity profiles of a Laguerre–Gaussian (LG) beam having a topological charge 20 and different RCBs at the end of the path. It is shown that under the same turbulence condition, highly complex RCBs are more resilient to the destructive effects of the atmospheric turbulence. In particular, for the RCBs generated with gratings having 30 spokes and more, the number of MISs of the received intensity patterns is changed by less than 1% even when the turbulence strength is high. But for the LG beam, its intensity ring is clearly broken in different places, which makes it impossible to follow its maximum intensity in the radial direction

Nonlinear sound-sheet microscopy: imaging opaque organs at the capillary and cellular scale.

Light-sheet fluorescence microscopy has revolutionized biology by visualizing dynamic cellular processes in three dimensions. However, light scattering in thick tissue and photobleaching of fluorescent reporters limit this method to studying thin or translucent specimens. Here we show that non-diffractive ultrasonic beams used in conjunction with a cross-amplitude modulation sequence and nonlinear acoustic reporters enable fast and volumetric imaging of targeted biological functions. We report volumetric imaging of tumor gene expression at the cm 3 scale using genetically encoded gas vesicles, and localization microscopy of currently uncharted cerebral capillary networks using intravascular microbubble contrast agents. Nonlinear sound-sheet microscopy provides a ∼64x acceleration in imaging speed, ∼35x increase in imaged volume and ∼4x increase in classical imaging resolution compared to the state-of-the-art in biomolecular ultrasound.

Generation of parabolic beam using an amplitude and phase modulated metasurface

In this work, non-diffraction parabolic beam is generated using a double-layer transmission metasurface in the microwave frequency range. A transmissive unit cell with bilayered substrates and three metallic layers is designed. By controlling the orientation angle and the opening angle of the intermediate ∈-shaped metallic layer, transmission amplitude from 0 to 1 and continuous phase shift from 0° to 360° can be modulated simultaneously. To experimentally verify the proposed concept and design, a transmissive metasurface is fabricated and measured at 20 GHz. The simulated and measured results are in good agreement with the theoretical results, and prove the generated parabolic beam still maintained non-diffraction and self-healing characteristics within the maximum non-diffraction distance of 40λ. The generated microwave parabolic beam with its properties can be applied to improving the distance and efficiency of WPT and near field modulation of complex EM waves.

Manipulating circular Airy beam dynamics with quadratic phase modulation in fractional systems under some diffraction modulations and potentials

Based on a split-step Fourier algorithm, the transmission of circular Airy beams with quadratic phase modulation (QPM) is investigated in the fractional Schrödinger equation (FSE) under diffraction modulations (periodic modulation, linear modulation and power function modulation) and external potentials (parabolic potential and linear potential). The results show that QPM is able to change the focusing position and intensity, as well as the transmission trajectory of the beam. In a periodic modulation, the circular Airy beam (CAB) exhibits periodic variation characteristics, and the beam splitting is retarded under the action of the QPM. The self-focusing distance of the beam is significantly reduced, and its transmission trajectory and beam width are altered by the QPM under the linear modulation. The CAB progressively evolves into a non-diffraction beam under the power function modulation, and the QPM is able to reduce the light intensity and increase the beam width as the Lévy index decreases. In a parabolic potential, CABs display autofocusing and defocusing behavior, and the QPM affects the intensity distribution and optical width of the beam. The CAB is deflected and evolves periodically in a linear potential. The beam width increases and gradually stabilizes with the addition of the QPM. The propagation of CABs controlled with QPM in parabolic and linear potentials is also analyzed in the frequency domain. The results demonstrate that we can control the transmission of CABs in an FSE optical system by rationally setting parameters such as QPM, modulation coefficients, and external potentials.

Scattering characteristics of non-diffracting Lommel beam by a metamaterial PEMC sphere

Scattering characteristics of non-diffracting Lommel beam by a metamaterial PEMC sphere

Observation of Boyer-Wolf Gaussian modes

Stable laser resonators support three fundamental families of transverse modes: the Hermite, Laguerre, and Ince Gaussian modes. These modes are crucial for understanding complex resonators, beam propagation, and structured light. We experimentally observe a new family of fundamental laser modes in stable resonators: Boyer-Wolf Gaussian modes. By studying the isomorphism between laser cavities and quadratic Hamiltonians, we design a laser resonator equivalent to a quantum two-dimensional anisotropic harmonic oscillator with a 2:1 frequency ratio. The generated Boyer-Wolf Gaussian modes exhibit a parabolic structure and show remarkable agreement with our theoretical predictions. These modes are also eigenmodes of a 2:1 anisotropic gradient refractive index medium, suggesting their presence in any physical system with a 2:1 anisotropic quadratic potential. We identify a transition connecting Boyer-Wolf Gaussian modes to Weber nondiffractive parabolic beams. These new modes are foundational for structured light, and open exciting possibilities for applications in laser micromachining, particle micromanipulation, and optical communications.

Generation of polygonal non-diffracting beams via angular spectral phases

In this study, an effective approach for generating polygonal non-diffracting beams (PNDBs) is demonstrated using optical caustics and cross-phases. The resulting structured light beams display a polygonal transverse structure and exhibit a significant intensity gradient and phase gradient. Diverse PNDBs can be generated by flexibly controlling the exponent factor of the cross-phases. The experimental results show that this beam has excellent non-diffracting properties and could stably capture and manipulate particles to move along polygonal trajectories. Furthermore, by adjusting the conversion rate parameter of the cross-phase, PNDBs can manipulate the motion state of the trapped particles, such as start and stop. These various PNDBs may be useful for potential applications as optical tweezers and in micromachining.

Single-molecule localization microscopy at 2.4-fold resolution improvement with optical lattice pattern illumination

Traditional camera-based single-molecule localization microscopy (SMLM), with its high imaging resolution and localization throughput, has made significant advancements in biological and chemical researches. However, due to the limitation of the fluorescence signal-to-noise ratio (SNR) of a single molecule, its resolution is difficult to reach to 5 nm. Optical lattice produces a nondiffracting beam pattern that holds the potential to enhance microscope performance through its high contrast and penetration depth. Here, we propose a new method named LatticeFLUX which utilizes the wide-field optical lattice pattern illumination for individual molecule excitation and localization. We calculated the Cramér-Rao lower bound of LatticeFLUX resolution and proved that our method can improve the single molecule localization precision by 2.4 times compared with the traditional SMLM. We propose a scheme using 9-frame localization, which solves the problem of uneven lattice light illumination. Based on the experimental single-molecule fluorescence SNR, we coded the image reconstruction software to further verify the resolution enhancement capability of LatticeFLUX on simulated punctate DNA origami, line pairs, and cytoskeleton. LatticeFLUX confirms the feasibility of using 2D structured light illumination to obtain high single-molecule localization precision under high localization throughput. It paves the way for further implementation of ultra-high resolution full 3D structured-light-illuminated SMLM.

Extension of optical radiation pressure force exerted on rigid sphere by non-diffracting beams to acoustical domain

Extension of optical radiation pressure force exerted on rigid sphere by non-diffracting beams to acoustical domain

Fiber end integrated surface plasma lens for circular airy beam shaping

This paper presents a circular Airy beam generator based on a fiber end integrated surface plasma lens. The surface plasma lens consists of a nano-annular slot and an array of series concentric circular grooves etched on the gold film coated on the fiber end. When the fiber light field illuminates the nano-annular slot, surface plasmon polaritons (SPPs) will be excited, then the SPPs propagates along the surface of the gold film, and will finally be decoupled into free space to generate circular Airy beam by the array of concentric circular grooves. The effect of the parameters of the plasma lens on the properties of the output circular Airy beam, such as self-focusing, focal spot size, is studied in detail via FDTD simulations. In addition, we found that the proposed plasma lens has a high tolerance to manufacturing errors. The case that instead of the nano-annular slit with a circular wheat-spike shaped structure is also investigated. In this case, due to the different photon spin response of the circular wheat-spike shaped structure, the device can generate circular Airy beam when the input fiber light field is right-handed circularly polarized (RHCP) light, and subwavelength Bessel-like nondiffracting beam when the input fiber light field is left-handed circularly polarized (LHCP) light. These results provide a highly integrated all-fiber circular Airy beam and subwavelength Bessel-like nondiffracting beam generation scheme, which may be useful in the areas of fiber end structured light beam shaping and fiber-integrated photonic devices.

Diffraction of a pseudo nondiffracting Bessel beam by a circular perfect electromagnetic conductor disk.

This study examined the diffraction of a pseudo nondiffracting Bessel beam by a perfect electromagnetic disk. The geometric optics beam waves were written from the geometry of the problem and related boundary conditions. The diffracted beam waves were derived by utilizing the relation between geometric optics and diffracted waves at the transition boundaries, considering the high frequency asymptotic expression of the scattered wave. The uniform scattered beam waves were expressed in terms of Fresnel functions with the uniform geometrical theory of the diffraction method. Thus, finite magnitudes were read at the transition boundaries. Finally, the obtained uniform expressions were investigated numerically for different groups of parameters.

Spin‐Selective Trifunctional Metasurfaces for Deforming Versatile Nondiffractive Beams along the Optical Trajectory

AbstractExploring and taming the diffraction phenomena and divergence of light are foundational to enhancing comprehension of nature and developing photonic technologies. Despite the numerous types of nondiffraction beam generation technologies, the 3D deformation and intricate wavefront shaping of structures during propagation have yet to be studied through the lens of nanophotonic devices. Herein, the dynamic conversion of a circular Airy beam (CAB) to a Bessel beam with a single‐layer spin‐selective metasurface is demonstrated. This spatial transformation arises from the interplay of 1D local and 2D global phases, facilitating the 3D control of non‐diffractive light fields. An additional overall phase gradient and orbital angular momentum are introduced, which effectively altering the propagation direction and transverse fields of complex amplitude beams along the optical path. The manifested samples exhibit superior defect resistance, laying a crucial application in micro/nanolithography technologies. This approach expands the in‐plane spin‐selective mechanism and leverages the out‐of‐plane propagation dimension, allowing for integrated high‐resolution imaging, on‐chip optical micromanipulation, and micro/nanofabrication within a versatile nanophotonic platform.

Open-top Bessel beam two-photon light sheet microscopy for three-dimensional pathology

Nondestructive pathology based on three-dimensional (3D) optical microscopy holds promise as a complement to traditional destructive hematoxylin and eosin (H&E) stained slide-based pathology by providing cellular information in high throughput manner. However, conventional techniques provided superficial information only due to shallow imaging depths. Herein, we developed open-top two-photon light sheet microscopy (OT-TP-LSM) for intraoperative 3D pathology. An extended depth of field two-photon excitation light sheet was generated by scanning a nondiffractive Bessel beam, and selective planar imaging was conducted with cameras at 400 frames/s max during the lateral translation of tissue specimens. Intrinsic second harmonic generation was collected for additional extracellular matrix (ECM) visualization. OT-TP-LSM was tested in various human cancer specimens including skin, pancreas, and prostate. High imaging depths were achieved owing to long excitation wavelengths and long wavelength fluorophores. 3D visualization of both cells and ECM enhanced the ability of cancer detection. Furthermore, an unsupervised deep learning network was employed for the style transfer of OT-TP-LSM images to virtual H&E images. The virtual H&E images exhibited comparable histological characteristics to real ones. OT-TP-LSM may have the potential for histopathological examination in surgical and biopsy applications by rapidly providing 3D information.

Open-top Bessel beam two-photon light sheet microscopy for three-dimensional pathology.

Nondestructive pathology based on three-dimensional (3D) optical microscopy holds promise as a complement to traditional destructive hematoxylin and eosin (H&E) stained slide-based pathology by providing cellular information in high throughput manner. However, conventional techniques provided superficial information only due to shallow imaging depths. Herein, we developed open-top two-photon light sheet microscopy (OT-TP-LSM) for intraoperative 3D pathology. An extended depth of field two-photon excitation light sheet was generated by scanning a nondiffractive Bessel beam, and selective planar imaging was conducted with cameras at 400 frames/s max during the lateral translation of tissue specimens. Intrinsic second harmonic generation was collected for additional extracellular matrix (ECM) visualization. OT-TP-LSM was tested in various human cancer specimens including skin, pancreas, and prostate. High imaging depths were achieved owing to long excitation wavelengths and long wavelength fluorophores. 3D visualization of both cells and ECM enhanced the ability of cancer detection. Furthermore, an unsupervised deep learning network was employed for the style transfer of OT-TP-LSM images to virtual H&E images. The virtual H&E images exhibited comparable histological characteristics to real ones. OT-TP-LSM may have the potential for histopathological examination in surgical and biopsy applications by rapidly providing 3D information.

Versatile polarization-converted non-diffractive Bessel beams based on fully phase-modulated metasurfaces.

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.