Nonparaxial Mathieu and Weber accelerating beams

Sidelobe suppression for accelerating beams

Although the control of trajectory, amplitude and beam-width in accelerating beams have been extensively investigated, sidelobes manipulation of such beams, which is required in many applications, has been surprisingly under-researched. This paper presents an approach for the generating of accelerating beams with significantly reduced sidelobes. The proposed method encompasses a two-step angular spectrum design, including employing a general model to establish the phase distribution and applying a stochastic parallel gradient descent (SPGD) algorithm to optimize the binary amplitude modulation. Experimental results confirm that the sidelobe intensity of accelerating beams can be reduced by over 50% with our method, thereby enhancing their applicability in many fields, such as micro-machining, particle manipulation, and optical communication.

Mathieu and Weber tightly autofocusing beams

We theoretically investigate the propagation dynamics of vectorial Mathieu and Weber tightly autofocusing beams, which are constructed based on nonparaxial Weber and Mathieu accelerating beams, respectively. They can automatically focus along the paraboloid and ellipsoid, and the focal fields represent the tightly focusing properties resembling that generated with a high NA lens. We demonstrate the influence of the beam parameters on the spot size and energy proportion of longitudinal component of the focal fields. It reveals that Mathieu tightly autofocusing beam supports a more superior focusing performance, of which the longitudinal field component with superoscillatory feature could be enhanced by decreasing the order and selecting the suitable interfocal separation of the beam. These results are expected to provide new insights for the autofocusing beams and the tight focusing of the vector beams.

Composite Diffraction-Free Beam Formation Based on Iteratively Calculated Primitives

To form a diffraction-free beam with a complex structure, we propose to use a set of primitives calculated iteratively for the ring spatial spectrum. We also optimized the complex transmission function of the diffractive optical elements (DOEs), which form some primitive diffraction-free distributions (for example, a square or/and a triangle). The superposition of such DOEs supplemented with deflecting phases (a multi-order optical element) provides to generate a diffraction-free beam with a more complex transverse intensity distribution corresponding to the composition of these primitives. The proposed approach has two advantages. The first is the rapid (for the first few iterations) achievements of an acceptable error in the calculation of an optical element that forms a primitive distribution compared to a complex one. The second advantage is the convenience of reconfiguration. Since a complex distribution is assembled from primitive parts, it can be reconfigured quickly or dynamically by using a spatial light modulator (SLM) by moving and rotating these components. Numerical results were confirmed experimentally.

Controllable self-rotating array beam with an arc-shaped accelerating trajectory

In this study, a modified interfering vortex phase mask (MIVPM) is proposed to generate a new type of self-rotating beam. The MIVPM is based on a conventional and stretched vortex phase for generating a self-rotating beam that rotates continuously with increasing propagation distances. A combined phase mask can produce multi-rotating array beams with controllable sub-region number. The combination method of this phase was analyzed in detail. This study proves that this self-rotating array beam has an effectively enhanced central lobe and reduced side lobe owing to adding a vortex phase mask compared with a conventional self-rotating beam. Furthermore, the propagation dynamics of this beam can be modulated by varying the topological charge and constant a. With an increase in the topological charge, the area crossed by the peak beam intensity along the propagation axis increases. Meanwhile, the novel self-rotating beam is used for optical manipulation under phase gradient force. The proposed self-rotating array beam has potential applications in optical manipulation and spatial localization.

Single optical element to generate a meter-scale THz diffraction-free beam

Diffraction-free electromagnetic beam propagates in free space without change in its two-dimensional transverse profile. Elongating diffraction-free length can benefit the practical application of this beam. Here, we demonstrate that a THz diffraction-free beam with meter-scale length can be achieved by using only one optical element. By circumscribing the line-shape of spherical harmonic function on a traditional axicon, such optical element is designed, and then can be fabricated by 3D-printing technique. Simulated, experimental, and theoretical results all show that the diffraction-free length of generated beam is over 1000 mm. Further analysis based on Fourier optics theory indicates that the spatial frequency of this beam has a comb distribution, which plays a key role during the beam generation process. Moreover, such distribution also demonstrates the beam generated by our invented optical element is not the Bessel beam, but a new diffraction-free beam. It is believed that this meter-scale THz diffraction-free beam can be useful in a non-contact and non-destructive THz imaging system for large objects.

Flexible trajectory control of Bessel beams with pure phase modulation

Spatial phase modulation has become an important method for the design of new self-accelerating light beams. Based on the transverse-longitudinal mapping of Bessel beam, we propose a method of pure phase modulation to directly convert a zero-order Bessel beam into a self-accelerating beam, of which the propagation trajectories can be flexibly predesigned. We experimentally demonstrate three typical types of curves that the modulated Bessel beam propagates along, and the parabolic, spiral, and teleporting self-accelarating beams are realized. The experimental results match the expected trajectory well. This method is simple to operate, and imposes fewer restrictions on the beam trajectory.

Circular Mathieu and Weber autofocusing beams

In this Letter, the new classes of non-paraxial autofocusing beams are introduced for the first time, to the best of our knowledge. We investigate both numerically and experimentally non-paraxial circular Mathieu and Weber autofocusing beams based on the solutions of the Helmholtz equation in elliptical and parabolic coordinates, respectively. The results show that such beams can significantly shorten the focus distance, and eliminate the intense oscillation effectively after the focusing point. The focal length and the peak intensity can be controlled by tunable parameters. In addition, we further experimentally realize their application of such beams in optical trapping.

Dual projectile beams

Accelerating beams, of which the Airy beam is an important representative, are characterized by intensity maxima that propagate along curved trajectories. In this work we present a simple approach to directly generate accelerating beams with controllable trajectories by means of binary phase structures that consist of only a π phase step modulation in comparison to previous studies where two-dimensional cubic phase modulations for example are required, and which have practical limitations due to their challenging fabrication with phase plates or diffractive optical elements (DOEs), or the spatially extended system needed for their generation at the Fourier plane. In our approach, two intensity maxima are formed that propagate along root parabolic trajectories in contrast to Airy and higher order caustic beams that propagate along a parabolic curve, hence we call these beams Dual Projectile Beams (DPBs). By tailoring a step or slit phase patterns with additional Fresnel lenses, we either generate hollow-core or abruptly focusing beams and control their curvatures. Moreover, using DPBs as a simpler complement to complex structured light fields, we demonstrate their versatility at the example of their interaction with nonlinear matter, namely the formation of a spatial soliton in a photorefractive material. We show that the formed solitary state propagates almost unchanged for a distance of several Rayleigh lengths. This light matter interaction can be regarded as a light beam deceleration. The simplicity of this approach makes these beams suitable for integrated optics and high-power laser applications using DOEs or meta-surfaces.

Self-Healing of Non-Hermitian Topological Skin Modes

A unique feature of non-Hermitian (NH) systems is the NH skin effect, i.e., the edge localization of an extensive number of bulk-band eigenstates in a lattice with open or semi-infinite boundaries. Unlike extended Bloch waves in Hermitian systems, the skin modes are normalizable eigenstates of the Hamiltonian that originate from the intrinsic non-Hermitian point-gap topology of the Bloch band energy spectra. Here, we unravel a fascinating property of NH skin modes, namely self-healing, i.e., the ability to self-reconstruct their shape after being scattered off by a space-time potential.

Manipulation of curved beams using beam-domain optimization

An efficient scheme for the design of aperture fields (distributed sources) that radiate arbitrary trajectory curved (accelerating) beams, with enhanced controllability of various beam features, is presented. The scheme utilizes a frame-based phase-space representation of aperture fields to overcome the main hurdles in the design for large apertures: First, it uses the a-priory localization of caustic beams to significantly reduce the optimization problem's variable space, to that of few Gaussian window coefficients accurately capturing those beams. Then, the optimization problem is solved in the reduced (local) spectral domain. We adopt a linearization approach that enables the solution by sequential application of conventional convex optimization tools, which are naturally compatible with the proposed phase-space representation. The localized nature of the Gaussian windows' radiation is used also for fast field evaluation at a greatly reduced number of optimization constraint points. The significant enhancement in the controllability over the various beam parameters is demonstrated through a range of examples.

Optical element to generate zero-order quasi-Bessel beam with "focal length"

An optical element has been invented to generate a zero-order quasi-Bessel beam with a certain distance to the element, which does not exist in the zero-order quasi-Bessel beam by using a traditional axicon. The cross section of designed element is an isosceles triangle whose equal sides are circumscribed by two semi-ellipses. Using a well-developed three-dimensional (3D)-printing technique, we have fabricated a series of elements working at terahertz (THz) frequency. Both simulated and experimental results clearly show that there is a certain distance between the generated quasi-Bessel beam and this element. A physical analysis based on geometric optics theory is performed to explain the obtained results. Because it is a refractive transmitted optical element, we propose that it can be also realized at another frequency band if the relevant processing techniques are available.

Experimental visualization of various cross sections through a butterfly caustic

Optical caustics and wavefronts of butterfly beams (BBs) derived by using a catastrophe theory determined by potential functions depending on the state and control variables are reported. Due to the high dimensionality for the control variables, BBs can be manipulated into various optical light structures. It is also demonstrated that these curious beams have relatively simple Fourier spectra that can be described as polynomials, and another way to generate BBs from the Fourier spectrum's perspective is provided. The dynamics for BBs are investigated by potential functions. Our experimental results agree well with the theoretical predictions. In addition to micro-manipulation and machining, these novel, to the best of our knowledge, caustic beams will pave the way for creating waveguide structures since they display high-intensity formations that evolve along curved trajectories.

Self-healing of a heralded single-photon Airy beam

Self-healing of an Airy beam during propagation is of fundamental interest and also promises important applications. Despite many studies of Airy beams in the quantum regime, it is unclear whether an Airy beam only including a single photon can heal after passing an obstacle because the photon may be blocked. Here we experimentally observe self-healing of a heralded single-photon Airy beam. Our observation implies that an Airy wave packet is robust against obstacle caused distortion and can restore even at the single-photon level.

Designing optical fields in inhomogeneous media

Designing optical fields with predetermined properties in source-free inhomogeneous media has been a long-sought goal due to its potential utilization in many applications, such as optical trapping, micromachining, imaging, and data communications. Using ideas from the calculus of variations, we provide a general framework based on the Helmholtz equation to design optical fields with prechosen amplitude and phase inside an inhomogeneous medium. The generated field is guaranteed to be the closest physically possible rendition of the desired field. The developed analytical approach is then verified via different techniques, where the approach's validity is demonstrated by generating the desired optical fields in different inhomogeneous media.

Propagation-invariant space-time caustics of light

Caustics are responsible for a wide range of natural phenomena, from rainbows and mirages to sparkling seas. Here, we present caustics in space-time wavepackets, a class of pulsed beams featuring strong coupling between spatial and temporal frequencies. Space-time wavepackets have attracted much attention with their propagation-invariant intensity profiles that travel at tunable superluminal and subluminal group velocities. These intensity profiles, however, have been largely restricted to an X-shape or similar pattern. We show that space-time caustics combine the propagation invariance of space-time wavepackets with the flexible design of caustics, allowing for customizable intensity patterns in space-time wavepackets. Our method directly provides the phase distribution needed to realize user-designed caustic patterns in space-time wavepackets. We show that space-time caustics can feature in a broad range of intriguing optical phenomena, including backward traveling caustics formed from purely forward propagating waves, and nondiffracting beams that evolve with time. Our findings should open the doors to an even wider range of structured light with spatiotemporal coupling.

Degree of paraxiality of an electromagnetic fractional multi-Gaussian Schell-model beam

The degree of paraxiality (DOP) of an electromagnetic fractional multi-Gaussian Schell-model (EM-FMGSM) beam is discussed, and the effect of the properties of the light source on its DOP is also studied. It is shown from the numerical results that the DOP of an EM-FMGSM beam is determined by the rms widths of the auto-correlation functions, the truncated parameter, the degree of polarization, and the boundary characteristics of its source. Moreover, the far-field divergence angle of the beam source is also investigated to illustrate the behaviors of the DOP.

Direct axial plane imaging of particle manipulation with nondiffracting Bessel beams

Optical manipulation with nondiffracting beams has been attracting great interest and finding widespread applications in many fields such as chemistry, physics, and biomedicine. Generally, optical manipulation is conducted in an optical microscopy system, which, in general, only allows for imaging motions of particles in the transverse plane, rendering the observation of dynamics processes occurring in the axial plane impractical. We propose and demonstrate an optical manipulation system that incorporates an axial plane imaging module. With this system, the trapping behavior in the transverse plane and the transportation process in the axial plane of a particle immersed in a Bessel beam were acquired simultaneously in real time.

Non-diffracting and self-accelerating Bessel beams with on-demand tailored intensity profiles along arbitrary trajectories

Owing to their robustness against diffraction, Bessel beams (BBs) offer special advantages in various applications. To enhance their applicability, we present a method to generate self-accelerating zeroth-order BBs along predefined trajectories with tunable z direction intensity profiles. The character of tunable z direction intensity profiles in non-diffracting self-accelerating BBs potentially can attract interest in the regimes of particle manipulation, microfabrication, and free-space optical interconnects.

Transverse spin dynamics in structured electromagnetic guided waves

We formulate and experimentally validate a set of spin–momentum equations which are analogous to the Maxwell’s equations and govern spin–orbit coupling in electromagnetic guided waves. The Maxwell-like spin–momentum equations reveal the spin–momentum locking, the chiral spin texture of the field, Berry phase, and the spin–orbit interaction in the optical near field. The observed spin–momentum behavior can be extended to other classical waves, such as acoustic, fluid, gas, and gravitational waves.

Spin–momentum locking, a manifestation of topological properties that governs the behavior of surface states, was studied intensively in condensed-matter physics and optics, resulting in the discovery of topological insulators and related effects and their photonic counterparts. In addition to spin, optical waves may have complex structure of vector fields associated with orbital angular momentum or nonuniform intensity variations. Here, we derive a set of spin–momentum equations which describes the relationship between the spin and orbital properties of arbitrary complex electromagnetic guided modes. The predicted photonic spin dynamics is experimentally verified with four kinds of nondiffracting surface structured waves. In contrast to the one-dimensional uniform spin of a guided plane wave, a two-dimensional chiral spin swirl is observed for structured guided modes. The proposed framework opens up opportunities for designing the spin structure and topological properties of electromagnetic waves with practical importance in spin optics, topological photonics, metrology and quantum technologies and may be used to extend the spin-dynamics concepts to fluid, acoustic, and gravitational waves.

Swallowtail-type diffraction catastrophe beams

We demonstrate a universal approach for generating high-order diffraction catastrophe beams, specifically for Swallowtail-type beams (abbreviated as Swallowtail beams), using diffraction catastrophe theory that was defined by potential functions depending on the control and state parameters. The three-dimensional curved caustic surfaces of these Swallowtail catastrophe beams are derived by the potential functions. Such beams are generated by mapping the cross sections of the high-order control parameter space to the corresponding transverse plane. Owing to the flexibility of the high-order diffraction catastrophe, these Swallowtail beams can be tuned to a diverse range of optical light structures. Owing to the similarity in their frequency spectra, we found that the Swallowtail beams change into low-order Pearcey beams under given conditions during propagation. Our experimental results are in close agreement with our simulated results. Such fantastic catastrophe beams that can propagate along curved trajectories are likely to give rise to new applications in micromachining and optical manipulation, furthermore, these diverse caustic beams will pave the way for the tailoring of arbitrarily accelerating caustic beams.

Abruptly autofocusing circular swallowtail beams

In this Letter, to the best of our knowledge, we report the first experimental demonstration of a new family of autofocusing beams, circular swallowtail beams (CSBs), based on the high-order swallowtail catastrophe, which were determined by potential functions depending on the state and control parameters. The dynamics of the CSBs is discussed here. These types of CSBs tend to automatically focus without external components. Numerical results showed the focal intensity increased significantly, and it was as much as 110 times in the initial plane when the radius of the main ring was 40. Additionally, in contrast to previous circular Pearcey and Airy beams, these CSBs appeared to have more diversity and tunability due to having more propagation trajectories and intensity distribution structures due to high-order diffraction catastrophe. The numerical simulations were verified by our experimental results. These diverse CSBs could have new applications in flexible optical manipulation. These various CSBs could be beneficial for potential applications in optical trapping, medical treatment, or micromachining.

Accelerating triangle-like singular beam

We demonstrate a type of singular beam that accelerates along a parabolic trajectory and has a cross-section intensity pattern exhibiting a dark central region surrounded by multiple rings with the innermost (main) ring resembling an equilateral triangle. The key to creating such beams is to replace the standard triangle with a rounded one, made up of six circular arcs connected end to end. The individual input phase mask for each arc can be analytically computed, and the whole input phase mask for the beam is thus obtained by piecing together these individual phases. Furthermore, the continuity of field forces of these triangle-like modes is discrete; that is, an index similar to the topological charge of vortex beams arises. Numerical results show that the energy flow in the beam's cross section circulates around the dark center along the triangle-like main ring, suggesting a possible application in orbiting particles along an irregular path.

Generation of a meter-scale THz diffraction-free beam based on multiple cascaded lens-axicon doublets: detailed analysis and experimental demonstration

An effective approach is proposed for obtaining a long-distance THz diffraction-free beam with meter-scale length. Multiple 3D-printed lens-axicon doublets are cascaded to form the generation system. In order to manifest the physical mechanism behind the generation process of this long-distance diffraction-free beam, we make a detailed comparative analysis of three beams: the ideal Bessel beam, the quasi-Bessel beam generated by single axicon, and the diffraction-free beam generated by the lens-axicon doublets. Theoretical results show that the zero-radial-spatial-frequency component plays a key role during the generation process of the third beam. Moreover, the intensities of this component are enhanced with the increase in the number of lens-axicon doublets, making the diffraction-free length longer. An experiment containing three lens-axicon doublets is performed to demonstrate the feasibility of our design. A 0.1-THz beam with one-meter diffraction-free length was successfully generated. Further experiments indicate that this THz diffraction-free beam also has a self-healing property. We believe that such long-distance diffraction-free beams can be used in practical THz remote sensing or imaging.

Degree of paraxiality of an anisotropic hollow multi-Gaussian Schell-model beam

Degree of paraxiality (DOP) of an anisotropic hollow multi-Gaussian Schell-model (HMGSM) beam is discussed, and the influence of parameters of the beam source on its DOP is studied. It is shown that the parameters of the beam source, including the anisotropy, boundary characteristic, beam waist width, and beam coherence width, may play an important role in its DOP. Moreover, in order to illustrate the behaviors of DOP, the far-field divergence angle of this beam source has also been investigated.

Multifunctional focusing and accelerating of light with a simple flat lens

The wavefronts emerging from phase gradient metasurfaces are typically sensitive to incident beam properties such as angle, wavelength, or polarization. While this sensitivity can result in undesired wavefront aberrations, it can also be exploited to construct multifunctional devices which dynamically vary their behavior in response to tuning a specified degree of freedom. Here, we show how incident beam tilt in a one dimensional metalens naturally offers a means for changing functionality between diffraction limited focusing and the generation of non-paraxial accelerating light beams. This attractively offers enhanced control over accelerating beam characteristics in a simple and compact form factor.

The Complex Charge Paradigm: A New Approach for Designing Electromagnetic Wavepackets

Singularities in optics famously describe a broad range of intriguing phenomena, from vortices and caustics to field divergences near point charges. The diverging fields created by point charges are conventionally seen as a mathematical peculiarity that is neither needed nor related to the description of electromagnetic beams and pulses, and other effects in modern optics. This work disrupts this viewpoint by shifting point charges into the complex plane, and showing that their singularities then give rise to propagating, divergence-free wavepackets. Specifically, point charges moving in complex space-time trajectories are shown to map existing wavepackets to corresponding complex trajectories. Tailoring the complex trajectories in this "complex charge paradigm" leads to the discovery and design of new wavepacket families, as well as unprecedented electromagnetic phenomena, such as the combination of both nondiffracting behavior and abruptly-varying behavior in a single wavepacket. As an example, the abruptly focusing X-wave-a propagation-invariant X-wave-like wavepacket with prechosen self-disruptions that enhance its peak intensity by over 200 times-is presented. This work envisions a unified method that captures all existing wavepackets as corresponding complex trajectories, creating a new design tool in modern optics and paving the way to further discoveries of electromagnetic modes and waveshaping applications.

Vector wave analysis of Airy beams upon reflection and refraction

As a kind of typical self-accelerating laser beam, Airy beams have attracted much attention due to their fascinating properties and various potential applications. In this work, we carry out a full vector wave analysis of Airy beams upon reflection and refraction. A hybrid method based on the angular spectrum representation and vector potential in the Lorenz gauge is introduced to describe the vectorial structure of Airy beams upon reflection and refraction. The explicit analytical expressions for the electric and magnetic field components of arbitrarily incident Airy beams reflected and refracted at an air-medium interface are derived in detail. Local-field patterns and magnitude profiles with different parameters are displayed. The analytical formulas obtained in this work can be practically applied to explore the local dynamical characteristics, including the energy, momentum, spin, and orbital angular momentum of Airy beams upon reflection and refraction.

Designing the phase and amplitude of scalar optical fields in three dimensions

The ability to generate any arbitrarily chosen optical field in a three-dimensional (3D) space, in the absence of any sources, without modifying the index of refraction, remains an elusive but much-desired capability with applications in various fields such as optical micromanipulation, imaging, and data communications, to name a few. In this work, we show analytically that it is possible to generate any desired scalar optical field with predefined amplitude and phase in 3D space, where the generated field is an exact duplicate of the desired field in case it is a solution of Helmholtz wave equation, or if the existence of such field is strictly forbidden, the generated field is the closest possible rendition of the desired field in amplitude and phase. The developed analytical approach is further supported via experimental demonstration of optical beams with exotic trajectories and can have a significant impact on the aforementioned application areas.

Manipulation and control of 3-D caustic beams over an arbitrary trajectory

We present an algorithm for manipulating and controlling 3-D field patterns, with energy confined to the narrow vicinity of predefined 3-D trajectories in free-space, which are of arbitrary curvature and torsion. This is done by setting the aperture field's phase to form smooth caustic surfaces that include the desired trajectory. The aperture amplitude distribution is constructed to manipulate both the on-axis intensity profile and the off-axis beam-width, and is updated iteratively. Once the aperture distribution is calculated, the radiation from a finite sampled aperture is computed numerically using a Fast Fourier Transform-based scheme. This allows for both verification of the design and examination of its sensitivity to parameters of realistic discrete implementation. The algorithm is demonstrated for the cases of an Airy beam of a planar trajectory, as well as for helical and conical-helical trajectory beams.

Recent Advances in Integrated Photonic Jet-Based Photonics

The study of accelerating Airy-family beams has made significant progress, not only in terms of numerical and experimental investigations, but also in conjunction with many potential applications. However, the curvature of such beams (and hence their acceleration) is usually greater than the wavelength. Relatively recently, a new type of localized wave beams with subwavelength curvature, called photonic hooks, was discovered. This paper briefly reviews the substantial literature concerning photonic jet and photonic hook phenomena, based on the photonic jet principle. Meanwhile, the photonic jet ensemble can be produced by optical wave diffraction at 2D phase diffraction gratings. The guidelines of jets’ efficient manipulation, through the variation of both the shape and spatial period of diffraction grating rulings, are considered. Amazingly, the mesoscale dielectric Janus particle, with broken shape or refractive index symmetry, is used to generate the curved photonic jet—a photonic hook—emerging from its shadow-side surface. Using the photonic hook, the resolution of optical scanning systems can be improved to develop optomechanical tweezers for moving nanoparticles, cells, bacteria and viruses along curved paths and around transparent obstacles. These unique properties of photonic jets and hooks combine to afford important applications for low-loss waveguiding, subdiffraction-resolution nanopatterning and nanolithography.

Experimental observation of three-dimensional non-paraxial accelerating beams

We experimentally realize three-dimensional non-paraxial accelerating beams associated with different coordinate systems. They are obtained by Fourier transforming a phase-modulated wave front in an aberration-compensated system. The phase pattern is encoded to include the phase and amplitude modulation for the accelerating beams with additional correction phase for the aberration compensation. These beams propagate along a circular trajectory, but they exhibit rather complex intensity patterns corresponding to the shape-invariant solutions in parabolic, prolate spheroidal and oblate spheroidal coordinate systems.

Free-space data-carrying bendable light communications

Bendable light beams have recently seen tremendous applications in optical manipulation, optical imaging, optical routing, micromachining, plasma generation and nonlinear optics. By exploiting curved light beams instead of traditional Gaussian beam for line-of-sight light communications, here we propose and demonstrate the viability of free-space data-carrying bendable light communications along arbitrary trajectories with multiple functionalities. By employing 39.06-Gbit/s 32-ary quadrature amplitude modulation (32-QAM) discrete multi-tone (DMT) signal, we demonstrate free-space bendable light intensity modulated direct detection (IM-DD) communication system under 3 different curved light paths. Moreover, we characterize multiple functionalities of free-space bendable light communications, including bypass obstructions transmission, self-healing transmission, self-broken trajectory transmission, and multi-receiver transmission. The observed results indicate that bendable light beams can make free-space optical communications more flexible, more robust and more multifunctional. The demonstrations may open a door to explore more special light beams enabling advanced free-space light communications with enhanced flexibility, robustness and functionality.

Spectrally tunable chiral Bragg reflectors for on-demand beam generation

We demonstrate the generation of spectrally tunable phase-dependent wavefronts, using the 2D Airy as the primary test case, via a polymer-stabilized cholesteric liquid crystal (PSCLC) element. Specifically, we use a novel spatial light modulator (SLM) based projection system to photo-align the initial helix angle landscape of the PSCLC so that it imparts the appropriate cubic phase profile to the reflected beam. This element is spectrally selective, with a reflection bandwidth of ≈ 100 nm, and electrically tunable from λ = 530 nm to 760 nm. Under both green and red laser illumination, the element is shown to conditionally form an Airy beam depending on the position of the electrically tailored reflection band. We briefly demonstrate the generality of this approach by producing PSCLC elements which form a computer-generated hologram and a higher-order Mathieu beam.

Degree of paraxiality of an electromagnetic multi-Gaussian Schell-model beam

The degree of paraxiality (DOP) of an electromagnetic multi-Gaussian Schell-model (EM-MGSM) beam was discussed, and the dependence of DOP on the characteristics of beam sources was investigated. It is shown that the parameters of beam sources, including the rms widths of the auto-correlation functions, the degree of polarization, and the boundary characteristics, play an important role in the DOP of the beam. To explain these phenomena, the far-zone divergence angle of the EM-MGSM beam was further discussed.

Femtosecond Mathieu Beams for Rapid Controllable Fabrication of Complex Microcages and Application in Trapping Microobjects

Structured laser beam based microfabrication technology provides a rapid and flexible way to create some special microstructures. As an important member in the propagation of invariant structured optical fields, Mathieu beams (MBs) exhibit regular intensity distribution and diverse controllable parameters, which makes it extremely suitable for flexible fabrication of functional microstructures. In this study, MBs are generated by a phase-only spatial light modulator (SLM) and used for femtosecond laser two-photon polymerization (TPP) fabrication. Based on structured beams, a dynamic holographic processing method for controllable three-dimensional (3D) microcage fabrication has been presented. MBs with diverse intensity distributions are generated by controlling the phase factors imprinted on MBs with a SLM, including feature parity, ellipticity parameter q, and integer m. The focusing properties of MBs in a high numerical aperture laser microfabrication system are theoretically and experimentally investigated. On this basis, complex two-dimensional microstructures and functional 3D microcages are rapidly and flexibly fabricated by the controllable patterned focus, which enhances the fabrication speed by 2 orders of magnitude compared with conventional single-point TPP. The fabricated microcages act as a nontrivial tool for trapping and sorting microparticles with different sizes. Finally, culturing of budding yeasts is investigated with these microcages, which demonstrates its application as 3D cell culture scaffolds.

Generation of spirally accelerating optical beams

We developed a generalized spectral phase superposition approach for generating accelerating optical beams along arbitrary trajectories. Such beams can be customized by predefining an appropriate superimposed phase pattern that consists of multiple sub-phases. We generated a spirally accelerating beam in a three-dimensional space and developed an algorithm to improve the uniformity of the intensity along the trajectory by introducing phase-shift factors. We also experimentally verified our numerical simulations. The proposed approach breaks the conventional convex trajectory restrictions. These various accelerating beams would pave the way for optically moving particles along a desired trajectory. The generation of such arbitrary accelerating beams is likely to give rise to new applications in flexible optical manipulation, wave front control, and optical transportation and guidance of particles.

Depth-extended, high-resolution fluorescence microscopy: whole-cell imaging with double-ring phase (DRiP) modulation

We report a depth-extended, high-resolution fluorescence microscopy system based on interfering Bessel beams generated with double-ring phase (DRiP) modulation. The DRiP method effectively suppresses the Bessel side lobes, exhibiting a high resolution of the main lobe throughout a four- to five-fold improved depth of focus (DOF), compared to conventional wide-field microscopy. We showed both theoretically and experimentally the generation and propagation of a DRiP point-spread function (DRiP-PSF) of the imaging system. We further developed an approach for creating an axially-uniform DRiP-PSF and successfully demonstrated diffraction-limited, depth-extended imaging of cellular structures. We expect the DRiP method to contribute to the fast-developing field of non-diffracting-beam-enabled optical microscopy and be useful for various types of imaging modalities.

Axial resolution enhancement of light-sheet microscopy by double scanning of Bessel beam and its complementary beam

The side lobes of Bessel beam will create significant out-of-focus background when scanned in light-sheet fluorescence microscopy (LSFM), limiting the axial resolution of the imaging system. Here, we propose to overcome this issue by scanning the sample twice with zeroth-order Bessel beam and another type of propagation-invariant beam, complementary to the zeroth-order Bessel beam, which greatly reduces the out-of-focus background created in the first scan. The axial resolution can be improved from 1.68 μm of the Bessel light-sheet to 1.07 μm by subtraction of the two scanned images across a whole field-of-view of up to 300 μm × 200 μm × 200 μm. The optimization procedure to create the complementary beam is described in detail and it is experimentally generated with a spatial light modulator. The imaging performance is validated experimentally with fluorescent beads as well as eGFP-labeled mouse brain neurons.

Construction, characteristics, and constraints of accelerating beams based on caustic design

Caustic methods have been proposed for wavefront design to enable light beams propagating along curved trajectories, namely accelerating beams. Here we elaborate the complete construction, remarkable characteristics, and hidden constraints of these methods. It is found that accelerating beams based on the caustic design have not only a well-known curved intensity distribution but also a linear phase distribution along the caustic proportional to the curved length, as if light field indeed moved along the caustic. Moreover, with this characteristic, further light-ray analyses are implemented to illustrate the constraints of caustic design in different cases. We expect our work will clarify some confusion on the effectiveness and applicability of caustic methods, and thus facilitate the design of accelerating beams for various applications.

Free-space creation of ultralong anti-diffracting beam with multiple energy oscillations adjusted using optical pen

A light beam propagating over an infinite anti-diffracting distance requires infinite power to preserve its shape. However, the fundamental barrier of finite power in free space has made the problem of diffraction insurmountable in recent decades. To overcome this limitation, we report an approach that employs the multiple energy oscillation mechanism, thereby permitting the creation of a light beam with an ultralong anti-diffracting distance in free space. A versatile optical pen is therefore developed to manipulate the number, amplitude, position and phase of energy oscillations for a focusing lens so that multiple energy oscillations can be realized. A light beam with a tunable number of energy oscillations is eventually generated in free space and propagates along a wavy trajectory. This work will enable the extension of non-diffractive light beams to an expanded realm and facilitate extensive developments in optics and other research fields, such as electronics and acoustics.

Free-space coupling enhancement of micro-resonators via self-accelerating beams

We study free-space coupling of optical fields to the whispering-gallery-mode resonators by employing self-accelerating beams orbiting a semicircle. The best coupling condition is obtained through theoretical analysis, in accord with the numerical results. Comparing with the conventional Gaussian-like beams, much enhanced coupling efficiency is achieved with such self-accelerating beams, particularly when a large numerical aperture of an optical system is used or a higher-order azimuthal mode is considered. Conditions with slight deviation from the ideal radius of self-accelerating beams are further discussed, aiming to realize an optimized high coupling efficiency.

Dynamically tunable multi-lobe laser generation via multifocal curved beam

Beams with curved properties, represented by Airy beam, have already shown potential applications in various fields. Here we propose a simple method to achieve a multifocal curved beam (MCB). The scheme is based on the ability of microspheres to control the distribution of the light field. Combined with the caustic effect, the dynamic control of the beam curvature and the foci can be realized. The simulation results confirm the mechanism behind this phenomenon. Furthermore, MCB is applied experimentally into the end-pumped microchip laser. This work has verified the theory of MCB and achieved a dynamically tunable multi-lobe laser, which has a wide application prospect.

Synchrotron radiation from an accelerating light pulse

Synchrotron radiation-namely, electromagnetic radiation produced by charges moving in a curved path-is regularly generated at large-scale facilities where giga-electron volt electrons move along kilometer-long circular paths. We use a metasurface to bend light and demonstrate synchrotron radiation produced by a subpicosecond pulse, which moves along a circular arc of radius 100 micrometers inside a nonlinear crystal. The emitted radiation, in the terahertz frequency range, results from the nonlinear polarization induced by the pulse. The generation of synchrotron radiation from a pulse revolving about a circular trajectory holds promise for the development of on-chip terahertz sources.

Observation of Self-Bending and Focused Ultrasound Beams in the Megahertz Range

Self-bending (or self-accelerating) and nondiffracting acoustic beams, such as Airy beams, have the potential to focus around obstacles that are directly in the beam path. Here, we demonstrate the self-bending and focusing properties of Airy beams in the ultrasound domain using finite difference time-domain simulations at 5.2 MHz. The phase profiles of self-bending Airy beams are determined from the Airy function. This beam is then transmitted experimentally using a linear array transducer connected to a 128 channel Vantage Verasonics operating at 5.2 MHz. The performance of self-bending beams is compared to conventional focused ultrasound beams in the presence of a strong scattering obstacle (steel rod). The ability of self-bending Airy beams to bypass obstacles is characterized in terms of their relative energy retention at peak intensity, that was found experimentally to be 50.5% for traditional focused beams whereas 71.5% for Airy beams, proving that self-bending beams performed better than conventional beams in terms of relative energy retention with no significant change in the focal profiles. However, it is observed that, in absolute terms, self-bending beams focus less energy than traditional focused beams.

Independent amplitude and trajectory/beam-width control of nonparaxial beams

We show that it is possible to generate non-paraxial optical beams with pre-engineered trajectories and designed maximum amplitude along these trajectories. The independent control of these two degrees of freedom is made possible by engineering both the amplitude and the phase of the optical wave on the input plane. Furthermore, we come to the elegant conclusion that the beam width depends solely on the local curvature of the trajectory. Thus, we can generate beams with pre-defined amplitude and beam-width by appropriately selecting the local curvature. Our theoretical results are in excellent agreement with numerical simulations. We discuss about methods that can be utilized to experimentally generate such beam. Our work might be useful in applications where precise beam control is important such as particle manipulation, filamentation, and micromachining.

Generation of single or double parallel breathing soliton pairs, bound breathing solitons, moving breathing solitons, and diverse composite breathing solitons in optical fibers

Interactions of two truncated Airy pulses with arbitrarily initial relative phases, initial pulse intervals, and different soliton order are numerically investigated in optical fibers. When the soliton order is 1, depending on different initial pulse intervals, the initial in-phase Airy pulses may evolve to single breathing solitons, bound breathing solitons, and single parallel breathing solitons. While the out-of-phase Airy pulses may evolve to parallel or repulsive soliton pairs with breathing or weak breathing, after radiating away some dispersive waves. When the initial relative phases take arbitrary values except 0 and π, moving single breathing solitons and repulsive or parallel soliton pairs will form. Moreover, the whole temporal profiles may become asymmetric. The repulsive soliton pairs consist of two moving breathing solitons with different intensities, moving velocities, and breathing periods. The most interestingly is that, when the soliton order is larger than one, we observe double bound breathing solitons, double parallel breathing soliton pairs, and diverse composite breathing solitons which consist of two or more different breathing solitons. one can effectively manipulate and select the soliton expected and its evolution dynamics by adjusting the soliton order, initial pulse intervals, and initial relative phases.

Accelerating polygon beam with peculiar features

We report on a novel kind of accelerating beams that follow parabolic paths in free space. In fact, this accelerating peculiar polygon beam (APPB) is induced by the spectral phase symmetrization of the regular polygon beam (RPB) with five intensity peaks, and it preserves a peculiar symmetric structure during propagation. Specially, such beam not only exhibits autofocusing property, but also possesses two types of accelerating intensity maxima, i.e., the cusp and spot-like structure, which does not exist in the previously reported accelerating beams with a single kind of lobes. We also provide a detailed insight into the theoretical origin and characteristics of this spatially accelerating beam through catastrophe theory. Moreover, an experimental scheme based on a digital micromirror device (DMD) with the binary spectral hologram is proposed to generate the target beam by precise modulation, and a longitudinal needle-like focus is observed around the focal region. The experimental results confirm the peculiar features presented in the theoretical findings. Further, the APPB is verified to exhibit self-healing property during propagation with either obstructed cusp or spot reconstructing after a certain distance. Hence, we believe that the APPB will facilitate the applications in the areas of particle manipulation, material processing and optofludics.

Degree of paraxiality of an anisotropic generalized multi-Gaussian Schell-model beam

The degree of paraxiality of an anisotropic generalized multi-Gaussian Schell-model (GMGSM) beam is discussed and shown to be affected by the anisotropy and boundary characteristics of the source. Numerical results are presented to show the influence of these factors.

Selectively transporting small chiral particles with circularly polarized Airy beams

Based on the full wave simulation, we demonstrate that a circularly polarized vector Airy beam can selectively transport small chiral particles along a curved trajectory via the chirality-tailored optical forces. The transverse optical forces can draw the chiral particles with different particle chirality towards or away from the intensity maxima of the beam, leading to the selective trapping in the transverse plane. The transversely trapped chiral particles are then accelerated along a curved trajectory of the Airy beam by the chirality-tailored longitudinal scattering force, rendering an alternative way to sort and/or transport chiral particles with specified helicity. Finally, the underlying physics of the chirality induced transverse trap and de-trap phenomena are examined by the analytical theory within the dipole approximation.

Optical amplification of Airy beams by photorefractive two-wave mixing

We propose and demonstrate nonlinear amplifications of self-accelerating Airy beams by two-wave mixing in photorefractive crystals both numerically and experimentally. By employing a broad Gaussian beam as the pump beam, we show that weak signal Airy beams can be significantly amplified under both diffusion and drift mechanisms. It is revealed that not only higher optical gains but also faster response time can be achieved in the presence of an external electric field, where the drift mechanism dominates. We verify that the self-accelerating and self-healing characteristics of the Airy beams are well preserved during the nonlinear amplification.