Thirty years ago, Coullet et al. proposed that a special optical field exists in laser cavities bearing some analogy with the superfluid vortex. Since then, optical vortices have been widely studied, inspired by the hydrodynamics sharing similar mathematics. Akin to a fluid vortex with a central flow singularity, an optical vortex beam has a phase singularity with a certain topological charge, giving rise to a hollow intensity distribution. Such a beam with helical phase fronts and orbital angular momentum reveals a subtle connection between macroscopic physical optics and microscopic quantum optics. These amazing properties provide a new understanding of a wide range of optical and physical phenomena, including twisting photons, spin-orbital interactions, Bose-Einstein condensates, etc., while the associated technologies for manipulating optical vortices have become increasingly tunable and flexible. Hitherto, owing to these salient properties and optical manipulation technologies, tunable vortex beams have engendered tremendous advanced applications such as optical tweezers, high-order quantum entanglement, and nonlinear optics. This article reviews the recent progress in tunable vortex technologies along with their advanced applications.

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Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities

Light-sheet microscopy facilitates rapid, high-contrast, volumetric imaging with minimal sample exposure. However, the rapid divergence of a traditional Gaussian light sheet restricts the field of view (FOV) that provides innate subcellular resolution. We show that the Airy beam innately yields high contrast and resolution up to a tenfold larger FOV. In contrast to the Bessel beam, which also provides an increased FOV, the Airy beam's characteristic asymmetric excitation pattern results in all fluorescence contributing positively to the contrast, enabling a step change for light-sheet microscopy.

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Light-sheet microscopy using an Airy beam

Structured light refers to the generation and application of custom light fields. As the tools and technology to create and detect structured light have evolved, steadily the applications have begun to emerge. This roadmap touches on the key fields within structured light from the perspective of experts in those areas, providing insight into the current state and the challenges their respective fields face. Collectively the roadmap outlines the venerable nature of structured light research and the exciting prospects for the future that are yet to be realized.

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Roadmap on structured light

Compared with conventional optical elements, 2D photonic metasurfaces, consisting of arrays of antennas with subwavelength thickness (the ‘meta-atoms’), enable the manipulation of light–matter interactions on more compact platforms. The use of metasurfaces with spatially varying arrangements of meta-atoms that have subwavelength lateral resolution allows control of the polarization, phase and amplitude of light. Many exotic phenomena have been successfully demonstrated in linear optics; however, to meet the growing demand for the integration of more functionalities into a single optoelectronic circuit, the tailorable nonlinear optical properties of metasurfaces will also need to be exploited. In this Review, we discuss the design of nonlinear photonic metasurfaces — in particular, the criteria for choosing the materials and symmetries of the meta-atoms — for the realization of nonlinear optical chirality, nonlinear geometric Berry phase and nonlinear wavefront engineering. Finally, we survey the application of nonlinear photonic metasurfaces in optical switching and modulation, and we conclude with an outlook on their use for terahertz nonlinear optics and quantum information processing. Photonic metasurfaces can be used to control the polarization, phase and amplitude of light. Nonlinear metasurfaces enable giant nonlinear optical chirality, realization of the geometric Berry phase, wavefront engineering, and optical switching and modulation, and hold potential for on-chip applications.

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Nonlinear photonic metasurfaces

The diffraction of electrons through a nanoscale hologram that imprints a certain phase modulation on the electrons’ wavefunction produces a non-spreading electron Airy beam that follows a parabolic trajectory and can reconstruct its original shape after passing an obstacle. Light, as is widely known, travels in straight lines. Yet a few years ago it was shown that specially tailored light beams can follow a curved trajectory, without spreading. Such beams follow a waveform known from quantum mechanics, called the Airy function, a concept originally developed by the astronomer Sir George Biddell Airy in work on the trajectories of light in rainbows. Now, with the demonstration of Airy beams consisting of free electrons, new possibilities for manipulating electrons are in prospect. Airy electron beam arcs were generated by the diffraction of electrons through a nanoscale hologram, which imprints a specific phase modulation on the electrons' wavefunction. These beams can bend in space without any external force, stay localized over distances of up to 100 metres and self-heal after passing an obstacle. Possible applications include use in high-performance electron microscopes and as a basis for a new type of electron interferometer. Within the framework of quantum mechanics, a unique particle wave packet exists1 in the form of the Airy function2,3. Its counterintuitive properties are revealed as it propagates in time or space: the quantum probability wave packet preserves its shape despite dispersion or diffraction and propagates along a parabolic caustic trajectory, even though no force is applied. This does not contradict Newton’s laws of motion, because the wave packet centroid propagates along a straight line. Nearly 30 years later, this wave packet, known as an accelerating Airy beam, was realized4 in the optical domain; later it was generalized to an orthogonal and complete family of beams5 that propagate along parabolic trajectories, as well as to beams that propagate along arbitrary convex trajectories6. Here we report the experimental generation and observation of the Airy beams of free electrons. These electron Airy beams were generated by diffraction of electrons through a nanoscale hologram7,8,9, which imprinted on the electrons’ wavefunction a cubic phase modulation in the transverse plane. The highest-intensity lobes of the generated beams indeed followed parabolic trajectories. We directly observed a non-spreading electron wavefunction that self-heals10, restoring its original shape after passing an obstacle. This holographic generation of electron Airy beams opens up new avenues for steering electronic wave packets like their photonic counterparts, because the wave packets can be imprinted with arbitrary shapes5 or trajectories6.

Generation of electron Airy beams

Airy beams have so far been generated by linear diffractive elements. Now, scientists show that they can also be created by a nonlinear process, opening the door to all-optical beam control and production at wavelengths unavailable by conventional methods.

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Nonlinear generation and manipulation of Airy beams

We study the Cerenkov-type second-harmonic generation in several different two-dimensional nonlinear photonic structures formed in birefringent crystals with the 3 m symmetry. Depending on the degree of birefringence, we observe either single or double Cerenkov-like second-harmonic rings. We discuss the properties of these parametrically generated rings and show that their sixfold azimuthal modulation is associated with the hexagonal symmetry of the individual ferroelectric domains.

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Cerenkov-Type Second-Harmonic Generation in Two-Dimensional Nonlinear Photonic Structures

We present experimentally the control of free space propagation of an Airy beam. This beam is generated by a nonlinear wave mixing process in an asymmetrically poled nonlinear photonic crystal. Changing the quasi-phase matching conditions, e.g., the crystal temperature or pump wavelength, alters the location of the Airy beam peak intensity along the same curved trajectory. We explain that the variation in the beam shape is caused by noncollinear interactions. Owing to the highly asymmetric shape of nonlinear crystal in the Fourier space, these noncollinear interactions are still relatively efficient for positive (nonzero) phase mismatch.

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Control of free space propagation of Airy beams generated by quadratic nonlinear photonic crystals

We observe experimentally a novel type of nonlinear diffraction in the process of two-wave mixing on a nonlinear quadratic grating. We demonstrate that when the nonlinear grating is illuminated simultaneously by two noncollinear beams, a second-harmonic diffraction pattern is generated by a virtual beam propagating along the bisector of the two pump beams. The observed diffraction phenomena is a purely nonlinear effect that has no analogue in linear diffraction.

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Noa Voloch-Bloch

Papers

Nonlinear generation and manipulation of Airy beams

Generation of electron Airy beams

Cerenkov-Type Second-Harmonic Generation in Two-Dimensional Nonlinear Photonic Structures

Control of free space propagation of Airy beams generated by quadratic nonlinear photonic crystals

Nonlinear diffraction from a virtual beam