Optical vortex knots - one photon at a time

Generation for high-dimensional caustics and artificially tailored structured caustic beams

We theoretically propose and demonstrate topological parabolic umbilic beams (PUBs) with high-dimensional caustic by mapping catastrophe theory into optics. The PUBs are first experimentally observed via dimensionality reduction. Due to the high-dimensionality, such light beams exhibit rich caustic structures characterized by optical singularities where the high-intensity gradient appears. Further, we propose an improved caustic approach to artificially tailored structured beams which exhibit significant intensity gradient and phase gradient. The properties can trap and drive particles to move along the predesigned trajectory, respectively. The advantages for structured caustic beams likely enable new applications in flexible particle manipulation, light-sheet microscopy, and micromachining.

Vortex rings in paraxial laser beams

Interference of a fundamental vortex-free Gaussian beam with a co-propagating plane wave leads to nucleation of a series of vortex rings in the planes transverse to the optical axis; the number of rings grows with vanishing amplitude of the plane wave. In contrast, such interference with a beam carrying on-axis vortex with winding number l results in the formation of |l| rings elongated and gently twisted in propagation direction. The twist handedness of the vortex lines is determined by the interplay between dynamic and geometric phases of the Gaussian beam and the twist angle grows with vanishing amplitude of the plane wave. In the counter-propagating geometry the vortex rings nucleate and twist with half-wavelength period dominated by the interference grating in propagation direction.

Accurate and rapid measurement of optical vortex links and knots

Optical vortices can evolve in light fields, of which the singularity evolution forms dark lines with complex topological structures, knotted or linked. We propose a method to more accurately and rapidly measure the topology of optical vortex fields. To accurately locate the phase singular points, phase measurement based on digital holography and, further, a numerical search algorithm, are utilized. A motor-driven right-angle prism enables the implementation of a single exposure of hologram for each measurement along the propagation direction, greatly improving the measurement speed. The three-dimensional (3D) spatial distributions of several typical vortex links and knots are experimentally reconstructed. The proposed method is expected to rapidly observe the 3D evolution of other complicated, or even vector, fields.

The local intrinsic curvature of wavefronts allows to detect optical vortices

We describe a method for effectively distinguishing the radiation endowed with optical angular momentum, also known as optical vortex, from ordinary light. We show that by detecting the inversion of the transverse intrinsic curvature sign (ITICS) an optical vortex can be locally recognized. The method is effective under conditions of huge importance for the exploitation of optical vortices, such as the far field of the source and access to a small fraction of the wavefront only. The validity of the method has been verified with table-top experiments with visible light, and the results show that a measurement performed over a transverse distance smaller than 4% of the beam diameter distinguishes a vortex from a Gaussian beam with a significance of 93.4%. New perspectives are considered for the characterization of vortices, with potential impact on the detection of extra-terrestrial radiation as well as on broadcast communication techniques.

Hybrid topological evolution of multi-singularity vortex beams: generalized nature for helical-Ince-Gaussian and Hermite-Laguerre-Gaussian modes

A generalized family of scalar structured Gaussian modes including helical-Ince-Gaussian (HIG) and Hermite-Laguerre-Gaussian (HLG) beams is presented with physical insight upon the hybrid topological evolution nature of multi-singularity vortex beams carrying orbital angular momentum. Considering the physical origins of intrinsic coordinates aberration and the Gouy phase shift, a closed-form expression is derived to characterize the general modes in astigmatic optical systems. Moreover, a graphical representation, singularities hybrid evolution nature (SHEN) sphere, is proposed to visualize the topological evolution of the multi-singularity beams, accommodating HLG, HIG, and other typical subfamilies as characteristic curves on the sphere surface. The salient properties of SHEN sphere for describing the precise singularities splitting phenomena, exotic structured light fields, and Gouy phase shift are illustrated with adequate experimental verifications.

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

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.

Tunable near-infrared optical vortex parametric laser with versatile orbital angular momentum states

We demonstrate a tunable vortex laser with versatile orbital angular momentum (OAM) states based on a singly resonant optical parametric oscillator formed of a noncritical phase-matching LiB₃O₅ crystal. The selective generation of a signal (idler) output with three OAMs, including an upconverted (negative) OAM, is achieved simply by appropriate shortening (or extending) of the cavity. The compact cavity configuration also allows for the generation of the signal (idler) output with various OAMs by simply tuning the signal wavelength. The vortex output is tuned within the wavelength region of 0.74 to 1.84 μm with a maximum pulse energy of 2.16 mJ from a pump energy of 9.3 mJ.

Singular knot bundle in light

As the size of an optical vortex knot, imprinted in a coherent light beam, is decreased, nonparaxial effects alter the structure of the knotted optical singularity. For knot structures approaching the scale of wavelength, longitudinal polarization effects become non-negligible, and the electric and magnetic fields differ, leading to intertwined knotted nodal structures in the transverse and longitudinal polarization components, which we call a knot bundle of polarization singularities. We analyze their structure using polynomial beam approximations and numerical diffraction theory. The analysis reveals features of spin-orbit effects and polarization topology in tightly focused geometry, and we propose an experiment to measure this phenomenon.

Creating Complex Optical Longitudinal Polarization Structures

In this Letter, we show that it is possible to structure the longitudinal polarization component of light. We illustrate our approach by demonstrating linked and knotted longitudinal vortex lines acquired upon nonparaxially propagating a tightly focused subwavelength beam. The remaining degrees of freedom in the transverse polarization components can be exploited to generate customized topological vector beams.