Optical vortices generically arise when optical beams are combined. Recently, we reported how several laser beams containing optical vortices could be combined to form optical vortex loops, links and knots embedded in a light beam (Leach et al 2004). Here, we describe in detail the experiments in which vortex loops form these structures. The experimental construction follows a theoretical model originally proposed by Berry and Dennis, and the beams are synthesised using a programmable spatial light modulator and imaged using a CCD camera.
In the past decade, optical vortex knots with axial dimensions on the order of $10^2-10^5$ wavelengths ($λ$) have been implemented in the laboratory. However, many potential applications require a drastic reduction on the the size of these knots to the order of $λ$. In this work, we show the first measurement of an optical vortex knot (trefoil) with an axial length of $1.99\, λ$ contained within a volume ($x\times y\times z$) of $1.90\times 2.19\times 1.99 \, λ^3$. Prior to focusing, the laser light is linearly polarized ($x$, horizontal) and we observe the knot in the dominant $x$ polarizatio…
Optical knots and links have attracted great attention because of their exotic topological characteristics. Recent investigations have shown that the information encoding based on optical knots could possess robust features against external perturbations. However, as a superior coding scheme, it is also necessary to achieve a high capacity, which is hard to be fulfilled by existing knot-carriers owing to the limit number of associated topological invariants. Thus, how to realize the knot-based information coding with a high capacity is a key problem to be solved. Here, we create a type of nest…
The fundamental polarization singularities of monochromatic light are normally associated with invariance under coordinated rotations: symmetry operations that rotate the spatial dependence of an electromagnetic field by an angle $θ$ and its polarization by a multiple $γθ$ of that angle. These symmetries are generated by mixed angular momenta of the form $J_γ= L + γS$ and they generally induce Möbius-strip topologies, with the coordination parameter $γ$ restricted to integer and half-integer values. In this work we construct beams of light that are invariant under coordinated rotations for arb…
A simple analytical way of creating superpositions of Bessel-Gaussian light beams with knotted nodal lines is proposed. It is based on the equivalence between the paraxial wave equation and the two-dimensional Schrödinger equation for a free particle. The $2D$ Schrödinger propagator is expressed in terms of Bessel functions, which allows to obtain directly superpositions of beams with a desired topology of nodal lines. Four types of knots are constructed in the explicit way: the unknot, the Hopf link, the Borromean rings and the trefoil. It is also shown, using the example of the figure-eight …
Making use of the equivalence between paraxial wave equation and two-dimensional Schrödinger equation, Gaussian beams of monochromatic light, possessing knotted nodal structures are obtained in an analytical way. These beams belong to the wide class of paraxial beams called the Hypergeometric-Gaussian beams [E. Karimi, G. Zito, B. Piccirillo, L. Marrucci and E. Santamato, Opt. Lett. {\bf 32}, 3053(2007)]. Four topologies are dealt with: the unknot, the Hopf link, the Borromean rings and the trefoil. It is shown in the numerical way that neutral polarizable particles placed in such light fields…
Spatial light modulators (SLMs) are popular tools for generating structured light fields and have fostered numerous applications in optics and photonics. Here, we explore the limits of what fields these devices are capable of generating and detecting in the context of so-called vortex beams carrying orbital angular momentum (OAM). Our main contributions are to quantify (theoretically and experimentally) how the pixelation of the SLM screen affects the quality of the generated vortex mode and to offer useful heuristics on how to optimise the performance of the displayed digital hologram. In so …
In hydrodynamics, vortex generation upon the transition from smooth laminar flows to turbulence is generally accompanied by increased dissipation. However, plane vortices can provide transport barriers and decrease losses, as it happens in numerous geophysical, astrophysical flows and in tokamaks. Photon interactions with matter can affectlight transportin waveguides in unexpected and somewhat counterintuitive ways resembling fluid dynamics. Here, we demonstrate dramatic impact of light vortex formation in micro-structured optical fibres on the energy dissipation. We show possibility of vortic…
Acoustic toroidal vortices with programmable links and knots
National Laboratory of Solid State Microstructures & School of Advanced Manufacturing Engineering, Nanjing University（南京大学固体微结构物理国家重点实验室与先进制造工程学院）；College of Engineering and Applied Sciences & Collaborative Innovation Center of Advanced Microstructures, Nanjing University（南京大学工程与应用科学学院与先进微结构协同创新中心）；Centre for Disruptive Photonic Technologies, School of Physical and Mathematical Sciences, Nanyang Technological University（南洋理工大学物理与数学学院破坏性光子技术中心）；School of Electrical and Electronic Engineering, Nanyang Technological University（南洋理工大学电气与电子工程学院）；Jiangsu Key Laboratory of Artificial Functional Materials & Jiangsu Physical Science Research Center, Nanjing University（南京大学江苏省人工功能材料重点实验室与江苏物理科学研究中心）
The composite optical beams being a result of superposition, are a promising way to study the orbital angular momentum and its effects. Their wide range of applications makes them attractive and easily available due to the growing interest in the Spatial Light Modulators (SLM). In this paper, we present a simple method for generating composite vortex patterns with high symmetry. Our method is simple, flexible and gives perfectly aligned beams, insensitive to mechanical vibrations. This method is based on the ability to split SLM cells between phase patterns that are to be superposed. This appr…
We present a set of paraxial light beams with cylindrical symmetry, smooth and localized transversal profile carrying finite power, that develop intensity singularities when they are focused in a linear medium, such as vacuum. They include beams with orbital angular momentum and with radial polarization, in which case they develop punctual phase and polarization singularities surrounded by infinitely bright rings, along with singular longitudinal fields. In practice, these effects are manifested in focal intensities and spot sizes, vortex bright ring intensities and radii, and strengths of the…
We have experimentally investigated the evolution properties of multiramp fractional vortex beams (MFVBs) in free space, by using a fundamental Gaussian beam reflecting from a phase-modulated spatial light modulator. The issue about the total vortex strength of such MFVBs is systematically addressed, and our result reveals the dependence of the total vortex strength depends on both the non-integer topological charge $α$ and the multiramp number $m$ contained in initial multiramp phase structures. In the near-field region, vortices contained in MFVBs are unstable and it is hard to effectively c…
Vortex fiber nulling is a method for spectroscopically characterizing exoplanets at small angular separations, $\lesssimλ/D$, from their host star. The starlight is suppressed by creating an optical vortex in the system point spread function, which prevents the stellar field from coupling into the fundamental mode of a single-mode optical fiber. Light from the planet, on the other hand, couples into the fiber and is routed to a spectrograph. Using a prototype vortex fiber nuller (VFN) designed for monochromatic light, we demonstrate coupling fractions of $6\times10^{-5}$ and $>0.1$ for the sta…
We describe and demonstrate how 3D magnetic field alignment can be inferred from single absorption images of an atomic cloud. While optically pumped magnetometers conventionally rely on temporal measurement of the Larmor precession of atomic dipoles, here a cold atomic vapour provides a spatial interface between vector light and external magnetic fields. Using a vector vortex beam, we inscribe structured atomic spin polarisation in a cloud of cold rubidium atoms, and record images of the resulting absorption patterns. The polar angle of an external magnetic field can be deduced with spatial Fo…
We demonstrate spontaneous formation of a nonlinear vortex cluster state in a microcavity exciton-polariton condensate with time-periodic sign flipping of its topological charges at the GHz scale. When optically pumped with a ring-shaped nonresonant laser, the trapped condensate experiences intricate high-order mode competition and fractures into two distinct trap levels. The resulting mode interference leads to robust condensate density beatings with periodic appearance of orderly arranged phase singularities. Our work opens new perspectives on creating structured free-evolving light, and sin…
The motion of noncircular two-dimensional vortices is shown to depend on a form of coupling between vortex ellipticity and the gradient of fluid density. The approach is based on the perspective that an elliptic vortex can be described as the projection of a virtual construct, a circular vortex with a symmetry axis that is tilted with respect to the direction of propagation. The resulting kinetic equation offers insights into how tilt and vortex velocity coevolve in few-body nonequilibrium settings such as vortex pair nucleation and annihilation. The model is developed and applied in associati…
We model propagation of far-red-detuned optical vortex beams through a Bose-Einstein Condensate using nonlinear Schrödinger and Gross-Pitaevskii equations. We show the formation of coupled light/atomic solitons that rotate azimuthally before moving off tangentially, carrying angular momentum. The number, and velocity, of solitons, depends on the orbital angular momentum of the optical field. Using a Bessel-Gauss beam increases radial confinement so that solitons can rotate with fixed azimuthal velocity. Our model provides a highly controllable method of channelling a BEC and atomic transport.
Neglecting the electric field component along the light's propagation direction is a common practice, known as paraxial approximation. However, experimental evidence and theory on the head-on excitation of atoms by Laguerre-Gaussian beams reveal that the full vector character of the light field has to be taken into account. Optical vortices are a large family of fields, being Laguerre-Gaussian only one particular case. Now we extend the study of the applicability of the paraxial approximation to a broader set of optical vortices by considering the interaction of atoms with generalized Laguerre…
Analogies between non-trivial topologies of matter and light have inspired numerous studies, including defect formation in structured light and topological photonic band-structures. Three-dimensional topological objects of localized particle-like nature attract broad interest across discipline boundaries from elementary particle physics and cosmology to condensed matter physics. Here we show how simple structured light beams can be transformed into optical excitations of atoms with considerably more complex topologies representing three-dimensional particle-like Skyrmions. This construction ca…
