Experiments with twisted light

The generic – that is, stable under perturbations – nodes of the field in a monochromatic light beam are optical vortices. We describe here their connection to Chladni's nodal lines in the oscillations of metal plates, as well as a few experiments that have been performed with optical vortices. We will describe how optical vortices can be generated experimentally; how it can be shown that they possess orbital angular momentum; how individual photons can be sorted according to their vortex state; and how optical vortices can be used to demonstrate higher-dimensional quantum entanglement.     

TRANSIENT OPTICAL VORTICES IN THE PROCESS OF PATTERN FORMATION IN A KERR SLICE SYSTEM WITH SINGLE FEEDBACK

The transient process of the optical pattern formation in a Kerr medium is numerically studied. We find that the process is accompanied by transient optical vortices in the far field. The temporal evolutions of the appearance and disappearance of the vortices are presented. All vortices will vanish when the system approaches its steady state. The number of vortices versus time is given.     

Pinning of vortices in a Bose-Einstein condensate by an optical lattice

We consider the ground state of vortices in a Bose-Einstein condensate. We show that turning on a weak optical periodic potential leads to a transition from the triangular Abrikosov vortex lattice to phases where the vortices are pinned by the optical potential. We discuss the phase diagram of the system for a two-dimensional optical periodic potential with one vortex per optical lattice cell. We also discuss the influence of a one-dimensional optical periodic potential on the vortex ground state. The latter situation has no analog in other condensed-matter systems.     

Generation of optical vortices with tunable intensity modulation

We analyze vortex properties of the optical beams generated by a spiral phase plate (SPP) which cannot modulate the phase of the incident beam range from 0 to 2π nicely, and find that the vortices have intensity modulation (IM) with central bright speckle. We construct an improved SPP to produce high quality optical vortices with definite IM. Theoretical analysis and real experiments show that this improved SPP can be used to produce optical vortices with configurable intensity modulation degree and without central bright spot.     

Fluid dynamical enstrophy and the number of optical vortices in a paraxial beam

Vortex-bearing optical beams have a tendency to maintain the maximum number of vortices during propagation. This tendency is reminiscent of the concept of enstrophy, which is a conserved quantity in two-dimensional fluid dynamics, and which is given in terms of the vorticity in the fluid. We derive the optical equivalent for the fluid vorticity and show that it represents the optical topological charge density in paraxial beams. It then follows that the optical equivalent of the enstrophy represents the total number of optical vortices on a cross-section of the beam. We then argue that this concept forms an important part of the tendency of paraxial beams to maintain their maximum number of vortices. As part of the derivation we provide a summary of some of the pertinent topological properties of phase functions.     

Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering

We report a method for generation of arbitrary shape and array of optical vortices by use of a superposition of coherent elementary vortices based on helical phase spatial filtering in spatial frequency domain. In this method, a helical phase spatial filter (HPSF) is placed in the spatial frequency plane of a 4-f imaging processing system. We demonstrated that the output field distribution represents the convolution between the input field and an elementary vortex field introduced by the HPSF, which results in a special shape or array of optical vortices determined by the “degenerate” properties of coherent elementary vortices and the distribution formats of the input field.     

Generation of Circular Optical Vortex Array

We report on a novel optical vortex array named circular optical vortex array, which is generated by the superposition of two concentric perfect optical vortices. The circular optical vortex array has a constant topological charge of +1 or ?1, the number and sign of which are determined by the topological charges of the two perfect optical vortices. Moreover, the radius of the circular optical vortex array is easily adjusted by using the cone angle of an axicon. Furthermore, the circular optical vortex array and multiple circular optical vortex array can be rotated by changing the initial phase difference of the perfect optical vortices on demand. This work demonstrates a complex structured optical field, which is of significance for applications such as optical tweezers, micro‐particle manipulation, and optical imaging.     

Intensity correlation properties of high-order optical vortices passing through a rotating ground-glass plate

We study the intensity correlation properties of optical vortices passing through a rotating ground-glass (RGG) plate and compare them with those of the TEM(00) mode of an He-Ne laser beam passed through the same RGG. We have observed that the intensity correlation curves for optical vortices decrease much faster than the corresponding curve for a TEM(00) mode of the He-Ne laser. The rate of decay of the correlation increases with the increase of order of the vortices. Our experimentally observed results are supported by exact analytical results.     

Current-driven transformations of a skyrmion tube and a bobber in stepped nanostructures of chiral magnets

It has been over 30 years since the concept of optical vortices was first proposed by Coullet et al.in 1989,and the field of structured beams has grown extremely.In the last two decades,partially coherent vortex beams(PCVBs)have received increasing interest in the fields of optical manipulation,optical communication,optical imaging,etc.,and great progress has been made in the area of the coherence singularities,generation methods,topological charge measurements,and promising applications of PCVBs.In this review,we firstly outline the basic concepts of PCVBs.We explicate the relationship between the coherence vortices and optical vortices,and the evolution behavior of optical vortices to coherence vortices is summarized in detail.We discuss a special form of coherence singularity,ring dislocation,mathematically and physically.The ring dislocation in the correlation functions under low coherence is dependent on the mode indices,which provide a feasible approach to measure mode indices of PCVBs.Subsequently,we summarize the various methods for measuring the topological charge of PCVBs,highlight the measurement method based on the cross-correlation function,and a physical explanation on the relation between ring dislocation and topological charge is given.After that,we review the recent advances on experimental generation of several kinds of PCVBs.Lastly,we give an overview on the potential applications of PCVBs.     

Selective generation of high-order optical vortices from a single phase wedge

We demonstrate that it is possible to generate high-order optical vortices from a single phase wedge by applying an incident beam with an annular intensity distribution. Various topological charges of optical vortices are realized by a static phase wedge when the position and radius of the annular illumination are changed accordingly.     

Partially incoherent optical vortices in self-focusing nonlinear media

We observe stable propagation of spatially localized single- and double-charge optical vortices in a self-focusing nonlinear medium. The vortices are created by self-trapping of partially incoherent light carrying a phase dislocation, and they are stabilized when the spatial incoherence of light exceeds a certain threshold. We confirm the vortex stabilization effect by numerical simulations and also show that the similar mechanism of stabilization applies to higher-order vortices.     

Matter-wave gap vortices in optical lattices

We predict the existence of spatially localized nontrivial topological states of a Bose-Einstein condensate with repulsive atomic interactions confined by an optical lattice. These nonlinear localized states, matter-wave gap vortices, carry a vortexlike phase dislocation and exist in the gaps of the matter-wave band-gap spectrum due to the Bragg scattering. We discuss the structure, stability, and formation dynamics of the gap vortices in the case of two-dimensional optical lattices.     

Making an optical vortex and its copies using a single spatial light modulator

We demonstrate a technique for making copies of optical vortices with the same topological charge using a single spatial light modulator. It has been shown that by using suitable diffractive optical elements, several copies of optical vortices with the same topological charge could be created. We have devised diffractive optical elements using a single spatial light modulator which could be used to make a vortex and its copies without inverting the charge. The nature of the topological charge was investigated with the interferometric technique. The experimental results are verified with the theoretical analysis. We anticipate that our results may find applications ranging from optical manipulation to quantum information.     

Topology of Knotted Optical Vortices

Optical vortices as topological objects exist ubiquitously in nature. In this paper, by making use of the Duan's topological current theory, we investigate the topology in the closed and knotted optical vortices. The topological inner structure of the optical vortices are obtained, and the linking of the knotted optical vortices is also given.     

Symmetry breaking of optical vortices: birth and annihilation of singularities in the evanescent field

The interaction of optical vortices (or phase singularities, or screw dislocations) with ordinary matter is treated with a simple approach. Using the total internal reflection phenomenon and the superposition of four plane waves incident on a material with a refractive index lower than the original propagating medium, we are able to show the birth and annihilation of optical vortices in an evanescent field with curved topological features. Until now, this phenomenon has been explored only in free space propagation. By a suitable tuning process involving the incident angles and the amplitudes of the incident plane waves, it is possible to create unusual topological features of optical vortices in the vicinity of the material. We believe that this work can open new aspects of curved optical vortex manipulation in near-field optics.     

散射光场中的光学涡旋

散射光场中的光学涡旋叶茂，王鹏业，戴建华，张洪钧（四川大学物理系成都６１００６４）（中国科学院物理研究所北京１０００８０）ＯｐｔｉｃａｌＶｏｒｔｉｃｅｓｉｎＡＴｈｅｒｍａｌＲａｙｌｅｉｇｈＳｃａｔｔｅｒｉｎｇＬｉｇｈｔＦｉｅｌｄ￥ＭａｏＹｅ；ｐｅｎｇ...     

Shearograms of an optical phase singularity

Shearograms are known to represent phase gradients but when vortices are present in the optical field, these do not represent true phase gradients. Phase gradients of an optical phase singularity are presented. A lateral shear interferometer is used for obtaining shearograms of optical fields with vortices. A diffractive phase element is used to generate vortices. It is shown that shearograms can be used in the detection of optical vortices. Shearogram of speckle field is also presented.     

利用非传统螺旋相位调控高阶涡旋光束的拓扑结构

本文提出一种利用非传统螺旋相位调控高阶涡旋光束拓扑结构的方法.数值模拟并实验研究了具有不均匀旋转梯度的非传统螺旋相位对高阶涡旋光束的调控行为.结果表明, 携带有非传统螺旋相位的高阶涡旋光束在传输过程中, 将退化为沿一条直线排列的多个一阶相位奇点, 并且, 这种非传统螺旋相位对高阶涡旋光束的调控特性, 可抑制相位噪声等扰动所引起的拓扑结构随机退化现象.本文的结论为涡旋光束拓扑结构的调控提供了一种可行的新途径, 在基于涡旋光束的光学通信、光学操控等方面具有潜在应用.     

Topological reactions of optical correlation vortices

It is now well-appreciated that the correlation functions of partially coherent optical wavefields may possess phase singularities with properties similar to those that appear in monochromatic wavefields. Though much work has been done to investigate the generic properties of such correlation vortices, little effort has gone towards studying topological reactions associated with these vortices. In this paper we investigate three such reactions: (1) The break-up of a second-order optical vortex into first-order correlation vortices. (2) Creation and annihilation of correlation vortices. (3) The behavior of correlation vortices on propagation. These results clearly demonstrate the relationship between optical vortices and correlation vortices, and suggest the possible use of correlation vortices as a probe of the statistical properties of a field or a medium.     

Structure of optical vortices

Helical modes of light can be focused into toroidal optical traps known as optical vortices, which are capable of localizing and applying torques to small volumes of matter. Measurements of optical vortices created with the dynamic holographic optical tweezer technique reveal an unsuspected dependence of their structure and angular momentum flux on their helicity. These measurements also provide evidence for a novel optical ratchet potential in practical optical vortices.