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.     

Dynamics of topological multipoles: II. Creation, annihilation, and evolution of nonparaxial optical vortices

The behavior of nonparaxial combined beams transferring two or four optical vortices with opposite topological charges (topological dipole or quadrupole) is studied. The paraxial and nonparaxial approaches are compared. It is shown that the behavior of a topologically neutral wave system is well characterized by the position of a representative point on the parametric plane. It is found that there exists a large region on this plane for which spatial trajectories of the optical vortices, both for dipoles and quadrupoles, do not intersect the focal plane, i.e., the vortices cannot exist within the forbidden zone. At the edges of the forbidden zone, the vortices are either created or annihilated. In contrast, there exists a region on the parametric plane for which the optical vortices can exist only near the waist plane.     

The structure of a nonparaxial Gaussian beam near the focus: II. Optical vortices

Exact analytical solutions of Maxwell’s equations describing the behavior of a nonparaxial optical vortex in the vicinity of a focal waist are obtained using the Whittaker method of scalar potentials, the point complex source method, and approximate Davis boundary conditions. It is shown that nonparaxial optical vortices in free space fall into three large groups: even and odd vortices with preferential circular polarization and azimuthally symmetric TE and TM vortices. The fields of even and odd nonparaxial vortices agree well with the fields of guided homogeneous and inhomogeneous vortices of a weakly guiding fiber. In the paraxial approximation, the expressions obtained for the fields are transformed to the fields of paraxial optical vortices. In the focal region, a nonparaxial beam experiences elliptic deformation of the cross section. This elliptic deformation is shown to result from the asymmetric location of regions with negative energy flows. The reversal of sign of the topological charge and the helicity of a combination of even and odd vortices causes both rotation of the dislocation axis through π/2 and longitudinal displacement of the focal spot, which are the transverse and the longitudinal optical Magnus effects.     

自散焦非局域非线性材料中的光学涡旋孤子

通过数值模拟的方法对非局域非线性自散焦材料中的光学 涡旋孤子的传输特性以及相互作用特性进行了研究. 研究表明, 拓扑荷|m|=1的非局域涡旋孤子是稳定的, 而拓扑荷|m|>1的非局域涡旋孤子均具有拓扑不稳定性. 在微扰存在的情况下以及在近距离相互作用的过程中, |m|>1的涡旋孤子会分裂成一系列的|m|=1的涡旋孤子. 非局域涡旋孤子与局域涡旋孤子具有相同的长距离相互作用模式, 即点涡旋相互作用模式. 但两者的短距离相互作用存在一些差别, 在相同的距离下, 两涡旋间的相互绕转的周期随着材料的非局域响应长度增大而增大. 关键词： 非局域非线性薛定谔方程 自散焦 涡旋孤子     

Three-dimensional nonlinear lattices: from oblique vortices and octupoles to discrete diamonds and vortex cubes

We construct a variety of novel localized topological structures in the 3D discrete nonlinear Schr?dinger equation. The states can be created in Bose-Einstein condensates trapped in strong optical lattices and crystals built of microresonators. These new structures, most of which have no counterparts in lower dimensions, range from multipole patterns and diagonal vortices to vortex "cubes" (stack of two quasiplanar vortices) and "diamonds" (formed by two orthogonal vortices).     

Optical vortices in focal regions

Optical vortices in focal regions are studied using the Debye approximation. We discuss how scalar vortices give rise to different intensity structures in the focal region for a certain class of apertures. Vortices in cylindrical symmetric polarization distributions form new complex structures in the focal region, and in some cases the intensity is no longer zero on the optical axis. In particular, we find that for an azimuthal polarization distribution the local circulation deviates from that of the vortex impinging on the lens. On the other hand, upon using a radially polarized field distribution combined with an annular aperture, only the electric-field component along the optical axis remains, and the field structure is the same as in the scalar case.     

Phase singularity of surface plasmon polaritons generated by optical vortices

We demonstrate an experimental result that shows the phase singularity of surface plasmon waves generated by the direct transform of optical vortices at normal incidence focused on a structureless metal surface. The near-field two-dimensional intensity distribution near the focal plane is experimentally examined by using near-field scanning optical microscopy and shows a good agreement with the finite-difference time-domain simulation result. The experimental realization demonstrates a potential of the proposed excitation scheme to be reconfigured locally with advantages over structures milled into optically thick metallic films for plasmonics applications involving plasmonic vortices.     

Phase singularities and coherence vortices in linear optical systems

It is demonstrated for a time-invariant linear optical system that there exists a definite connection between the optical vortices (phase singularities of the field amplitude) which appear when it is illuminated by spatially coherent light and the coherence vortices (phase singularities of the field correlation function) which appear when it is illuminated by partially coherent light. Optical vortices are shown to evolve into coherence vortices when the state of coherence of the field is decreased. Examples of the connection are given. Furthermore, the generic behavior of coherence vortices in linear optical systems is described.     

Vortex streets in a cavity with higher-order standing waves

Recently a laser analog of vortex generation behind an obstacle in a flow was demonstrated. Vortex generation occurs when tilted waves of different transverse structures are simultaneously excited in a laser. We have generalized this phenomenon to higher-order standing waves. Here typical phenomena expected for optical vortices, such as the excitation and disappearance of single vortices out of and into dark lines and dark areas, as well as vortex-pair creation and annihilation become apparent.     

Duality between phase vortices and Argand-plane caustics

Singularities in the mappings of complex two-dimensional vortical wavefields to Argand space are used here to investigate the duality between vortices in the physical field and caustic-like structures in the Argand plane. Such map singularities are exemplified via a method of optical vortex generation based on low-pass filtering of two-dimensional noise. The presence of Argand-plane fold caustics crossing the Argand-plane origin is tied to changes in vortex numbers in the physical wavefield. Increasing the low-pass filter cutoff leads to higher-order Argand-plane caustic singularities, such as the hyperbolic umbilic catastrophe. This work presents a duality between vortices and caustics, explores the Argand plane as a tool in analysing optical wavefields, and provides a new environment for studying catastrophes.     

Scalar dispersion by coherent structures in uniformly sheared flow generated in a water tunnel

In order to investigate the role of coherent structures as mechanisms of scalar dispersion, we studied measurements of a passive scalar plume released in a uniformly sheared turbulent flow generated in a water tunnel. The flow had homogeneous turbulence properties in the measurement domain and contained hairpin vortices similar to those in boundary layers, and so was an ideal test bed to study the effects of coherent structures on turbulent dispersion, free from the effects of inhomogeneities or boundaries. Measurements of the velocity and concentration fields were acquired simultaneously using stereo particle image velocimetry and planar laser-induced fluorescence. We found that dye was preferentially located far away from vortices and was less likely to appear in close proximity to vortices, which is attributed to the high dissipation at the periphery of the vortices. However, we also found that dye was not directly correlated with the uniform momentum zones in the flow, suggesting a more complex relationship exists between these zones, the locations of vortices, and dye transport. Considering scalar flux events rather than simply the presence of dye as our condition of interest, a conditional eddy analysis demonstrated that hairpin vortices are responsible for the large scalar flux events as well as the large Reynolds stress events in the flow. The fact that the Reynolds stress was correlated with the scalar flux further confirmed that coherent structures are dominant mechanisms for scalar transport. Furthermore, we found that the scalar flux vector was preferentially inclined by 155° and ?25° with respect to the streamwise direction, and was thus approximately orthogonal to the planes of the legs of the most common upright and inverted hairpin structures in the flow. These findings demonstrate that coherent structures play an important and intricate role in turbulent diffusion.     

Transformation of optical vortices by polarization dynamic holograms

Results of theoretical and experimental studies of regularities in the transformation of the topological and polarization structures of optical vortices by polarization dynamic holograms formed by pulse Gaussian and singular light beams in dye solutions are presented.     

Singularities in speckled speckle

Speckle patterns produced by random optical fields with two (or more) widely different correlation lengths exhibit speckle spots that are themselves highly speckled. Using computer simulations and analytic theory we present results for the point singularities of speckled speckle fields, namely, optical vortices in scalar (one polarization component) fields and C points in vector (two polarization components) fields. In single correlation length fields both types of singularities tend to be more or less uniformly distributed. In contrast, the singularity structure of speckled speckle is anomalous; for some sets of source parameters vortices and C points tend to form widely separated giant clusters, for other parameter sets these singularities tend to form chains that surround large empty regions. The critical point statistics of speckled speckle is also anomalous. In scalar (vector) single correlation length fields phase (azimuthal) extrema are always outnumbered by vortices (C points). In contrast, in speckled speckle fields, phase extrema can outnumber vortices and azimuthal extrema can outnumber C points by factors that can easily exceed 10(4) for experimentally realistic source parameters.     

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.     

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.     

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.     

利用全息法在偶氮聚合物薄膜中记录涡旋光场

利用全息技术在偶氮聚合物薄膜中记录了拓扑荷数q=–1,1,2,4的涡旋光场,并将记录的原始叉形光栅与计算全息光栅进行对比,对不同拓扑荷数涡旋光的记录速率和偶氮材料的可重复擦写性能进行了测试;记录完成后,将复现涡旋光与高斯光束干涉,并与原始涡旋光和原始叉形光栅对比,分析了记录质量.实验结果表明:高阶涡旋光场的全息叉形光栅会在记录过程中发生劈裂,轻微劈裂的涡旋光束仍维持一个稳定的环状结构;全息记录过程中不同拓扑荷数的涡旋光束记录速率较为统一,偶氮材料可经过上百次的擦写而不出现疲劳;再现涡旋光与原始涡旋光在光强分布结构上保持高度一致,再现涡旋光的干涉条纹与原始涡旋全息光栅保持高度一致,涡旋光及其携带的拓扑荷信息可被有效记录和读取.     

Modulated optical vortices

Single-beam optical gradient force traps created by focusing helical modes of light are known as optical vortices. Modulating the helical pitch of such a mode's wave front yields a new class of optical traps whose dynamically reconfigurable intensity distributions provide new opportunities for controlling motion in mesoscopic systems. An implementation of modulated optical vortices based on the dynamic holographic optical tweezer technique is described.     

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.     

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.