拓扑视角下的光学涡环

涡旋环是一种广泛存在于流体和气体中的可传播环形结构,其与拓扑学中的纽结理论密切相关。近年来,随着光场调控技术的发展,时空光场在时间和空间维度的紧密联系为研究光学拓扑结构提供了良好的平台。文章将回顾近期关于光学涡环的系列研究,介绍光学涡环产生过程中的物理机制;并分别从拓扑和结构光两个视角出发,详细讨论由光学涡环延伸出的光学相位拓扑结构,包括标量光学霍普夫子及光学相位莫比乌斯环。     

Propagation of optical vortices in coiled weakly guiding optical fibers

The structure of the l = 1 modes of regularly coiled weakly guiding optical fibers with round cross section is determined. The l = 1 modes are shown to be represented by two right-and left-hand polarized stable optical vortices, as well as by TE and TM modes. The polarization corrections to the scalar propagation constant are found. The stability of an optical vortex transmitted along a coiled fiber is estimated. The parameters for optimal coiling at which the transmission of vortices along the fibers is the most stable with respect to fiber perturbations are determined.     

Optical vortices in anisotropic optical fibers with torsional stress

Analytical expressions for the higher-order modes with the azimuthal number equal to unity and for corresponding propagation constants of optical fibers with linear anisotropy of the fiber material and a circular anisotropy induced by torsional mechanical stress been obtained at practically important relationships between fiber parameters. The possibility of stable propagation of optical vortices in these fibers and the dependence of characteristics of sustained optical vortices on the fiber parameters are demonstrated.     

Optical vortices in low-mode fibers: III. Dislocation reactions, phase transitions, and topological birefringence

Topological birefringence of waves in optical fibers resulting from the spin-orbit interaction in the field of optical vortices is manifested, as a rule, in the form of Rytov-Magnus unified optical effect. At the same time, the field transformations caused by this effect are not explicitly related to the evolution of phase dislocations of longitudinal and transverse components of the electric and the magnetic fields. This relation can be provided by the dislocation reactions proposed by Berry. As opposed to the Berry’s approach, where dislocation reactions at the wavefront surface are considered, it is suggested in this work that topological reactions at the specific characteristic surface of the wave field formed by the coordinate representation of the transverse components of the Poynting vector be considered. Using the action of topological birefringence in a low-mode optical fiber as an example, it is shown that the course of a topological reaction in a vector optical field is accompanied by rigorous conservation of the total topological index of the characteristic surface and does not depend on the presence of an interface (where topological charges can originate and annihilate). The total topological index of a dislocation reaction is found to be equal to the absolute value of the sum of the topological charge and the spirality of the vector wave field.     

Optical sorting using an array of optical vortices with fractional topological charge

An array of optical vortices with fractional topological charge is generated using a phase-only Talbot array illuminator and used to sort microparticles. Our theoretical analysis and experimental results reveal that when a particle passes through a fractional vortex array, it will be driven by two forces, intensity-gradient force and phase-gradient force, and the cooperation of these two forces can improve its ability in optical sorting because of the special intensity and phase distribution of the fractional optical vortex array. Larger angle separation could be obtained with moderate laser power.     

Optical control of vortices in dense media of gas-filled optical fibers

The problem of the formation of optical vortices in a medium composed of three-level atoms is analyzed with allowance for local-field effects in off-resonance Raman regimes of ??-scheme interaction. The possibility of optical control of the vortex dynamics without disturbing their stability is demonstrated in the optically dense medium of a hollow fiber filled with ⁸⁷Rb vapor.     

Temporal correlation vortices and topological dispersion

Interference measurements of a polychromatic partially coherent light source verify the existence of a temporal correlation vortex. Topological dispersion is found to destabilize this singularity.     

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.     

Photonic crystal fibers with material anisotropy

In this paper we are modeling the interplay of material and form birefringence in photonic crystal fibers. We introduce an efficient numerical method for the calculation of the modal structure. Our approach relies solving the fully vectorial wave equation for the transverse magnetic field and the respective propagation constants using a plane wave expansion. The method accounts for a simple form of material anisotropy. Our analysis is relevant to certain application areas, and in particular to fiber sensing, where material birefringence arises for instance due to transversally applied mechanical stress. We analyze the influence of material birefringence on the modal birefringence and the state of polarization of the fundamental mode.     

Measuring the topological charge of optical vortices with an axicon

We analyzed the spatial spectrum of the diffraction intensity pattern of an ideal Bessel beam and found an implicit rule that the number of the bright rings in the spatial spectrum is equal to the topological charge of the Bessel beam. The radius of the bright and dark rings has some relation with the topological charge and can be determined accurately. It provides us with a new way for measuring the topological charge of an optical vortex through its diffraction intensity pattern after an axicon. The results of simulation coincide with the theory.     

Imprinting vortices in a Bose-Einstein condensate using topological phases

Vortices were imprinted in a Bose-Einstein condensate using topological phases. Sodium condensates held in a Ioffe-Pritchard magnetic trap were transformed from a nonrotating state to one with quantized circulation by adiabatically inverting the magnetic bias field along the trap axis. Using surface wave spectroscopy, the axial angular momentum per particle of the vortex states was found to be consistent with 2 variant Planck's over 2pi or 4 variant Planck's over 2pi, depending on the hyperfine state of the condensate.     

Colossal anisotropy in diluted magnetic topological insulators

We consider dilute magnetic doping in the surface of a three dimensional topological insulator where a two dimensional Dirac electron gas resides. We find that exchange coupling between magnetic atoms and the Dirac electrons has a strong and peculiar effect on both. First, the exchange-induced single ion magnetic anisotropy is very large and favors off-plane orientation. In the case of a ferromagnetically ordered phase, we find a colossal magnetic anisotropy energy, of the order of the critical temperature. Second, a persistent electronic current circulates around the magnetic atom and, in the case of a ferromagnetic phase, around the edges of the surface.     

Measuring the topological charge of optical vortices with a single plate

Measuring the topological charge(TC) of optical vortex beams by the edge-diffraction pattern of a single plate is proposed and demonstrated. The diffraction fringes can keep well discernible in a wide three-dimensional range in this method. The redundant fringes of the diffracted fork-shaped pattern in the near-field can determine the TC value, and the orientation of the fork tells the handedness of the vortex. The plate can be opaque or translucent, and the requirement of the translucent plate ...     

Vortex rings and plasma toroidal vortices in homogeneous infinite media. III. Diffusion anisotropy effect in vortices

The effect of diffusion anisotropy of material particles in toroidal vortices (TVs) is experimentally studied in plasma TVs in air, in vortex rings in air and water. The essence of this effect consists in the fact that diffusion coefficients of material particles in TVs in the direction perpendicular to the rotation axis D _⊥ are much lower than in the direction parallel to this axis D _‖. The coefficient D _⊥ is determined for propane molecules in air TVs, and the dependence of the coefficient D _⊥ of ink particles in water TVs on the rotation angular velocity ω is studied. It is shown that the coefficient D _⊥ can decrease with increasing ω by a factor of 10–25 in comparison with the coefficient D _‖.     

Shared aperture metasurface antenna for electromagnetic vortices generation with different topological charges

Vortex beams carrying orbital angular momentum (OAM) have aroused great interest of both scientific and engineering communities. Encouragingly, generating OAM with different topological charges in a shared aperture is regarded as a potential route to expanding the communication capacity, which yet is an academic challenging task. In this work, a paradigm of designing metasurface-based shared aperture antenna for generating polarization-dependent vortex beams with distinct topological charges is proposed. Anisotropic unit cells that can tailor different resonance phase profiles in two orthogonal orientations are used to assemble a metasurface reflector. As a proof-of-concept, a planar reflector antenna is designed with two Vivaldi sources, which can generate x- and y-polarized vortex beams with topological charges of l=-1 and l=-2, respectively. Both the simulation results and the measurement results are in good agreement, which demonstrates the feasibility of our design. Significantly, this work provides a new route to achieving vortex beams carrying different topological charges in the same frequency band, which may have potential applications in communication systems.     

Generation of optical vortices in multihelical optical fibers

It is theoretically demonstrated that multihelical fibers are capable to change the topological charge of the incoming field by l units in the transmitted and reflected light. The magnitude of the change in the topological charge coincides with the number of coaxial helicoids forming the fiber core. This can be used in designing generators of optical vortices (OVs) from Gaussian beams: broadband ones in transmitted light and narrowband ones in reflected light.     

Optical properties for topological insulators with metamaterials

The two fields of topological insulators and metamaterials are independent. In this Letter, we firstly investigate the Fresnel coefficients for the reflected and refracted electromagnetic waves across the interface between topological insulators and left-handed metamaterials. Then, we derive the exact analytic expressions for Kerr and Faraday rotations. By way of multiple reflections method, we demonstrate that perfect lens with left-handed metamaterials slab and topological insulators can be designed. On the other hand, the processes of reflection and refraction are investigated in the case of topological insulator and chiral metamaterial. Then, we give the reflection and transmission coefficients of topological insulator with a chiral medium slab. Lastly, the potential applications of these results are discussed.