Vortex Topological Charge Research Articles

Reversals of Orbital Angular Momentum Transfer and Radiation Torque

The transfer of orbital angular momentum (OAM) from a vortex wave field to an object is interesting for developing vortex-based acoustic or optical tweezers, particularly for biomedical applications. When the object is not aligned with the vortex's core, it is unclear how OAM transfer relates to energy transfer. The author finds that here the ratio of torque to absorbed power is not given by---and can even be opposite to---the ratio of vortex topological charge to angular frequency. This suggest a negative radiation torque, associated with energy absorption, that spins an off-core axisymmetric object around its center of mass, in the direction opposite to the wave vortex's handedness.

Structured spin angular momentum in highly focused cylindrical vector vortex beams for optical manipulation.

We investigate the spin properties of a family of cylindrical vector vortex beams under a focusing condition. The spin-orbit interaction is demonstrated by comparing the energy flow and spin flow density of the focused field to those of the incident field. This spin-orbit interaction is analyzed to construct the desired distribution of spin angular momentum for optical manipulation. The structured spin angular momentum of the focused field can transfer to the optical torque for the non-magnetic absorptive particle. The influences of polarization topological charge, vortex topological charge and wavelength on optical torque in the hot-spot of focused field are summarized for three typical particles. Such results may be exploited in practical optical manipulation, particularly for optically induced rotations.

Domain wall and three dimensional duality

We discuss 1/2 BPS domain walls in the 3d mathcal{N}=4 supersymmetric gauge theory which is self-dual under the 3d mirror symmetry. We find that if a BF-type coupling is introduced, invariance of the BPS domain wall under the duality transformation can be explicitly seen from the classical BPS equations. It has been known that particles and vortices are swapped under the 3d duality transformations. We show that Noether charges and vortex topological charges localized on the domain walls are correctly exchanged under the 3d mirror symmetry.

Electro-optical coupling of a circular Airy beam in a uniaxial crystal.

This paper investigates theoretically and numerically on the electro-optical coupling (EOC) for a circular Airy beam (CAB) propagating along the optical axis of a uniaxial crystal after deducing the wave coupling equations of EOC. For a circularly polarized incident CAB, EOC can be used to generate vortex beam by coupling the incident left-handed component into the right-handed vortex component with a vortex topological charge of 2. What's more, EOC plays important role in enhancing or suppressing the abrupt autofocusing, the most important property of CABs, for both left-handed and right-handed components. Near the focal plane, EOC can result in electrically controllable optical "needle" and "cage", which shall be interesting in micromanipulation. In addition, EOC can influence or even forbid the exchange between spin angular momentum (SAM) and orbit angular momentum (OAM). For a linearly polarized incident CAB, its two Cartesian field components of the beam cannot only couple their powers to each other, but also lead to the changes of the intensity pattern and polarization distributions. The polarization state becomes spatially inhomogeneous, and possesses vortex phase with a topological charge of 2 during propagation. EOC presents a new way to control an Airy beam fast and efficiently.

Dielectric geometric phase optical elements fabricated by femtosecond direct laser writing in photoresists

We propose to use a femtosecond direct laser writing technique to realize dielectric optical elements from photo-resist materials for the generation of structured light from purely geometrical phase transformations. This is illustrated by the fabrication and characterization of spin-to-orbital optical angular momentum couplers generating optical vortices of topological charge from 1 to 20. In addition, the technique is scalable and allows obtaining microscopic to macroscopic flat optics. These results thus demonstrate that direct 3D photopolymerization technology qualifies for the realization of spin-controlled geometric phase optical elements.

A random wave model for the Aharonov–Bohm effect

We study an ensemble of random waves subject to the Aharonov–Bohm effect. The introduction of a point with a magnetic flux of arbitrary strength into a random wave ensemble gives a family of wavefunctions whose distribution of vortices (complex zeros) is responsible for the topological phase associated with the Aharonov–Bohm effect. Analytical expressions are found for the vortex number and topological charge densities as functions of distance from the flux point. Comparison is made with the distribution of vortices in the isotropic random wave model. The results indicate that as the flux approaches half-integer values, a vortex with the same sign as the fractional part of the flux is attracted to the flux point, merging with it in the limit of half-integer flux. We construct a statistical model of the neighbourhood of the flux point to study how this vortex-flux merger occurs in more detail. Other features of the Aharonov–Bohm vortex distribution are also explored.

Orbital angular momentum of an elliptic optical vortex embedded into the Gaussian beam

We consider an elliptic optical vortex embedded into a Gaussian beam. For such a beam, explicit closed-form expressions are derived for the complex amplitude and the normalized orbital angular momentum (OAM). It is shown that the elliptic Gaussian vortex (EGV) has a fractional OAM. The maximal OAM value equal to the vortex topological charge n is achieved at zero ellipticity of the vortex. The major axis of the intensity ellipse in the beam cross section rotates in propagation, turning by a 90-degree angle from the initial plane to the focal plane of a spherical lens. There are n intensity nulls on the major axis of the EGV intensity ellipse. The distance between the nulls varies during the beam propagation and with changing degree of ellipticity. At a fixed degree of ellipticity, the distance between the intensity nulls is maximal in the focal plane. At zero ellipticity, all nulls are "gathering" into a single on-axis n-times degenerate intensity null. The experimental results are consistent with the theory.

Model of random center vortex lines in continuous 2+1 -dimensional spacetime

A picture of confinement in QCD based on a condensate of thick vortices with fluxes in the center of the gauge group (center vortices) is studied. Previous concrete model realizations of this picture utilized a hypercubic space-time scaffolding, which, together with many advantages, also has some disadvantages, e.g., in the treatment of vortex topological charge. In the present work, we explore a center vortex model which does not rely on such a scaffolding. Vortices are represented by closed random lines in continuous 2+1-dimensional space-time. These random lines are modeled as being piece-wise linear, and an ensemble is generated by Monte Carlo methods. The physical space in which the vortex lines are defined is a torus with periodic boundary conditions. Besides moving, growing and shrinking of the vortex configurations, also reconnections are allowed. Our ensemble therefore contains not a fixed, but a variable number of closed vortex lines. This is expected to be important for realizing the deconfining phase transition. We study both vortex percolation and the potential V (R) between quark and anti-quark as a function of distance R at different vortex densities, vortex segment lengths, reconnection conditions and at different temperatures. We find three deconfinement phase transitions, as a function of density, as a function of vortex segment length, and as a function of temperature.

Cultivation of lemon fields.

The sign rule requires that adjacent singularities on a contour have opposite signs and hence cultivation of lemon only fields poses problem as all lemons have positive index. In this paper we show that the interference of three linearly polarized plane waves can create regions of ellipse and vector fields in 2-dimensions (2D) in which a lemon lattice is interlaced in a V-point lattice. The lemons appear at intensity maxima of the lattice structure while the V-points take care of index conservation by sitting at intensity minima. In the Stokes field S12, lemons and disclinations (V-points) appear as phase vortices of topological charge + 1 and -2 respectively. In the polarization distribution the constant azimuth lines (a-lines) are seen running through lemon and disclination alternatively obeying the sign rule [24]. We envisage that such polarization lattice structure may lead to novel concept of structured polarization illumination methods in super resolution microscopy.

Vectorial optical vortex filtering for edge enhancement

We propose to use a super-structured waveplate (called an S-waveplate) for vectorial optical vortex filtering, and experimentally demonstrate the radial Hilbert transform and selective edge enhancement. Based on the Jones calculus of polarization states and Fourier analysis, we calculate and analyze the point spread function of an optical 4-f system including an S-waveplate filter having the vectorial vortex of topological charge 1 (TC = 1). Numerical simulations and optical experiments demonstrate that a vectorial optical vortex filter can be used to implement selective edge enhancement with an analyzer before the output plane. The edge enhancement can be obtained even when the center of the filter is off-axis or the illuminating light is non-monochromatic.

Optical vortex driven charge current loop and optomagnetism in fullerenes

Endohedral molecular magnets, e.g. as realized in fullerenes containing DySc2N, are promising candidates for molecular electronics and quantum information processing. For their functionalization an ultrafast local magnetization control is essential. Using full ab initio quantum chemistry calculations we predict the emergence of charge current loops in fullerenes with an associated orbital magnetic moment upon irradiation with weak light vortex pulses that transfer orbital angular momentum. The generated current is controllable by the frequency, the vortex topological charge, and the intensity of the light. Numerical and analytical results show that an ultraviolet vortex femtosecond pulse with an intensity ∼1013 W/cm2 generates non-invasively nA unidirectional surface current with an associated magnetic field of hundreds μT at the center of the fullerene.

Structured caustic vector vortex optical field: manipulating optical angular momentum flux and polarization rotation.

A caustic vector vortex optical field is experimentally generated and demonstrated by a caustic-based approach. The desired caustic with arbitrary acceleration trajectories, as well as the structured states of polarization (SoP) and vortex orders located in different positions in the field cross-section, is generated by imposing the corresponding spatial phase function in a vector vortex optical field. Our study reveals that different spin and orbital angular momentum flux distributions (including opposite directions) in different positions in the cross-section of a caustic vector vortex optical field can be dynamically managed during propagation by intentionally choosing the initial polarization and vortex topological charges, as a result of the modulation of the caustic phase. We find that the SoP in the field cross-section rotates during propagation due to the existence of the vortex. The unique structured feature of the caustic vector vortex optical field opens the possibility of multi-manipulation of optical angular momentum fluxes and SoP, leading to more complex manipulation of the optical field scenarios. Thus this approach further expands the functionality of an optical system.

Unveiling pseudospin and angular momentum in photonic graphene.

Pseudospin, an additional degree of freedom inherent in graphene, plays a key role in understanding many fundamental phenomena such as the anomalous quantum Hall effect, electron chirality and Klein paradox. Unlike the electron spin, the pseudospin was traditionally considered as an unmeasurable quantity, immune to Stern-Gerlach-type experiments. Recently, however, it has been suggested that graphene pseudospin is a real angular momentum that might manifest itself as an observable quantity, but so far direct tests of such a momentum remained unfruitful. Here, by selective excitation of two sublattices of an artificial photonic graphene, we demonstrate pseudospin-mediated vortex generation and topological charge flipping in otherwise uniform optical beams with Bloch momentum traversing through the Dirac points. Corroborated by numerical solutions of the linear massless Dirac-Weyl equation, we show that pseudospin can turn into orbital angular momentum completely, thus upholding the belief that pseudospin is not merely for theoretical elegance but rather physically measurable.

Polygonal micro-whirlpools induced in ferrofluids

We report on the observation of the polygonal whirlpools in the thin layer of ferrofluid under illumination with a laser beam carrying optical vortex and in the presence of a vertical magnetic field. This kind of structures have attracted attention after discovering a hexagonal storm in Saturn’s atmosphere. Our polygonal whirlpools were created in a closed system (no free surfaces) in micro-scale (whirlpool diameter <20 μm) by the use of holographic optical tweezers. The polygonal shape was changed by varying the magnetic field strength or value of the optical vortex topological charge.

Fast switchable optical vortex generator based on blue phase liquid crystal fork grating

Optical vortices have great potentials in optical communications, quantum computations, micro-manipulations and so on. At present, fast switching and reconfiguring of these beam vortices are still challenges. We proposed a blue phase liquid crystal fork grating by applying a vertical electric field with a forked electrode to the polymer stabilized blue phase liquid crystal cell. A fork shaped phase profile with alternation of isotropic and ordinary refractive indices in the lateral direction is thus obtained. Both fork gratings and fork grating array with different topological charges are demonstrated. They permit rapid optical vortex switching and topological charge tuning, and also exhibit excellent polarization independency and high efficiency.

Vortex algebra by multiply cascaded four-wave mixing of femtosecond optical beams.

Experiments performed with different vortex pump beams show for the first time the algebra of the vortex topological charge cascade, that evolves in the process of nonlinear wave mixing of optical vortex beams in Kerr media due to competition of four-wave mixing with self-and cross-phase modulation. This leads to the coherent generation of complex singular beams within a spectral bandwidth larger than 200nm. Our experimental results are in good agreement with frequency-domain numerical calculations that describe the newly generated spectral satellites.

Formation of optical vortices with topological charge [formula omitted] and [formula omitted] by use of the S-waveplate

We theoretically and experimentally demonstrate the generation of optical vortices using an S-waveplate, fabricated by femtosecond laser writing in silica glass. It is shown that this method allows to form orthogonally polarized vortices with fractional topological charge. At the double wavelength of the S-waveplate, the superposition of orthogonally polarized optical vortices with topological charge l=1/2 was generated. After separating the resulting beam with polarizer, optical vortices of topological charge l=1/2 were obtained. Vortices of fractional topological charge were detected by interfering the vortex beam with a Gaussian beam. A slightly laterally misadjusted Michelson interferometer was used for detection of vortices with integer topological charge.

Coordinate invariance in stochastic singular optics

The study of optical vortices in stochastic optical fields involves various quantities, including the vortex density and topological charge density, that are defined in terms of local expectation values of the distributions of optical vortices. The complexity of these quantities often poses a formidable challenge. Here, we address this challenge with the aid of the invariance that these quantities have with respect to rotations of the coordinate axes. This property allows one to express the quantities in terms of singlets of the SO(2) group that represents the coordinate rotations, resulting in expressions that are significantly simpler. We also show that the singlets can help to identify relationships among the different quantities.

Broadband generation of azimuthally and radially polarized beams with twisted low-birefringent optical fibres

We report on the highly effective broadband generation of azimuthally and radially polarized cylindrical vector beams directly from an incident optical vortex of topological charge ±1 with twisted low-birefringent optical fibres. This approach has an important advantage of almost avoiding the fundamental mode excitation, which can spoil the cylindrical symmetry of the generated beam. The effect of the rotation of a linear birefringence axis on this generation process is revealed.

Dynamics of polarization singularities in composite optical vortices

We study the dynamics of polarization singularities in the superposition of two off-axis optical vortices with orthogonal polarization states. The motion of C points, states of circular polarization, is described by varying parameters such as separation distance, constant phase difference and topological charge. We analyze the zeros of the Stokes parameters and find analytical solutions for particular cases. The results could be used to realize an alternative method to measure the vortex topological charge.