Dynamics of quantized vortices in rotating superfluid

Dynamics of interactive quantized vortices in rotating superfluid is studied theoretically. This work considers the basic system where superfluid is contained in a cylindrical vessel that rotates about its axis at an angular velocity. Although two-dimensional equilibrium patterns of vortex arrays are understood fairly well at present, there has been only a little amount of information on the dynamical aspects. Thus this work studies some typical dynamical problems, i.e., formation of vortex array and spin-down process. We describe also three-dimensional analysis which is much more troublesome than two-dimensional one.     

3D-vortex labyrinths in the near field of solid-state microchip laser

The usage of vortex-labyrinth fields and Talbot lattices as optical dipole traps for neutral atoms is considered for the wavelength of trapping radiation in the range 0.98–2.79 µm. The square vortex lattices generated in high Fresnel number solid-state microchip lasers are studied as a possible realization. The distribution of light field is obtained via a nonstationary computational model based on Maxwell–Bloch equations for a class-B laser, discrete Fox–Lee map with relaxation of inversion and a static model based on superposition of copropagating Gaussian beams. The spatial patterns obtained numerically and observed experimentally previously are interpreted as nonlinear superposition of vortices with helicoidal phase dislocations. The distribution of light field is approximated analytically by a sum of array of vortex lines and an additional parabolic subtrap. The separable optical trapping potential is proposed with similar intensity distribution. The factorization of the macroscopic wavefunction has led to the solution of the Gross–Pitaevsky equation for an ensemble of quantum particles trapped in a vortex labyrinth formed by a spatially periodic array of Laguerre–Gaussian beams.     

Dynamical Properties of Vortices in a Bose-Einstein Condensate in a Rotating Lattice

We present simulation results of the vortex dynamics in a trapped Bose-Einstein condensate in the presence of a rotating optical lattice. Changing the potential amplitude and the relative rotation frequency between the condensate and the optical lattice, we find a rich variety of dynamical phases of vortices. In particular, when the optical lattice rotates faster than the condensate, the competition between the pinning force and the interactions by nucleated interstitial vortices leads to the melting of vortex lattice, yielding a vortex liquid phase.     

Magnetic vortex state stability, reversal and dynamics in restricted geometries

Magnetic vortices are typically the ground states in geometrically confined ferromagnets with small magnetocrystalline anisotropy. In this article I review static and dynamic properties of the magnetic vortex state in small particles with nanoscale thickness and sub-micron and micron lateral sizes (magnetic dots). Magnetic dots made of soft magnetic material shaped as flat circular and elliptic cylinders are considered. Such mesoscopic dots undergo magnetization reversal through successive nucleation, displacement and annihilation of magnetic vortices. The reversal process depends on the stability of different possible zero-field magnetization configurations with respect to the dot geometrical parameters and application of an external magnetic field. The interdot magnetostatic interaction plays an important role in magnetization reversal for dot arrays with a small dot-to-dot distance, leading to decreases in the vortex nucleation and annihilation fields. Magnetic vortices reveal rich, non-trivial dynamical properties due to existance of the vortex core bearing topological charges. The vortex ground state magnetization distribution leads to a considerable modification of the nature of spin excitations in comparison to those in the uniformly magnetized state. A magnetic vortex confined in a magnetically soft ferromagnet with micron-sized lateral dimensions possesses a characteristic dynamic excitation known as a translational mode that corresponds to spiral-like precession of the vortex core around its equilibrium position. The translation motions of coupled vortices are considered. There are, above the vortex translation mode eigenfrequencies, several dynamic magnetization eigenmodes localized outside the vortex core whose frequencies are determined principally by dynamic demagnetizing fields appearing due to restricted dot geometry. The vortex excitation modes are classified as translation modes and radially or azimuthally symmetric spin waves over the vortex ground state. Studying the spin eigenmodes in such systems provides valuable information to relate the particle dynamical response to geometrical parameters. Unresolved problems are identified to attract attention of researchers working in the area of nanomagnetism.     

Splitting of a Multiply Quantized Vortex for a Bose-Einstein Condensate in an Optical Lattice

We study the splitting process of a multiply quantized vortex for a trapped highly oblate Bose-Einstein condensate in an optical lattice. Fourfold or sixfold splitting patterns are found in the dynamical evolution in square or triangular optical lattices, respectively. The relaxation time and angular momentum are also investigated to explore the properties of splitting. We find one singly quantized vortex or antivortex could be finally stabilized at the trap center.

     

Measurements of elliptically birefringent media parameters in optical vortex birefringence compensator

A new application of the optical vortex birefringence compensator has been presented. Two parameters of elliptically birefringent medium, an ellipticity angle and an optical path difference, can be measured simultaneously in the setup based on the C polarization type singularities generated using two Wollaston compensators. The theory and numerical investigations of the proposed method have been presented as well as some experiments verifying our theoretical predictions.     

Generation of vortex-type markers in a one-wave setup

What we believe to be a new arrangement of an optical vortex interferometer (OVI) is presented. In the proposed configuration the optical vortex lattice is generated in a one-wave setup by use of birefringent elements--Wollaston compensators. The obtained vortex lattice is regular and stable, which is necessary for predicted applications. The new OVI configuration allows the measurement of waves and optical media properties.     

光纤传感器在纸币凹版印刷特征识别中的应用

提出了两种用光纤传感器测试纸币凹版印刷的方案。其中动态检测方案利用了光纤位移传感器进行微位移测量的原理,静态检测方案利用了电磁波的散射原理,通过光纤表面粗糙度传感器来实现。按照实际要求,对两种方案的探测装置进行了设计,使其能更好地突出被测表面的特征。理论和实验结果都表明本文提出的两种方案是可行的,其中动态检测方案在一种新的专业级金融防伪设备中得到了应用,弥补了金融安全行业中机器识别凹版印刷特征的空白。     

Bose-Einstein Condensates in Dilute Trapped Atomic Gases

The static and dynamic behavior of dilute trapped Bose-Einstein condensates at low temperature follows from the Gross-Pitaevskii equation for the condensate and the Bogoliubov equations for the linearized small-amplitude normal modes. The uniform system serves to illustrate the theoretical methods and much of the basic physics. The principal new effect of the confining trap is to introduce an additional length scale (the size of the single-particle ground state) and energy scale (the single-particle ground-state energy). Most recent experiments use large condensates, when the repulsive interactions expand the condensate considerably and thus reduce the kinetic energy associated with the nonuniform density. In this regime (known as the "Thomas-Fermi" limit), the system can be treated as locally uniform, which greatly simplifies the analysis. When the condensate contains one or more vortex lines, the nonuniform trap potential and local line curvature drive the resulting vortex motion. Experiments have confirmed various predicted precessional motions in considerable detail. Mixtures of two distinct bosonic species allow for new coupled dynamical motions that alter the topology of the original single complex order parameter. In particular, application of near-resonant electromagnetic fields yields a coupled system that no longer has quantized circulation. Such experimental techniques created the first vortex line by spinning up one of the components. The introduction of optical traps has allowed the study of what are called "spinor" condensates. In this case, all hyperfine states are trapped, in contrast to the more common magnetic traps that confine only a subset of the various hyperfine states. The rotational invariance of the interparticle interactions significantly restricts the allowed states of these spinor condensates.     

Dynamics of field dislocations and disclinations in a few-mode fiber. IV. Formation of an optical vortex

The physical mechanisms responsible for the formation of an optical vortex in the field of a few-mode fiber have been investigated experimentally and theoretically. In an optical fiber with a parabolic refractive index profile an optical vortex is formed as a result of interaction between circularly polarized rotating pure edge dislocations of circularly polarized even and odd CP₁₁ modes. In a stepped-index fiber the formation of an optical vortex is also related to the simultaneous propagation of even and odd modes. The fields of these modes alter their structure over the fiber length and are not manifested by rotating edge dislocations. It has been found experimentally that a stable vortex does not alter its degree of polarization of the field at fiber lengths greater than 10 m. An unstable vortex, for which the product of the spin and the topological charge is always less than zero, periodically decays and recovers at a beat length of 0.65 m. It is noted that a stable optical vortex cannot be formed by orthogonally polarized LP₁₁ modes. This is because an optical vortex transfers additional angular momentum like the CP₁₁ modes whereas the LP₁₁ modes do not transfer additional angular momentum of the field. Pis’ma Zh. Tekh. Fiz. 23, 70–75 (March 12, 1997)     

Generation of optical vortices with an adaptive helical mirror

Generation of optical vortices using a new design of adaptive helical mirror (AHM) is reported. The new AHM is a reflective device that can generate an optical vortex of any desired topological charge, both positive and negative, within its breakdown limits. The most fascinating feature of the AHM is that the topological charge of the optical vortex generated with it can be changed in real time by varying the excitation voltage. Generation of optical vortices up to topological charge 4 has been demonstrated. The presence of a vortex in the optical field generated with the AHM is confirmed by producing both fork and spiral fringes in an interferometric setup. Various design improvements to further enhance the performance of the reported AHM are discussed. Some of the important applications of AHM are also listed.     

Signal analysis applied to vortex flowmeters

The signal taken directly from the sensor used in an industrial vortex flowmeter is processed so as to discern the effects of various process conditions on the measurement signal. A mathematical model of how the signal is generated in the vortex flowmeter is derived on the basis of these observations. The model has been used to predict the form of the signal from the flowmeter operating under various flow conditions. The spectrum of the predicted data has been analyzed and the results compared to corresponding results obtained using practical data from an actual flowmeter installed in a flow loop. The implication of this study is that signal processing and system identification techniques can be applied to enhance the quality of the measurement information provided to a supervisory control system     

Measuring local thermal fluxes during thermal exchange between a surface and a vortex structure

The effect of a vortex structure in a “dumped” flame on the intensity of heat exchange between this flame and a flat surface has been studied. An optical polarization technique is proposed for the visualization and measurement of an inhomogeneous temperature field at the surface and inside the heat exchanger wall. It is shown that the gas circulation in large vortex cells leads to an increase in the local thermal fluxes. In the range of Reynolds numbers 50400, a thermal flux from the “dumped” flame to a flat heat exchanger surface is 20–30% greater than that for an oncoming laminar flame.     

A Minimalist Single-Layer Metasurface for Arbitrary and Full Control of Vector Vortex Beams

Vector vortex beams (VVBs) possess ubiquitous applications from particle trapping to quantum information. Recently, the bulky optical devices for generating VVBs have been miniaturized by using metasurfaces. Nevertheless, it is quite challenging for the metasurface-generated VVBs to possess arbitrary polarization and phase distributions. More critical is that the VVBs' annular intensity profiles demonstrated hitherto are dependent on topological charges and are hence not perfect, posing difficulties in spatially shared co-propagation of multiple vortex beams. Here, a single-layer metasurface to address all those aforementioned challenges in one go is proposed, which consists of two identical crystal-silicon nanoblocks with varying positions and rotation angles (i.e., four geometric parameters throughout). Those four geometric parameters are found to be adequate for independent and arbitrary control of the amplitude, phase, and polarization of light. Perfect VVBs with arbitrary polarization and phase distributions are successfully generated, and the constant intensity profiles independent of their topological charges and polarization orders are demonstrated. The proposed strategy casts a distinct perception that a minimalist design of just one single-layer metasurface can empower such robust and versatile control of VVBs. That provides promising opportunities for generating more complex vortex field for advanced applications in structural light, optical micromanipulation, and data communication.     

A SiC bicrystal junction on the (0 0 0 1) plane

A SiC bicrystal junction in which two crystals superpose with a common (0001) plane has been investigated by optical microscopy and X-ray precession camera techniques. The behaviour of such a junction is discussed from the viewpoint of sintering and grain boundaries in SiC using a crystallographic concept of compound tessellation. Six examples of bicrystals are considered with respect to the observed and calculated superposing rotation angles and the densities of the superpositions.     

Microwave Transmission and Reflection for a Type-II Superconducting Superlattice in the Mixed State

The microwave reflection and transmission for a type-II superconducting superlattice in the mixed state are theoretically calculated based on the vortex dynamical model together with the transfer matrix method in a layered medium. The superlattice is made of alternating layers of high-temperature superconductors and dielectric materials. We analyze the microwave reflection and transmission as functions of the static magnetic field, the number of periods, and the thickness of the dielectric layer. It is shown that the reflection decreases as the static field increases. In addition, the reflection will be enhanced by increasing the number of periods.     

Three-dimensional Dammann vortex array with tunable topological charge

We describe a kind of true 3D array of focused vortices with tunable topological charge, called the 3D Dammann vortex array. This 3D Dammann vortex array is arranged into the structure of a true 3D lattice in the focal region of a focusing objective, and these focused vortices are located at each node of the 3D lattice. A scheme based on a Dammann vortex grating (DVG) and a mirror is proposed to provide a choice for changing the topological charge of the 3D Dammann vortex array. For experimental demonstration, a 5×5×5 Dammann vortex array is implemented by combining a 1×7 DVG, a 1×5 Dammann zone plate, and another 5×5 Dammann grating. The topological charge of this Dammann vortex array can be tuned (from -2 to +2 with an interval of +1) by moving and rotating the mirror to select different diffraction orders of the 1×7 DVG as the incident beam. Because of these attractive properties, this 3D Dammann vortex array should be of high interest for its potential applications in various areas, such as 3D simultaneous optical manipulation, 3D parallel vortex scanning microscope, and also parallel vortex information transmission.     

Angular distribution of an average solid angle subtended by a circular disc from multiple points uniformly distributed on a planar circular surface coaxial to the disc

Abstract

Average solid angles subtended by an external contour of a given body from several points are required for the calculation of radiation fluxes or particle beams that are incident on the body from multiple-point isotropic emitters of analogous kinds. To consider the refraction effects for fluxes of light propagating through various optical media, knowledge of the angular distributions of such average solid angles is necessary. In this paper the formula describing angular dependence of the average solid angle subtended by a circular disc from uniformly distributed points within the circular surface of a parallel and coaxial disc was derived analytically and used for the calculation of some representative results. The solution has been made in the cylindrical coordinate system. The final and some intermediate formulas were expressed as functions of the polar angle, of the radii of both discs and of the distance between their planes. These formulae were represented by superpositions of simple elementary functions, single integrals of, these superpositions and by incomplete and complete Legendre—Jacobi elliptic integrals of all three kinds. Mathematica 2.2.3 software was used to illustrate graphically the relationships between some computed data. These data indicate that the derived formula is directly applicable in any computer programs calculating the Legrendre—Jacobi elliptic integrals to estimate the fluxes of optical radiation and particle beams propagated within a non-absorbing homogeneous medium. The expressions obtained may also be used to calculate the fluxes of optical radiation propagated through various homogeneous media.     

Mechanical effects in a vortex device with a rotating core

The process of the appearance of forced rotation of an axial core mounted in a modified vortex tube in the direction opposite to the rotation of the air vortex and the precession of its axis have been studied. It has been established that dynamical bending of a metal axial core arises in the process of rotation which causes mechanical wear of its end part and fracture in the fastening area of the bearing without residual curvature of the core axis. The excitation of rotation and observed force effects are not related to the mechanical action of rotating air flow on the axial core.