Far-field detection of the dipole vortex

The energy flow lines (field lines of the Poynting vector) of electric dipole radiation exhibit a vortex structure in the near field when the dipole moment of the source is in circular rotation. The spatial extend of this vortex is smaller than a wavelength and may not be observable by a measurement in the near field. We show that the rotation of the field lines close to the source affects the image of the dipole in the far field, and this opens the possibility for observation of this vortex by a measurement in the far field.     

Nanoscale displacement of the image of an atomic source of radiation

Light emitted by an atomic source of radiation appears to travel along a straight line （ray） from the location of the source to the observer in the far field. However, when the energy flow pattern of the radiation is resolved with an accuracy better than an optical wavelength, it turns out that the field lines are usually curved. We consider electric dipole radiation, a prime example of which is the radiation emitted by an atom during an electronic transition, and we show that the field lines of energy flow are in general curves. Near the location of the dipole, the field lines exhibit a vortex structure, and in the far field they approach a straight line. The spatial extension of the vortex in the optical near field is of nanoscale dimension. Due to the rotation of the field lines near the source, the asymptotic limit of a field line is not exactly in the radially outward direction and as a consequence, the image in the far field is slightly shifted. This sub-wavelength displacement of the image of the source should be amenable to experimental observation with contemporary nanoscale-precision techniques.     

Subwavelength displacement of the far-field image of a radiating dipole

The field lines of the Poynting vector for light emitted by a dipole with a rotating dipole moment show a vortex pattern near the location of the dipole. In the far field, each field line approaches a straight line, but this line does not appear to come exactly from the location of the dipole. As a result, the image of the dipole in its plane of rotation seems displaced. Secondly, the image in the far field is displaced as compared with the image of a source for which the field lines run radially outward. It turns out that both image displacements are the same. The displacements are of subwavelength scale, and they depend on the angles of observation. The maximum displacement occurs for observation in the plane of rotation and equals lambda/pi, where lambda is the wavelength of the light.     

Interaction of a magnetic vortex with the probe field of a magnetic force microscope

The interaction of a magnetic vortex in a circular ferromagnetic nanoparticle with the probe field of a magnetic force microscope (MFM) is theoretically investigated. In the calculations, the probe field is approximated by the point dipole field. The rigid magnetic vortex model is used to describe the vortex state of magnetization. It is found that the effect of the probe field on the rigid magnetic vortex shell is similar to the effect of a uniform magnetic field parallel to the particle plane. The effect of the Z component of the probe field on the core of the vortex results in mutual probe-vortex attraction or repulsion. It is shown that the magnetization direction of the core of the vortex in the MFM probe field can be changed without a change in the shell vorticity direction.     

Surface currents on a perfect conductor, induced by a magnetic dipole

An oscillating magnetic dipole located near a perfect conductor induces a current density on the surface of the metal. We have derived an expression for this current density, and studied its field line patterns for various orientations of the dipole moment. When the dipole moment is perpendicular to the surface, the field lines are circles which run clockwise and counterclockwise. For a linear dipole oriented parallel to the surface, the field line pattern is much more complex, and it contains singular points. When the dipole moment rotates in a plane parallel to the surface, the field lines are spirals. A field line spirals inward from infinity to some given point, after which it spirals outward back to infinity. We have also considered the Poynting vector of the electromagnetic field near the surface, and we found that its field lines can have singular points or exhibit a vortex.     

Transmission of electric dipole radiation through an interface

We consider the transmission of electric dipole radiation through an interface between two dielectrics, for the case of a vertical dipole. Energy flows along the field lines of the Poynting vector, and in the optical near field these field lines are curves (as opposed to optical rays). When the radiation passes through the interface into a thicker medium, the field lines bend to the normal (as rays do), but the transmission angle is not related to the angle of incidence. The redirection of the radiation at the interface is determined by the angle dependence of the transmission coefficient. This near-field redistribution is responsible for the far-field angular power pattern. When the transmission medium is thinner than the embedding medium of the dipole, some energy flows back and forth through the interface in an oscillating fashion. In each area where field lines dip below the interface, an optical vortex appears just above the interface. The centers of these vortices are concentric singular circles around the dipole axis.     

Rotating spin-1/2 Bose-Einstein condensates in a gradient magnetic field with spin-orbit coupling

We study the ground-state phases of two-dimensional rotating spin–orbit coupled spin-1/2 Bose–Einstein condensates (BECs) in a gradient magnetic field. The competition between gradient magnetic field, spin–orbit coupling and rotation leads to a variety of ground-state phase structures. In the weakly rotation regime, as the increase of gradient magnetic field strength, the BECs experiences a phase transition from the unstable phase to the single vortex-line phase. The unstable phase presents the vortex lines structures along the off-diagonal direction. With magnetic field gradient strength increasing, the number of vortex lines changes accordingly. As the magnetic field gradient strength increases further, the single vortex-line phase with a single vortex line along the diagonal direction is formed. The phase diagram shows that the boundary between the two phases is linear with the relative repulsion λ≥1 and is nonlinear with λ<1. In the relatively strong rotation regime, in addition to the unstable phase and the single vortex-line phase, the vortex-ring phase is formed for the strong magnetic field gradient and rapid rotation. The vortex-ring phase shows the giant and hidden vortex structures at the center of ring. The strong magnetic field gradient makes the number of the vortices around the ring unchanged.     

Analytic solutions to Maxwell–London equations and levitation force for a general magnetic source in the presence of a long type-II superconducting cylinder

The interaction between a general magnetic source and a long type-II superconducting cylinder in the Meissner or mixed state is studied within the London theory. We first study the Meissner state and solve the Maxwell–London equations when the source is a magnetic monopole located at an arbitrary position. Then the field and supercurrent for a more complicated magnetic charge distribution can be obtained by superposition. A magnetic point dipole with arbitrary direction is studied in detail. It turns out that the levitation force on the dipole contains in general an angular as well as a radial component. By integration we obtain the field and supercurrent when the source is a two-dimensional monopole (a magnetically charged long thread along the axial direction), from which the results for a two-dimensional point dipole easily follow. In the latter case the levitation force points in the radial direction regardless of the orientation of the dipole. The case for a current carrying long straight wire parallel to the cylindrical axis is solved separately. The limit of ideal Meissner state is discussed in most cases. The case of mixed state is discussed briefly. It turns out that vortex lines along the axial direction and vortex rings concentric with the cylinder have no effect outside the cylinder and the levitation forces remain the same as in the case of the Meissner state.     

Diffusion anisotropy in a toroidal (ring) vortex in water

Diffusion of paint (ink) particles in a toroidal (ring) vortex in a density-homogeneous liquid (water) was experimentally studied. Particle diffusion anisotropy in rotating water of the vortex was detected. The effect consists in the fact that the particle diffusivity in the direction perpendicular to the rotation axis of the torus core is much lower than that in the direction parallel to the rotation axis.     

Macroscopic far-field observation of the sub-wavelength near-field dipole vortex

The energy flow lines of the radiation emitted by a rotating electric dipole moment have a vortex structure near the source. The spatial extend of this vortex is well below an optical wavelength. This near-field vortex has a macroscopic effect which could be observed in the far field.     

TWO-DIMENSIONAL ANGULAR MOMENTUM AND FERMION IN THE FIELD OF MAGNETIC-FLUX-TUBE

In this paper, we showed that the eigenvalues of two-dimensional angular momentum of a particle with charge a are integer valued. The problems of a Dirac particle in a field of vortex were discussed. When the vortex tends-to string, we found that the system admits of the existence of θ vacua. For massless fermions, a change in θ is equivalent to a Γ_s rotation, while the physical result is independent of θ. For massive fermions, CP invariance is broken except for θ=0,π; and the system exhibits the Witten effect.     

Clustering of the low-inertia particle number density field in random divergence-free hydrodynamic flows

We consider the diffusion of the low-inertia particle number density field in random divergence-free hydrodynamic flows. The principal feature of this diffusion is the divergence of the particle velocity field, which results in clustering of the particle number density field. This phenomenon is coherent, occurs with a unit probability, and must show up in almost all realizations of the process dynamics. We calculate the statistical parameters that characterize clustering in three-dimensional and two-dimensional random fluid flows and in a rapidly rotating two-dimensional random flow. In the former case, the vortex component of the random divergence-free flow generates a vortex component of the low-inertia particle velocity field, which generates a potential component of the velocity field through advection. By contrast, in the case of rapid rotation, a potential component of the velocity field is generated directly by the vortex component of the random divergence-free flow (linear problem).     

Particle captured by a field-modulating vortex through dielectrophoresis force

In microfluidic technology, dielectrophoresis (DEP) is commonly used to manipulate particles. In this work, the fluid-particle interactions in a microfluidic system are investigated numerically by a finite difference method (FDM) for electric field distribution and a lattice Boltzmann method (LBM) for the fluid flow. In this system, efficient particle manipulation may be realized by combining DEP and field-modulating vortex. The influence of the density ($\rho_{\rm p}$), radius ($r$), and initial position of the particle in the $y$ direction ($y_{\rm p0}$), and the slip velocity ($u_{0}$) on the particle manipulation are studied systematically. It is found that compared with the particle without action of DEP force, the particle subjected to a DEP force may be captured by the vortex over a wider range of parameters. In the $y$ direction, as $\rho_{\rm p}$ or $r $ increases, the particle can be captured more easily by the vortex since it is subjected to a stronger DEP force. When $u_{0}$ is low, particle is more likely to be captured due to the vortex-particle interaction. Furthermore, the flow field around the particle is analyzed to explore the underlying mechanism. The results obtained in the present study may provide theoretical support for engineering applications of field-controlled vortices to manipulate particles.     

Dynamics of the Photoinduced Rotation of a Spherical Particle in a Constant Electric Field

Technical Physics - The rotation of a spherical particle in a constant electric field (an effect found earlier) has been analyzed. The particle is illuminated to induce the electric dipole moment...     

Redistribution of energy flow in a material due to damping

The field lines of energy flow of the radiation emitted by a linear dipole in free space are straight lines, running radially outward from the source. When the dipole is embedded in a medium, the field lines are curves when the imaginary part of the relative permittivity is finite. It is shown that due to the damping in the material all radiation is emitted in directions perpendicular to the dipole axis, whereas for a dipole in free space the radiation is emitted in all directions except along the dipole axis. It is also shown that some field lines in the near field form semiloops. Energy flowing along these semiloops is absorbed by the material and does not contribute to the radiative power in the far field.     

Viscous Interaction Between a Vortex Tube and a Rotating Spherical Particle

The transient advection of a cylindrical vortex tube in a viscous incompressible flow field and its interaction with a rotating/spinning spherical particle has been investigated numerically at Reynolds numbers in the range of 20≤ Re≤200 for angular velocities of 0≤Ω≤0.5. The effects of vortex parameters such as size, circulation strength and initial position relative to the particle, on the temporal behavior of the lift and drag forces are studied. Vortex‐sphere interactions bring about major changes in the flow field particularly when coupled with particle rotation. It is observed that the forces acting on the particle are significantly influenced during the time that the vortex core is in the vicinity of the particle. The extent of these local changes are about ±30% in the drag coefficient and about ±200% in the lift coefficient as compared to flow over a rotating solid sphere with no vortex interaction. It is also found that a vortex with core radius between one and two particle diameters creates the strongest temporal variations in the lift and drag coefficients. Furthermore, maximum lift variations occur for the vortex‐particle head on collision, while a vortex with an offset distance of about one diameter from the principal flow axis generates the maximum drag variations.     

Numerical simulation evidence of dynamical transverse meissner effect and moving bose glass phase

We present 3D numerical simulation results of moving vortex lattices in the presence of 1D correlated disorder at zero temperature. Our results with field tilting confirm the theoretical predictions of a moving Bose glass phase, characterized by transverse pinning and dynamical transverse Meissner effect, the moving flux lines being localized along the correlated disorder direction. Beyond a critical transverse field, vortex lines exhibit along all their length a "kink" structure resulting from an effective static "tin roof" pinning potential in the transverse direction.     

Correlated magnetic vortex chains in mesoscopic cobalt dot arrays

Nucleation and annihilation of vortex states have been studied in two-dimensional arrays of densely packed cobalt dots. A clear signature of dipolar interactions both between single-domain state dots and vortex state dots has been observed from the dependence of vortex nucleation and annihilation fields on interdot separation. A direct consequence of these interactions is the formation of vortex chains as well as dipole chains aligned along the direction of the external field. In addition, short range correlation of chiralities within vortex chains has been observed using magnetic force microscopy imaging and has been attributed to cross-talking between adjacent elements.     

金属粒子阵列共振的偏振特性

当金属纳米粒子形成规则分布且阵列周期与单粒子的共振波长近似匹配时, 会形成一种特殊的阵列共振, 这种共振比单粒子的局域表面等离子体共振具有更窄的共振线宽和更高的共振强度. 基于修正的长波近似方法, 讨论了矩形阵列的消光截面与阵列因子和单粒子的极化率之间的关系; 并详细研究了在不同偏振的入射光照射下, 阵列因子随着电偶极子方向的改变而产生的变化, 以及这一效应对阵列共振和消光截面所产生的影响. 结果表明, 大型的方阵是偏振无关的; 在矩形阵列中, 沿着阵列两个轴向的相邻粒子之间的耦合形成了阵列因子的两个极值, 并且分别对应了散射截面的最小值.