Orbital angular momentum exchange in the interaction of twisted light with molecules

In the interaction of molecules with light endowed with orbital angular momentum, an exchange of orbital angular momentum in an electric dipole transition occurs only between the light and the center of mass motion; i.e., internal "electronic-type" motion does not participate in any exchange of orbital angular momentum in a dipole transition. A quadrupole transition is the lowest electric multipolar process in which an exchange of orbital angular momentum can occur between the light, the internal motion, and the center of mass motion. This rules out experiments seeking to observe exchange of orbital angular momentum between light beams and the internal motion in electric dipole transitions.     

利用干涉光场的相位涡旋测量拉盖尔-高斯光束的轨道角动量

对拉盖尔-高斯光束经多圆孔衍射屏在远场平面上形成的干涉光场的相位和零值线进行了计算模拟.当入射光束的轨道角动量量子数为零时,实部零值线与虚部零值线在干涉光场中心点不相交,因而在该点上不能形成相位涡旋.当入射光束的轨道角动量量子数为+1和-1时,实部零值线与虚部零值线在干涉光场中心垂直并相交,干涉光场相应位置处的相位涡旋的符号相反.当入射光束的轨道角动量量子数为±2和±3时,有四条零值线相交于干涉光场的中心点上,并且实部零值线和虚部零值线交替分布,该交点处形成的相位涡旋的拓扑荷的值恰好与拉盖尔-高斯光束的轨道角动量量子数相等.这种结果可以用来测量涡旋光束的轨道角动量.     

Interaction of translational and rotational modes of a molecular impurity in two-dimensional atomic crystals

The interaction between the translational and rotational degrees of freedom of a diatomic homonu-clear molecule that executes a motion at the site of a two-dimensional close-packed atomic matrix located on a close-packed atomic substrate (a molecular substitutional impurity in the crystal field of the two-dimensional lattice of a solidified rare gas) is investigated theoretically. The relationships describing the effective dynamic properties of an impurity rotator in the presence of translational excitations of its center of inertia are derived in the framework of consistent procedures on the basis of the Lagrangian (the functional-integral method) and Hamiltonian (the canonical-transformation method) formalisms. The inclusion of the translational-rotational interaction leads to a radical change in the inertial properties of the molecule. This manifests itself in a change in the form of the operator for the rotational kinetic energy as compared to the corresponding expression for a free rotator. The inertia tensor components for the molecule become functions of molecular orientation, and the molecule, in terms of rotational motion, transforms into a “parametric rotator” whose effective kinetic energy is represented as a generalized quadratic form of the angular momentum (or the angular velocity) components with a symmetry corresponding to the symmetry of the external crystal field. The translational-rotational interaction also results in the renormalization of the parameters of the crystal potential without a change in its initial form.     

Magnetic trapping of ultracold Rydberg atoms

We investigate the quantum dynamics of ultracold Rydberg atoms being exposed to a magnetic quadrupole field. A Hamiltonian describing the coupled dynamics of the electronic and center of mass motion is derived. Employing an adiabatic approach, the potential energy surfaces for intra-n-manifold mixing are computed. By determining the quantum states of the center of mass motion, we demonstrate that trapped states can be achieved if the total angular momentum of the atom is sufficiently large. This holds even if the extension of the electronic Rydberg state becomes equal to or even exceeds that of the ultracold center of mass motion.     

Poincaré-sphere equivalent for light beams containing orbital angular momentum

The polarization state of a light beam is related to its spin angular momentum and can be represented on the Poincaré sphere. We propose a sphere for light beams in analogous orbital angular momentum states. Using the Poincaré-sphere equivalent, we interpret the rotational frequency shift for light beams with orbital angular momentum [Phys. Rev. Lett. 80, 3217 (1998)] as a dynamically evolving geometric phase.     

Sharing a Common Origin Between the Rotational and Linear Doppler Effects

The well‐known linear Doppler effect arises from the linear motion between source and observer, while the less well‐known rotational Doppler effect arises from the rotational motion. Here, we present both theories and experiments illustrating the relationship between the rotational and linear Doppler effects. A spiral phaseplate is used to generate a light beam carrying orbital angular momentum and the frequency shift is measured arising from its rotational and/or linear motion. By considering either the motion‐induced time‐evolving phase or the momentum and energy conservation in light‐matter interactions, we derive the rotational Doppler shift, linear Doppler shift, and overall Doppler shift associated with rotational and linear motions. We demonstrate the relationship between rotational and linear Doppler shifts, either of which can be derived from the other effect, thereby illustrating their shared origin. Moreover, the close relationship between rotational and linear Doppler effects is also deduced for a more general moving rough surface.     

Intrinsic and extrinsic nature of the orbital angular momentum of a light beam

We explain that, unlike the spin angular momentum of a light beam which is always intrinsic, the orbital angular momentum may be either extrinsic or intrinsic. Numerical calculations of both spin and orbital angular momentum are confirmed by means of experiments with particles trapped off axis in optical tweezers, where the size of the particle means it interacts with only a fraction of the beam profile. Orbital angular momentum is intrinsic only when the interaction with matter is about an axis where there is no net transverse momentum.     

The propagation of a polarized gaussian beam in a smoothly inhomogeneous isotropic medium

In the frame of the eikonal-based complex geometrical optics, which describes the phase front and cross section of a light beam using the quadratic expansion of a complex-valued eikonal, we investigate the transverse deflections of a polarized Gaussian beam (GB) in a smoothly inhomogeneous isotropic medium, which is called the spin Hall effect of the beam. The linear complex-valued eikonal terms are introduced firstly to describe the polarization-dependent transverse shifts of the beam in the inhomogeneous medium. We find that the polarization-dependent transverse shifts of the beams include two parts: one originates from the coupling between the spin angular momentum and the extrinsic orbital angular momentum due to the curve trajectory of the center of gravity of the polarized GB, and the other from the coupling between the spin angular momentum and the intrinsic orbital angular momentum due to the rotation of the beam with respect to the central ray.     

On quadrupole and octupole gravitational radiation in the ANK formalism

Following the approach of Adamo–Newman–Kozameh (ANK) we derive the equations of motion for the center of mass and intrinsic angular moment for isolated sources of gravitational waves in axially symmetric spacetimes. The original ANK formulation is generalized so that the angular momentum coincides with the Komar integral for a rotational Killing symmetry. This is done using the Winicour–Tamburino Linkages which yields the mass dipole-angular momentum tensor for the isolated sources. The ANK formalism then provides a complex worldline in a fiducial flat space to define the notions of center of mass and spin. The equations of motion are derived and then used to analyse a very simple astrophysical process where only quadrupole and octupole contributions are included. The results are then compared with those coming from the post newtonian approximation.     

Resistance of nondiffracting vortex beam against amplitude and phase perturbations

The revival of the nondiffracting vortex beam after its interaction with the 2D on axis obstacle is examined. We show that the phase topology and the spatial distribution of the orbital angular momentum of the beam transmitted through the obstacle regenerate to the initial form during further free propagation. We verify that the healing effect appears even if the interaction is accompanied by the exchange of the orbital angular momentum.     

Second Order Lagrangian and Angular Momentum of Scalar Field

The class of second order Lagrangian for the scalar field is including free divergence terms giving rise to new canonical conservation laws by means of Noethers theorem. The appearance of a spin like tensor S within angular momentum is nothing but a redefinition of orbital angular momentum. S is mainly giving a new definition of center of mass for the field, indicating that the variation for the motion of singularities is nothing but a redefinition for the motion, since the sum for the additional forces, coming from divergence part of Lagrangian, is zero. Thus, the physical content of the theory will not be affected by the divergence part of Lagrangian, is zero. Thus, the physical content of the theory will not be affected by the divergence termes; it is only an other formulation.     

Beam moments and angular momentum in non-uniformly polarized beams

The angular momentum of non-uniformly totally polarized beams is investigated using methods from the beam characterization approach. The relationship between the elements of the beam matrix for the two components of the field and the angular momentum is given. The unconventional distribution of the polarization across the beam profile could result in contributions to both the spin and orbital terms of the angular momentum. To illustrate this, a particular example with a vortex beam is considered.     

Focusing of elliptically polarized Gaussian beams through an annular high numerical aperture

Based on the vectorial Debye theory,the focusing properties of the Gaussian beam through an annular high numerical aperture are studied numerically,including the intensity,the phase and the orbital angular momentum properties.Then the influence of certain parameters on the focusing properties is also investigated.It is shown that sub-wavelength elliptical light spots can be obtained.And there exists a vortex in the longitudinal component of the focused field even though the incident beam is Gaussian beam,indicating that the spin angular momentum of the elliptically polarized Gaussian beam is converted into the orbital angular momentum by the focusing.     

Rotational motions of optically trapped microscopic particles by a vortex femtosecond laser

The rotational motions of the optically trapped microscopic particles by the vortex femtosecond laser beam are investigated in this paper.Black particles can be trapped and rotated by a vortex femtosecond laser beam very effectively because the vortex beam carries orbital angular momentum due to the helical wave-front structure in assoication with the central phase singularity.Trapped black particles rotate in the vortex beam due to the absorption of the angular momentum transferred from the vortex beam.The rotating directions of the trapped particles can be modulated by reversing the topological charge of the optical vortex in the vortex femtosecond beam.And the rotating speeds of the trapped microscopic particles greatly depend on the topological charges of the vortex tweezer and the used pulse energies.     

Generalized model for orbital angular momentum states generated by parallel aligned phase wedges

A generalized model of a double-wedge phase element containing two side-by-side parallel phase ramps with arbitrary slope angles is proposed. We study the diffracted optical field of a double-wedge element in terms of orbital angular momentum states. Analytical calculations reveal how the radius and position of the illuminating laser beam affect the composition of orbital angular momentum generated by the phase wedges.     

单光子轨道角动量的传输特性研究

描述了高阶椭圆厄米-高斯光束及其单光子平均轨道角动量,并分析了一些与其单光子轨道角动量变化的有关情况,通过计算机仿真简要进行了说明.最后分析了单光子轨道角动量在空间某范围的概率分布及其变化情况.研究结果表明,高阶椭圆厄米-高斯光束与物质相互作用时,其单光子平均轨道角动量的变化幅度随接触物质材料的不同而异.     

Coherent-mode representation and orbital angular momentum spectrum of partially coherent beam

Orbital angular momentum of the coherent beam has been intensively studied and promises potential applications in free space optical communication. But the orbital angular momentum of partially coherent beam is not well known. In this communication the coherent-mode representation method is adopted to describe the partially coherent beam and the orbital angular momentum spectrum is introduced for the partially coherent beam. The characteristics of the orbital angular momentum spectrum of partially coherent beam are discussed. To study the influence of the partial coherence on the optical link, the channel capacity is studied, with two kinds of available mode separators included.     

Phase sensitive parametric amplification of optical vortex beams

Optical vortex beams with different topological charges are amplified in a travelling wave phase sensitive parametric interaction. Amplified beams observed either in the near field or in the far field domains exhibit patterns that depend on the relative phase between the pump and the vortex beams. Experimental results are compatible with the conservation of orbital angular momentum of the input beam whatever phase matching conditions.     

在大气湍流斜程传输中拉盖高斯光束的轨道角动量的研究

大气湍流引起大气折射率随机变化,导致空间不均匀性.拉盖高斯光束在大气湍流中传输时,空间不均匀性会使光子波函数改变,引起轨道角动量的变化.本文讨论了拉盖尔高斯光束在大气斜程传输时,湍流介质改变光子轨道角动量而形成不同的光子态.计算了螺旋谐波各分量所占光束总能量的权重,分析了拉盖高斯光束的轨道角动量的变化规律.