Geometrical optics of beams with vortices: Berry phase and orbital angular momentum Hall effect

We consider propagation of a paraxial beam carrying the spin angular momentum (polarization) and intrinsic orbital angular momentum (IOAM) in a smoothly inhomogeneous isotropic medium. It is shown that the presence of IOAM can dramatically enhance and rearrange the topological phenomena that previously were considered solely in connection to the polarization of transverse waves. In particular, the appearance of a new type of Berry phase that describes the parallel transport of the beam structure along a curved ray is predicted. We derive the ray equations demonstrating the splitting of beams with different values of IOAM. This is the orbital angular momentum Hall effect, which resembles the Magnus effect for optical vortices. Unlike the spin Hall effect of photons, it can be much larger in magnitude and is inherent to waves of any nature. Experimental means to detect the phenomena are discussed.     

Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media

We demonstrate experimentally an optical process in which the spin angular momentum carried by a circularly polarized light beam is converted into orbital angular momentum, leading to the generation of helical modes with a wave-front helicity controlled by the input polarization. This phenomenon requires the interaction of light with matter that is both optically inhomogeneous and anisotropic. The underlying physics is also associated with the so-called Pancharatnam-Berry geometrical phases involved in any inhomogeneous transformation of the optical polarization.     

Spin-dependent transverse force on a vortex light beam in an inhomogeneous medium

Spin-dependent effects on vortex light beams propagating in an inhomogeneous medium are demonstrated by solving the full three-component field Maxwell equations using the perturbation analysis. It is found that the hybrid Laguerre–Gauss modes with polarization-orbital angular momentum (OAM) entanglement are the vector solutions of the Maxwell equations in a graded-index medium. Focusing of linearly and circularly polarized vortex light beams in a cylindrical graded-index medium is investigated. It is shown that the vortex light beam undergoes an additional transverse force acting differently on circular polarized beams with opposite handedness. The wave shape variation with distance taking into account the spin–orbit and nonparaxial effects is analyzed. Effect of long-term periodical revival of wave packets due to mode interference in a graded-index cylindrical optical waveguide is demonstrated.     

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.     

Observation of orbital angular momentum transfer between acoustic and optical vortices in optical fiber

Acousto-optic interaction in optical fiber is examined from the perspective of copropagating optical and acoustic vortex modes. Calculation of the acousto-optic coupling coefficient between different optical modes leads to independent conservation of spin and orbital angular momentum of the interacting photons and phonons. We show that the orbital angular momentum of the acoustic vortex can be transferred to a circularly polarized fundamental optical mode to form a stable optical vortex in the fiber carrying orbital angular momentum. The technique provides a useful way of generating stable optical vortices in the fiber medium.     

Angular momentum of gaussian light beams

Analysis of the orbital angular momentum of paraxial light beams shows that a key role in the formation of this quantity is played by phase relations between longitudinal and transverse radiation fields. When a light beam is circularly polarized or has a helical wave front, the azimuthal component of the Poynting vector and the density of orbital angular momentum prove to be non-zero. In the case of circularly polarized radiation, the azimuthal component of the Poynting vector and the density of the orbital angular momentum can change the sign at different points in the cross section of the light beam, while the total orbital momentum of the beam remains quantized.     

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.     

Spin-to-orbital angular momentum conversion in spin Hall effect of light

From the viewpoint of classical electrodynamics, we identify the role of spin-to-orbital angular momentum conversion in spin Hall effect (SHE) of light. We introduce a distinct separation between spin and orbital angular momenta to clarify the spin–orbital interaction in conventional beam refraction. We demonstrate that the refractive index gradient can enhance or suppress the spin-to-orbital angular momentum conversion, and thus can control the SHE of light. We suggest that the metamaterial whose refractive index can be tailored arbitrarily may become a good candidate for amplifying or eliminating the SHE of light, and by properly facilitating the spin-to-orbital angular momentum conversion the SHE may be enhanced dramatically. The transverse spatial shifts governed by the spin-to-orbital angular momentum conversion, provide us a clear physical picture to clarify the role of refractive index gradient in the SHE of light. These findings provide a pathway for modulating the SHE of light and can be extrapolated to other physical systems.     

Probing Dual Asymmetric Transverse Spin Angular Momentum in Tightly Focused Vector Beams in Optical Tweezers

The spin-orbit interaction (SOI) of light generated by tight focusing in optical tweezers is regularly employed in generating angular momentum - both spin and orbital - the effects being extensively observed in trapped mesoscopic particles. Specifically, the transverse spin angular momentum (TSAM), which arises due to the longitudinal component of the electromagnetic field generated by tight focusing is of special interest, both in terms of fundamental studies and associated applications. This study provides an effective and optimal strategy for generating TSAM in optical tweezers by tightly focusing first-order radially and azimuthally polarized vector beams with no intrinsic angular momentum (AM) into a refractive index stratified medium. The choice of such input fields ensures that the longitudinal spin angular momentum (LSAM) arising from the electric (magnetic) field for the radial (azimuthal) polarization is zero. As a result, the effects of the electric and magnetic TSAM are exclusively observed separately in the case of input first-order radially and azimuthally polarized vector beams on single optically trapped birefringent particles. This research opens up new and simple avenues for exotic and complex particle manipulation in optical tweezers.     

Proposals for the generation of angular momentum from non-uniformly polarized beams

Several optical arrangements using non-uniformly polarized fields are proposed for generating beams with spin and/or orbital angular momentum. By choosing adequately the input beam polarization and the characteristics of the different proposed set-ups we can control the overall angular momentum of the output beam at will. The orbital angular momentum is analyzed with the beam moments theory and the spin term is evaluated using the averaged s₃ Stokes parameter.     

Light with a twist in its tail

Polarized light is a phenomenon familiar to anyone with a pair of polaroid sunglasses. Optical components that change the nature of the polarization from linear to circular are common in any undergraduate laboratory. Probably only physicists know that circularly polarized light carries with it an angular momentum that results from the spin of individual photons. Few physicists realize, however, that a light beam can also carry orbital angular momentum associated not with photon spin but with helical wavefronts. Beams of this type have been studied only over the last decade. In many instances orbital angular momentum behaves in a similar way to spin. But this is not always so: orbital angular momentum has its own distinctive properties and its own distinctive optical components. This article outlines the general behaviour of such beams; how they can be used to rotate microscopic particles; how they interact with nonlinear materials; the role they play in atom-light interactions and how the rotation of such beams results in a measurable frequency shift.     

Conservation of angular momentum, transverse shift, and spin Hall effect in reflection and refraction of an electromagnetic wave packet

We present a solution to the problem of reflection and refraction of a polarized Gaussian beam on the interface between two transparent media. The transverse shifts of the beams' centers of gravity are calculated. They always satisfy the total angular momentum conservation law for beams, but, in general, do not satisfy the conservation laws for individual photons as a consequence of the lack of the "which path" information in a two-channel wave scattering. The field structure for the reflected and refracted beams is analyzed. In the scattering of a linearly polarized beam, photons of opposite helicities are accumulated at the opposite edges of the beam: this is the spin Hall effect for photons, which can be registered in the cross-polarized component of the scattered beam.     

光在Metasurface中的自旋-轨道相互作用

探讨了光在Metasurface中的自旋-轨道相互作用, 理论分析了Metasurface 对圆偏振和线偏振光的转换. 结果表明: 光与具有空间非均匀性和各向异性性的Metasurface的相互作用导致了自旋-轨道角动量的耦合. 采用Metasurface与螺旋相位片组合在一起进行了验证实验, 所得实验结果与理论分析完全一致. 这些结论有助于我们更加深入理解Metasurface 对光的操控.     

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.     

Separation of spin angular momentum in space-variant linearly polarized beam

We show that the spin angular momentum (SAM) flux in a space-variant linearly polarized beam can be separated in the focal plane. Such a beam carries only orbital angular momentum (OAM) and develops a net SAM flux upon focusing. The radial splitting of the SAM flux density is mediated by the phase vortex (or OAM) and can be controlled by the topological charge of the phase vortex. Optical trapping experiments verify the separation of the SAM flux density. The proposed approach enriches the manipulation of the angular momentum of light fields and inspires more designs of focus engineering, which would benefit optical micromanipulation of microscopic particles.     

A simple analytical model of the angular momentum transformation in strongly focused light beams

A ray-optics model is proposed to describe the vector beam transformation in a strongly focusing optical system. In contrast to usual approaches based on the focused field distribution near the focal plane, we use the beam pattern formed immediately after the exit aperture. In this cross section, details of the output field distribution are of minor physical interest but proper allowance is made for transformation of the beam polarization state. This enables the spin and orbital angular momentum representations to be obtained, which are valid for any cross section of the transformed beam. Simple analytical results are available for a transversely homogeneous, circularly polarized incident beam confined by a circular aperture. Variations of the spin and orbital angular momenta of the output beam with change of the focusing strength are analyzed. The analytical results are in good qualitative and reasonable quantitative agreement with the results of numerical calculations performed for the Gaussian and Laguerre-Gaussian beams. The model supplies an efficient and physically transparent means for qualitative analysis of the spin-to-orbital angular momentum conversion. It can be generalized to incident beams with complex spatial and polarization structure.     

Electro-optically forbidden or enhanced spin-to-orbital angular momentum conversion in a focused light beam

We demonstrate that the conversion of spin-to-orbital angular momentum in a focused vectorial light beam can be forbidden or enhanced by the electric-field-erased or increased spatial anisotropy of a uniaxial crystal undergoing the Pockels effect. A focused right-handed circularly polarized quasi-Gaussian beam incident on an electro-optic crystal strontium barium niobate is taken to illustrate the effect, and a conversion-forbidden electric field E(0)=-16.87 kV/cm is found. Of special interest is that single photons generated in this effect exhibit an entanglement of 2 deg of freedom of spin and orbital angular momentum, and it is electro-optically controllable.     

Transverse spin structure of the nucleon from lattice-QCD simulations

We present the first calculation in lattice QCD of the lowest two moments of transverse spin densities of quarks in the nucleon. They encode correlations between quark spin and orbital angular momentum. Our dynamical simulations are based on two flavors of clover-improved Wilson fermions and Wilson gluons. We find significant contributions from certain quark helicity flip generalized parton distributions, leading to strongly distorted densities of transversely polarized quarks in the nucleon. In particular, based on our results and recent arguments by Burkardt [Phys. Rev. D 72, 094020 (2005)], we predict that the Boer-Mulders function h(1/1), describing correlations of transverse quark spin and intrinsic transverse momentum of quarks, is large and negative for both up and down quarks.     

Optical forces and torques in nonuniform beams of light

The spin angular momentum in an elliptically polarized beam of light plays several noteworthy roles in optical traps. It contributes to the linear momentum density in a nonuniform beam, and thus to the radiation pressure exerted on illuminated objects. It can be converted into orbital angular momentum, and thus can exert torques even on optically isotropic objects. Its curl, moreover, contributes to both forces and torques without spin-to-orbit conversion. We demonstrate these effects experimentally by tracking colloidal spheres diffusing in elliptically polarized optical tweezers. Clusters of spheres circulate deterministically about the beam's axis. A single sphere, by contrast, undergoes stochastic Brownian vortex circulation that maps out the optical force field.     

Spin-orbit interaction and evolution of optical eddies in perturbed weakly directing optical fibers

The transformation of the angular momentum of an optical eddy in a weakly directing perturbed optical fiber is analyzed within the spin-orbit operator representation. The case of fibers with anisotropy of the core and cladding materials and the case of fibers with an elliptic cross section are considered. The spectrum of polarization corrections to the scalar propagation constant is determined for fibers of two types. For both the strongly anisotropic and elliptic fibers, the spin angular momentum of the linearly polarized LV eddy is suppressed and the orbital angular momentum is characterized by simple oscillations with a beating length dependent only on the spin-orbit parameter of an unperturbed fiber. The orbital and spin angular momenta of the circularly polarized CV eddy in the anisotropic fiber interchange in the elliptic fiber. The orbital angular momentum can be completely restored in the strongly anisotropic fiber, whereas only the spin angular momentum is completely restored in the elliptic fiber.