Spin Angular Momentum Density Research Articles

Controlling the Abrupt Autofocusing of Circular Airy Vortex Beam via Uniaxial Crystal

The propagation of many kinds of structured light beams in uniaxial crystal has been investigated. However, the investigation of the evolution of these structured light beams after the uniaxial crystal is lacking. In this paper, an evolution formula of a light beam after passing through a uniaxial crystal is derived. Based on the formula, controlling the autofocusing of a circular Airy vortex beam (CAVB) via a uniaxial crystal is studied. It is found that a uniaxial crystal can prolong the focal length of the autofocusing. By changing the crystal length, the relative weight of the left- and right-hand circular polarization components and the relative value between the orbital and spin angular momentum densities of the beam’s focal plane can be adjusted flexibly. In addition, other optical elements can be inserted between the crystal and the focus to further adjust the focal plane field distribution. The influences of inserting x- and y-polarization polarizers on the intensity distribution are calculated as examples.

Effect of optical spatial coherence on localized spin angular momentum density in tightly focused light [Invited

Optical coherence is one of the most fundamental characteristics of light and has been viewed as a powerful tool for governing the spatial, spectral, and temporal statistical properties of optical fields during light-matter interactions. In this work, we use the optical coherence theory developed by Emil Wolf as well as the Richards-Wolf's vectorial diffraction method to numerically study the effect of optical coherence on the localized spin density of a tightly focused partially coherent vector beam. We find that both the transverse spin and longitudinal spin, with the former induced by the out-of-phase longitudinal field generated during strong light focusing and the latter induced by the vortex phase in the incident beam, are closely related to the optical coherence of the incident beam, i.e., with the decrease of the transverse spatial coherence width of the incident beam, the magnitude of the spin density components decreases as well. The numerical findings are interpreted well with the two-dimensional degrees of polarization between any two of the three orthogonal field components of the tightly focused field. We also explore the roles of the topological charge of the vortex phase on enhancing the spin density for the partially coherent tightly focused field. The effect of the incident beam's initial polarization state is also discussed.

Near-Field Behaviors of Internal Energy Flows of Free-Space Electromagnetic Waves Induced by Electric Point Dipoles

Both orbital and spin energy fluxes constitute the internal flows decomposed from a Poynting vector. For generic electromagnetic waves propagating through source-free media, these energy fluxes are quadratic in field variables so that their properties are not easily predictable. Notwithstanding, their near-field behaviors play important roles in nanoscale photonics. For time-oscillatory fields, we found two hitherto-overlooked distinctions between the two internal flows. The first is an unequal level between them because the vorticity of an orbital energy flux plays a role comparable to a spin energy flux itself. The second is regarding the electric-magnetic dual symmetry in handling the two internal flows, whence the reactive helicity plays a role as important as the electromagnetic helicity. By helicity conservation, an inter-electric-magnetic transport is possible for the spin angular momentum density, while the electric and magnetic constituents of orbital energy fluxes admit only respective intra-electric and intra-magnetic transports. We have tested the validities of all these claims by exemplarily taking the electromagnetic fields induced by an electric point dipole, either a linear or a circular one. We have thus made new contributions not only in deriving explicit forms of the internal energy flows but also in revealing the magnetic activities hidden under the electromagnetic waves induced by electric point dipoles.

Diffraction of an off-axis vector-beam by a tilted aperture

Manifestations of orbital angular momentum induced effects in the diffraction of a radially polarized vector beam by an off-axis tilted aperture are studied both experimentally and theoretically. Experiments were carried out to extract the degree of circular polarization, which was shown to be proportional to the on-axis component of the spin angular momentum density. We report a clear separation of the regions of dominance of the right and left circular polarizations associated with positive and negative topological charges respectively, which is reminiscent of the standard vortex-induced transverse shift, albeit in the diffraction scenario. The experimental results are supported by model simulations and the agreement is quite satisfactory. The results are useful to appreciate the orbit-orbit related effects due to unavoidable misalignment problems (especially for vortex beams).

Dependence of spin angular momentum density on helicity of ellipse field singularities

We numerically demonstrate the role of helicity of ellipse field singularities on spin angular momentum density. We consider both bright and dark ellipse field singularities to demonstrate this effect. It is found that as the helicity of C-point inverted, the spin angular momentum density undergoes 180° rotation. In case of bright C-point the z-component of the spin angular momentum density has always a central maxima irrespective of value of polarization singularity index, whereas for dark C-points there is always a central minima in the z-component of the spin angular momentum density. The number of minima around the central dark point in the longitudinal component for dark C-point singularity with C-point index (IC) is given by (|2IC−2|).

Near-field analysis of electromagnetic chirality in the Mie scattering by a dielectric sphere

We revisit the Mie scattering in view of electromagnetic chirality, especially in the near field of a scattering sphere. To this goal, we take the simplest two-dielectric system where both an embedding medium and an embedded sphere are loss-free, non-magnetic, and dielectric. For a given linearly polarized incident wave, the net chirality should vanish when integrated over the whole space. The reactive chirality indicating the divergence-full spin angular momentum density shows an analogous behavior. Meanwhile, the electromagnetic chirality obtained in response to a circularly polarized incident wave exhibits distinct super-chiral behaviors. In addition, we examined key bilinear parameters for another incident wave, where two orthogonal linearly polarized waves are combined without a phase delay.

The zero helicity and chirality of optical vortices

We show that any uniformly linearly-polarised paraxial vortex mode carrying orbital angular momentum (OAM) has zero spin angular momentum (SAM) density, but exhibits non-zero helicity density distributions. Such a mode then possesses chirality as confirmed by experiment and so can engage with chiral matter. We show that confining the treatment for the general paraxial fields only to leading order leads directly to agreement of our theory with the experimental results, provided we ensure that crucially the paraxial fields obey duality. We find that the space integral of the helicity and chirality densities vanish identically for all such optical vortex modes without specifying the kind of mode. These generally applicable properties of optical vortex modes carrying orbital angular momentum thus assert that without optical spin due to elliptical wave polarisation of index σ, an optical vortex alone cannot possess total helicity, even though it always exhibits non-zero helicity density distributions.

Spin Hall effect of fractional order radially polarized beam in its tight focusing

Different from the traditional radially polarized beams, the fractional order radially polarized beam possess the symmetry broken structure of the polarization state distribution. The symmetry broken of the optical beams’ intrinsic structure can lead to the spin–orbit coupling of light. In this paper, we investigate the tight focusing of the fractional order radially polarized beam and show some interesting phenomena induced by the symmetry broken structure of the polarization state distribution. Firstly, the intensity and the spin angular momentum density are split in the focal plane, and the focal field intensity distribution can be controlled (split or focused) by modulating the initial phase of the polarization state. Furthermore, just like the spin angular momentum, the orbital angular momentum density also is split into two opposite parts (positive and negative). Though, the evolutions of the spin and the orbital angular momentum are different: as the change of the initial phase of the polarization state, the spin angular momentum distribution just is rotated slightly, yet the orbital angular momentum distribution is reversed. All these phenomena can be considered as the manifestations of the spin Hall effect of the fractional order radially polarized beam. Our results provide further potential applications of the vector beams in the focal field shaping.

Ultrafast Spin‐to‐Orbit and Orbit‐to‐Local‐Spin Conversions of Tightly Focused Hybridly Polarized Light Pulses

Spin–orbit interaction (SOI) has provided a new viable roadmap for the development of spin‐based photonics devices. However, existing strategies to control the SOI focus commonly on tailoring the spatial dimension of light fields yet neglecting the inherent temporal one. Herein, ultrafast temporal effects on both spin‐to‐orbit and orbit‐to‐local‐spin conversions based on the time‐assistant vectorial diffractive theory and the fast Fourier transformation are first presented. Such interconversions depend upon whether the incident hybridly vectorial light pulse carries vortex phase or not in a single high numerical aperture geometry. For the case of the absence of vortex phase, it is found that it enables orbit angular momentum‐carrying transverse component fields, and the resultant orbit angular momentum embedded within focused light fields remains constantly revolving as time elapses, which indicates that the controllable spin‐to‐orbit conversion occurs. By contrast, it is revealed that hybridly polarized vectorial‐vortex light pulses allow access to the locally excited circular polarization at the focus, and this induced local circular polarization is independent of ultrafast varying time, whereas the resulting spin angular momentum density components experience the alternation between the appearance and annihilation over time, thus giving rise to the tunable orbit‐to‐local‐spin conversion. These exotic ultrafast interconversions not only breathe a new life into the area of ultrafast photonics, but refresh our understanding on the paradigm of photonic SOI.

Harnessing of inhomogeneously polarized Hermite–Gaussian vector beams to manage the 3D spin angular momentum density distribution

Abstract We propose vector modes based on inhomogeneously polarized Hermite–Gaussian (HG) vector beams, providing complete structural conservation of the beams during propagation. Like uniformly polarized mode beams, these beams provide structural stability (or invariance) of both the intensity and the polarization state, in turn ensuring the stability of other field characteristics, including the angular momentum. We determine the conditions imposed on the HG mode composition in the transverse components of the electromagnetic field in order to control the three-dimensional characteristics of the field, such as intensity, polarization, and spin angular momentum (SAM). For the visual analysis of the polarization state of inhomogeneously polarized beams, we use the transverse distribution of the vector of three Stokes parameters. The correspondence of the third Stokes parameter to the distribution of the longitudinal component of the SAM is used for experimental measurements. The theoretical analysis is clearly illustrated by numerical simulations and confirmed by experimental results.

Optical spin sorting chain.

Transverse spin angular momentum of light is a key concept in recent nanophotonics to realize unidirectional light transport in waveguides by spin-momentum locking. Herein we theoretically propose subwavelength nanoparticle chain waveguides that efficiently sort optical spins with engineerable spin density distributions. By arranging high-refractive-index nanospheres or nanodisks of different sizes in a zigzag manner, directional optical spin propagation is realized. The origin of efficient spin transport is revealed by analyzing the dispersion relation and spin angular momentum density distributions, being attributed to guided modes that possess transverse spin angular momenta. In contrast to conventional waveguides, the proposed asymmetric waveguide can spatially separate up- and down-spins and locate one parity inside and the other outside the structure. Moreover, robustness against bending the waveguide and its application as an optical spin sorter are presented. Compared to previous reports on spatial engineering of local spins in photonic crystal waveguides, we achieved miniaturization of the entire footprint down to the subwavelength scale.

Focal field properties of toroidal double-mode vector beams

Integer-order vector beams maintain their polarization properties under the paraxial diffraction condition. Fractional-order vector beam with irregular phase change that leading to changeable focusing properties has aroused huge interest research. Herein, we proposed and experimentally generated a double-mode concentric annular fractional vector beam. Based on the modal superposition, the intensity and spin angular momentum (SAM) density are characterized by periodic changes from rotational symmetry to axial symmetry as the topological coefficient increases. These results reveal that the fractional topological coefficients have a great potential degree of freedom. The experimental results are exploited in this work to emphasize the important connection between fractional coefficient and SAM density.

Influence of initial phase of polarization on tight focusing of vector beam

Generally, the influence of initial phase of polarization distribution of incident vector beams always is ignored in its tight focusing, because it just induce the whole rotation of polarization distribution. In this paper, we show some distinctive effects induced by the initial azimuthal phase of polarization distribution in the tight focusing of radially polarized and azimuthal-variant hybrid vector beams. For these two types of vector beams, the initial azimuthal phase of polarization distribution induces two types rotation, the whole polarization rotation and the combined polarization rotation including the polarization distribution rotation and phase difference rotation, respectively. Furthermore, two methods are presented for modulating energy flow density and spin angular momentum density in the focal region, the synchronous and asynchronous rotation, which denote two polarization unit vectors with the same or different initial phase. Our results indicate the light–matter interaction can be induced by the polarization distribution rotation of incident vector beams in its tight focusing, and provide a possible connection with the rotational Doppler effect of optical vector beams.

Spin density in partially coherent surface-plasmon-polariton vortex fields

We examine the spin angular momentum (SAM) density associated with the recently introduced [Phys. Rev. A 100, 053833 (2019)], partially coherent surface-plasmon-polariton (SPP) vortex fields at a metal-air interface. We show that the vortices appearing in such structured SPP fields induce a SAM density both in the interface plane and in the direction normal to the interface. We find that the radial and azimuthal SAM densities are caused solely by the SPP electric-field correlations. However, besides the intrinsic spin component induced by the complex SPP wave vector, the azimuthal SAM density remarkably carries also a spin component created by the elementary SPPs comprising the partially coherent vortex field. The normal SAM density, on the other hand, arises mainly due to the SPP magnetic-field correlations. Our analysis specifically demonstrates that the state of coherence of the partially coherent SPP vortex field plays an essential role in shaping the SAM density distributions. Our findings can find applications to near-field particle manipulation and in spin-based integrated photonic circuit design.

Real spin angular momentum and acoustic spin torque in a topological phononic crystal

The topological one-way waveguide mode of the acoustic wave has recently been demonstrated in various meta-structure systems. Here, we show that in a topological phononic crystal with a symmetry-broken acoustic unit cell, the topological state possesses not just a “spin-like” pseudospin mode but also real spin angular momentum. By rotating the double-square units, the band of the phononic crystal will become inverse and induce both topological phase transition and spin angular momentum reversal. As such, by putting two topologically different systems together, the spin angular momentum dependent one-way interface modes can be selectively excited by acoustic spin sources, exhibiting robust transport protected by tight spin-momentum locking. The spin angular momentum density distribution in the unit cell and edge states shows that in addition to the pseudospin, there is a strong correlation between the real spin angular momentum and topological properties in this acoustic system, producing the topologically selective acoustic torque. Revealing the real spin angular momentum and associated acoustic spin torque properties of these topological phononic and acoustic systems will give people a more general understanding about symmetric breaking wave systems and help people to explore more potential applications of acoustic spins in various topological systems.

Comment on “Canonical momentum, angular momentum, and helicity of circularly polarized Airy beams” by Y. Hui et al. [Phys. Lett. A 384 (2020) 126284

In this comment we re-examine the problem and obtain new results for the canonical momentum density, orbital angular momentum density and spin angular momentum density of elliptically polarized Airy beams in the paraxial approximation. In contrast to the results of [1] the canonical momentum density and orbital angular momentum density do not depend on beam polarization.

Bipolar-variant spin angular momentum and its evolution in a tight focusing process

We design and generate the bipolar-variant spin angular momentum (SAM) carried by vector optical field and theoretically investigate the evolution of the bipolar-variant SAM in the tight focusing process. It is found that the longitudinal SAM density annihilates and the purely transverse SAM density appears in the focal plane, and the evolution of the complex singularities of SAM into $V$-point singularities is also studied. We further extend the study to general bipolar-variant SAM, and give the theoretical explanation of the annihilation and appearance of different components of SAM density. We believe the presentation of the bipolar-variant SAM can greatly enrich the study of SAM as well as the singular optics. Meanwhile, the evolution of the bipolar-variant SAM in the focusing process is interesting and important in revealing the focal properties of SAM of the photon, and the purely transverse SAM in the focal plane with a spin axis orthogonal to the propagation direction opens up avenues in optical trapping and manipulation, especially for optically induced rotations.

Continuity equation for spin angular momentum in relation to optical chirality

Spin and orbital angular momenta are separately observable properties of light. Both of them can interact with matter, causing an exchange between each other and generating an optical torque on the matter. However, thus far, we have been unable to separately discuss the transfer of the spin and orbital angular momenta or the origin of the optical torques with regard to them. Here, we consider the optical chirality density and propose an approach to analyzing the transfer of spin and orbital angular momenta separately by considering this property. Our approach is based on a continuity equation for spin angular momentum density. This equation is derived from an extended proportional relation between the chirality flux density and spin angular momentum density in sources-added space. Our findings will greatly facilitate the study of angular momentum interaction between light and matter.

Direct observation of the effects of spin dependent momentum of light in optical tweezers

We demonstrate that tight focusing of a circularly polarized Gaussian beam in optical tweezers leads to spin-momentum locking—with the transverse momentum density (Poynting vector) being helicity-dependent, while the transverse spin angular momentum density becomes independent of helicity. We further use a stratified medium in the path of the trapping beam in our optical tweezers setup to enhance the magnitude of the transverse momentum and the electric field intensity in the radial direction with respect to the beam axis and cause them to significantly overlap. This overlap allows us to experimentally observe the circular motion of a birefringent particle, trapped off-axis, in response to an input circularly polarized fundamental Gaussian beam carrying no intrinsic orbital angular momentum (OAM). The circular motion is dependent on the helicity of the input beam so that we can identify it as the signature of the elusive Belinfante spin in propagating light beams obtained in our optical tweezers configuration. Our results can be extended to beams carrying intrinsic OAM leading to simple routes for achieving complex manipulation of micro-machines or other mesoscopic matter using optical tweezers.

Vector Lissajous laser beams.

We consider a new type of vector beam, the vector Lissajous beams (VLB), which is of double order (p,q) and a generalization of cylindrical vector beams characterized by single-order p. The transverse components of VLBs have an angular relationship corresponding to Lissajous curves. A theoretical and numerical analysis of VLBs was performed, showing that the ratio and parity of orders (p,q) affect the properties of different components of the electromagnetic field (EF) (whether they be real, imaginary, or complex). In addition, this allows one to engineer the imaginary part of the longitudinal component of the electromagnetic field and control the local spin angular momentum density, which is useful for optical tweezers and future spintronics applications.