Transverse Spin Angular Momentum Research Articles

Tight focusing of the vector optical field with polarization varying along complex curves of the Poincaré sphere.

Different from the scalar optical field with spatially uniform polarization, the vector optical field exhibits inhomogeneous distribution of polarization on the cross section. Manipulating the variation of polarization in a single optical beam is important to acquire a flexible and controllable focused optical field. Previous studies mainly focused on the vector optical field with its polarization varying along a circular trajectory of the Poincaré sphere. Here, we demonstrate the tight focusing behaviors of the vector optical field with the polarization varying along complex curves of the Poincaré sphere, which is generated by the joint modulation of azimuthal phase and amplitude distributions of orthogonally polarized components. The longitudinal polarization component with a multipolar pattern in rotational symmetry can be achieved with similar distribution of the total focused field. The transverse and longitudinal spin angular momentum distributions in the focal space are discussed. Approximately pure transverse spin angular momentum can be constructed and manipulated in the focal space, which provides the possibility to manipulate the 3D spin flux for the applications of nano and spin photonics.

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

AbstractThe 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.

Advances in light transverse momenta and optical lateral forces

Harnessing linear and angular momenta of light is one of the cornerstones in modern optics and has found tremendous applications in optical circuits, particle manipulation, metrology, quantum information processing, etc. Emerging theoretical protocols and experimental explorations have created a surge of interest in light lateral momenta and forces, which are perpendicular to the light wave propagation direction. However, there is yet a lack of a comprehensive and holistic overview of transverse momenta (both linear and angular) as well as of optical lateral forces (OLFs). In this article, we first review the most recent transverse momenta including the transverse spin angular momentum, optical skyrmions, as well as lateral momenta from directional side scattering, spin–orbit interaction, and surface plasmon polaritons. Since optical forces result from the momentum exchange between light and matter, the transverse momentum consequently gives rise to intriguing OLFs, which is the second topic of this article. Additional non-trivial lateral forces that combine optics with other effects from thermodynamics, electricity, and microfluidics, are also discussed. It should be emphasized that these momenta and forces ubiquitously exist in a broad range of optical phenomena and have often been neglected due to their unpredicted underlying physics and shortage of experimental means, especially prior to the last decade.

Customization and Information Encoding of Longitudinally Polarized Light Fields

The tightly focused structured light field displays a non‐negligible component of the electric field in the direction of propagation, i.e., the longitudinal light field. The longitudinal light field results in various novel optical phenomena, such as transverse spin angular momentum and 3D topological light fields. However, it remains a challenge to generate customized longitudinal light fields. Here, based on inverse design theory, the longitudinal light field can be customized on demand under the tightly focusing condition, which allows to generate the longitudinal light field with controllable structured distribution for propagating waves or manipulate the complex structures for all the three components of the electric field. In experiment, an experimental system is built integrating the generation, customization, and detection of structured longitudinal light field, and the customization of the longitudinal light fields with various patterns is experimentally realized. The customized longitudinal light field structures may find applications such as information encoding, long‐distance light manipulation, and novel light–matter interactions. As an example, information encoding is realized by the structured longitudinal light fields.

The appearance and annihilation of the spin angular momentum for the multi-polar vector optical field in the focal plane

Vector optical fields (VOFs) with space-variant polarizations have attracted great attention in various areas, and the VOFs have been applied to study the spin angular momentum (SAM) of the photon, leading to many new effects and applications. Here, we propose the multi-polar coordinate and design and generate the multi-polar VOF (MP-VOF) with an arbitrary even number of singularities. We further find that the SAM appears or annihilates in the focal plane, which means the processes of “0-1” and “1-0” of the SAM can be accomplished in propagation. The corresponding theoretical explanation is also provided, indicating that the SAM appears or annihilates due to the interaction of the fields at central symmetric positions on the wavefront. Moreover, the appearance of transverse SAM (also known as the “photonic wheel”) can also be achieved in tight focusing cases. In this way, we can achieve three cases of SAM under different conditions, including purely longitudinal SAM, purely transverse SAM, and three-dimensional SAM with both components. This new kind of MP-VOF significantly enriches the family of VOFs and provides new insights in studying the focal behavior of the SAM, which can be applied in realms such as spin absorbing particles in a more flexible way.

Spin-orbit interactions in plasmonic crystals probed by site-selective cathodoluminescence spectroscopy.

The study of spin-orbit coupling (SOC) of light is crucial to explore the light-matter interactions in sub-wavelength structures. By designing a plasmonic lattice with chiral configuration that provides parallel angular momentum and spin components, one can trigger the strength of the SOC phenomena in photonic or plasmonic crystals. Herein, we explore the SOC in a plasmonic crystal, both theoretically and experimentally. Cathodoluminescence (CL) spectroscopy combined with the numerically calculated photonic band structure reveals an energy band splitting that is ascribed to the peculiar spin-orbit interaction of light in the proposed plasmonic crystal. Moreover, we exploit angle-resolved CL and dark-field polarimetry to demonstrate circular-polarization-dependent scattering of surface plasmon waves interacting with the plasmonic crystal. This further confirms that the scattering direction of a given polarization is determined by the transverse spin angular momentum inherently carried by the SP wave, which is in turn locked to the direction of SP propagation. We further propose an interaction Hamiltonian based on axion electrodynamics that underpins the degeneracy breaking of the surface plasmons due to the spin-orbit interaction of light. Our study gives insight into the design of novel plasmonic devices with polarization-dependent directionality of the Bloch plasmons. We expect spin-orbit interactions in plasmonics will find much more scientific interests and potential applications with the continuous development of nanofabrication methodologies and uncovering new aspects of spin-orbit interactions.

Time-Varying Optical Spin-Orbit Interactions in Tight Focusing of Self-Torqued Beams

Self-torque has recently been observed as a novel property of light that features time-varying orbital angular momentum (OAM) along a light pulse. This property offers an additional degree of freedom for manipulating light fields and light-matter interactions on ultrafast time scales. In this work, we theoretically study the self-torque's role in modulating tightly focused fields and reveal spin-orbit interactions (SOIs) in the focused fields using time-dependent vectorial diffraction theory. It is found that time-varying SOIs occur between the spin angular momentum (SAM), intrinsic OAM and extrinsic OAM. Specifically, the spin-to-orbit conversion, orbit-to-local-spin conversion, and optical spin-Hall effect are observed in the focused self-torqued beams. In particular, when the incident beams are circularly polarized, the time-dependent transverse SAM distributions will appear in the focal plane. Moreover, the self-torque of the focused light fields can be controlled via spin-to-orbit conversion. These observations could benefit potential applications in ultrafast light field modulation, microscopy, and optical manipulation.

Nonreciprocity in optical fiber radiation modes induced by spin–momentum locking

Nonreciprocity in optical fibers are opening new avenues for fields such as quantum computing and quantum photonics. In this study we explore the chiral properties of the radiation modes of optical fibers and show that whispering gallery mode resonances, as part of radiation modes, carry specific transverse spin angular momenta. The transverse spin angular momentum is different for forward and backward propagating radiation modes, hence indicating spin–momentum locking. As a result of spin–momentum locking, a nonreciprocity in the emission coupling of an atomic transition with a specific spin into the forward and backward propagating modes is observed. Modeling an atomic transition by a classical dipole that rotates clockwise or anticlockwise, we optimize the position of the dipole within the optical fiber to achieve maximum nonreciprocity between the coupling of the dipole emission into the forward or backward propagating mode. We find near-perfect nonreciprocity in both radiation and guided modes and further outline the fiber diameter and dipole position to achieve this state. This study not only shows the rich physics of fiber radiation modes within the context of light–matter interaction but also complements previous studies of nonreciprocity in subwavelength waveguides.

Elastic Spin and Orbital Angular Momenta.

Motivated by recent theoretical and experimental interest in the spin and orbital angular momenta of elastic waves, we revisit canonical wave momentum, spin, and orbital angular momentum in isotropic elastic media. We show that these quantities are described by simple universal expressions, which differ from the results of Chaplain etal. [Phys. Rev. Lett. 128, 064301 (2022)PRLTAO0031-900710.1103/PhysRevLett.128.064301] and do not require separation of the longitudinal and transverse parts of the wave field. For cylindrical elastic modes, the normalized z component of the total (spin+orbital) angular momentum is quantized and equals the azimuthal quantum number of the mode, while the orbital and spin parts are not quantized due to the spin-orbit geometric-phase effects. In contrast to the claims of the above article, longitudinal, transverse, and "hybrid" contributions to the angular momenta are equally important in general and cannot be neglected. As another example, we calculate the transverse spin angular momentum of a surface Rayleigh wave.

Manipulating Transverse Spin Angular Momentum with Symmetrically Modulated Hybridly Polarized Vector Optical Field

Transverse spin angular momentum (SAM) of photon, also known as ‘photonic wheel’, has attracted much attention, owing to its extraordinary properties and broad application prospect. Thus, it is essential to flexibly manipulate the transverse SAM in order to satisfy different needs. In this article, we design and generate a new kind of symmetrically modulated hybridly polarized vector optical field (SM-HP-VOF), and pure transverse SAM can be achieved based on the tightly focused SM-HP-VOF. Through adjusting the parameters of the SM-HP-VOF, the shape, intensity, and symmetry of the transverse SAM can be modulated. Moreover, by adding a segmented vortex phase distribution to the SM-HP-VOF, the transverse SAM becomes more concentrated and stronger, indicating that the orbital angular momentum can be a catalyst in modulating transverse SAM. Such results can provide a new avenue in studying and modulating transverse SAM, which would have potential applications in various areas including chip optical circuitry, optical quantum computing, and optical trapping and manipulation.

Spin‐Controlled Reconfigurable Excitations of Spoof Surface Plasmon Polaritons by a Compact Structure

AbstractThe photonic spin Hall effect (SHE) arises from the spin–orbit interaction of lights and plays an important role in light–matter interactions. The phenomenon of spin‐momentum locking validates photonic SHE with unprecedented abilities in wave manipulation. Here, the directional coupling and spin‐momentum locking in spoof surface plasmon polaritons (SSPP) are demonstrated. The transverse spin angular momentum in SSPP is calculated using effective medium theory and the study shows the spin direction is inherently locked to the propagation direction, thus manifesting the spin–orbit interaction of electromagnetic (EM) waves. The spin‐momentum locking is further verified by projecting linearly and circularly polarized waves onto a scatterer‐SSPP structure. It is observed that the helicity of the incident EM wave governs the propagation direction of excited SSPP modes and the directional coupling originates from constructive and destructive interferences of two orthogonal modes. Reconfigurable transmissions of SSPPs are further demonstrated. The proposed design can find applications in reconfigurable sensors, antennas, and power dividers. This approach demonstrates the spin‐momentum locking in SSPPs and introduces new degrees of freedom to manipulate SSPPs by engineering the helicity and interference of EM waves.

On-chip spin-orbit locking of quantum emitters in 2D materials for chiral emission

Light carries both spin angular momentum (SAM) and orbital angular momentum (OAM), which can be used as potential degrees of freedom for quantum information processing. Quantum emitters are ideal candidates towards on-chip control and manipulation of the full SAM–OAM state space. Here, we show coupling of a spin-polarized quantum emitter in a monolayer W S e 2 with the whispering gallery mode of a S i 3 N 4 ring resonator. The cavity mode carries a transverse SAM of σ = ± 1 in the evanescent regions, with the sign depending on the orbital power flow direction of the light. By tailoring the cavity–emitter interaction, we couple the intrinsic spin state of the quantum emitter to the SAM and propagation direction of the cavity mode, which leads to spin–orbit locking and subsequent chiral single-photon emission. Furthermore, by engineering how light is scattered from the WGM, we create a high-order Bessel beam which opens up the possibility to generate optical vortex carrying OAM states.

Relativistic high-order harmonic generation of spatiotemporal optical vortices

It is well known that light can possess spin angular momentum (SAM) and orbital angular momentum (OAM) in the longitudinal direction. Interesting novel light with transverse SAM or OAM has also been discovered recently, with the latter being called spatiotemporal optical vortices. Here we present a route to generate spatiotemporal optical vortices by means of high harmonic generation from relativistic laser plasma interactions. Three-dimensional particle-in-cell simulations show the evidence of edge dislocations in wave front structures and circulating energy flow in space-time. Further calculations of the SAM, OAM and total angular momentum confirm the harmonics carrying pure transverse OAM with noninteger values. The results open up a possibility to generate intense spatiotemporal optical vortices in the extreme ultraviolet region with attosecond duration.

Manipulating the transverse spin angular momentum and Belinfante momentum of spin-polarized light by a tilted stratified medium in optical tweezers

In the recent past, optical tweezers incorporating a stratified medium have been exploited to generate complex translational and rotational dynamics in mesoscopic particles due to the coupling between the spin and orbital angular momentum of the light, generated as a consequence of the tight focusing of light by a high numerical aperture objective lens into the stratified medium. Here, we consider an optical tweezers system with a tilted stratified medium (direction of stratification at an angle with the axis of the incident beam), and show that for input circularly polarized Gaussian beams, the resulting spin-orbit interaction deeply influences the generation of transverse spin angular momentum (TSAM) and Belinfante momentum of light, and allows additional control on their magnitude. Importantly, the TSAM generated in our system consists of both the orthogonal components, which is in sharp contrast to the case of evanescent waves and surface plasmons, where only one of the TSAM components are generated. The broken symmetry due to the tilt ensures that, depending upon the helicity of the input beam, the magnitude of the mutually orthogonal components of the TSAM depend entirely on the tilt angle. This may prove to be an effective handle in exotic spin-controlled manipulation of particles in experiments.

Transversely oriented cylindrically polarized optical fields.

Cylindrical vector (CV) beams have nonuniform polarization vector distribution with a singularity line directed along the optical axis. In this paper, we propose a method to synthesize transversely oriented cylindrically polarized optical fields in the focal region with a singularity line perpendicular to the optical axis. The scheme is based on the time-reversal method, the vectorial diffraction theory, and the 4Pi optical configuration. Both transversely oriented radially polarized and azimuthally polarized optical fields are demonstrated. The superposition of transverse cylindrically polarized optical fields leads to a peculiar distribution carrying controllable transverse spin angular momentum (SAM) and transverse orbital angular momentum (OAM) that may find applications in optical tweezing, light-matter interaction, and unidirectional beam propagation excitation.

Controlled transfer of transverse orbital angular momentum to optically trapped birefringent microparticles

We report on the observation and measurement of the transfer of transverse angular momentum to birefringent particles several wavelengths in size. A trapped birefringent particle is much larger than the nano-particles systems for which transverse angular momentum was previously investigated. The larger birefringent particle interacts more strongly with both the trapping beam and fluid surrounding it. This technique could be used to transfer transverse angular momentum for studies of diverse micro-systems. Thus, it can be used for investigation of the dynamics of complex fluids in 3D as well as for shear on cell mono-layers. The trapping of such a particle with highly focused light is complex and can lead to the emergence of effects such as spin--orbit coupling. We estimate the transfer of spin angular momentum using Stokes measurements. We outline the physics behind the construction of the beam used to control the particles, perform quantitative measurement of transverse spin angular momentum transfer, as well as demonstrate the generation of fluid flow around multiple rotation axes.

Understanding of transverse spin angular momentum in tightly focused linearly polarized vortex beams.

Spin angular momentum (SAM) is widely used in spin-dependent unidirectional optical interfaces, optical manipulation, integrated optical signal processing, laser structuring and other fields, but its physical mechanism has not been fully understood so far. In this work, we investigate the three-dimensional (3D) SAM in tightly focused x-polarized first-order vortex beams from the perspectives of light field itself, phase distribution, and focusing propagation. It is shown that the distribution of three orthogonal components of SAM at the focal plane has pseudo two-fold rotational symmetry, because the cycloidal rotation of the electric field of the tightly focused vortex beam is opposite. The 3D SAM distribution in the focal region is visualized by mapping the 3D distribution of state of polarization (SoP). In addition, a principle experimental method for identifying the transverse SAM by using the direction of particle's rotation axis in optical tweezers is proposed.

Spiraling light: from donut modes to a Magnus effect analogy

Abstract The insight that optical vortex beams carry orbital angular momentum (OAM), which emerged in Leiden about 30 years ago, has since led to an ever expanding range of applications and follow-up studies. This paper starts with a short personal account of how these concepts arose. This is followed by a description of some recent ideas where the coupling of transverse orbital and spin angular momentum (SAM) in tightly focused laser beams produces interesting new effects. The deflection of a focused light beam by an atom in the focus is reminiscent of the Magnus effect known from aerodynamics. Momentum conservation dictates an accompanying light force on the atom, transverse to the optical axis. As a consequence, an atom held in an optical tweezer will be trapped at a small distance of up to λ/2π away from the optical axis, which depends on the spin state of the atom and the magnetic field direction. This opens up new avenues to control the state of motion of atoms in optical tweezers as well as potential applications in quantum gates and interferometry.

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.

Purely transverse spin angular momentum modulated by the singularity phase

We present the hybrid polarized vector optical fields (HP-VOFs) with multi singularities, and find that the purely longitudinal spin angular momentum (SAM) can partially transform into transverse SAM in tight focusing process. The concept of singularity phase is further proposed, providing additional degrees of freedom in modulating polarization configuration on the wave front. After introducing the singularity phase, purely transverse SAM is achieved for the tightly focused HP-VOF with multi singularities, indicating that the singularity phase can play a role as a catalyst to generate the purely transverse SAM in the tight focusing process. This is a new method to achieve purely transverse SAM, which would have potential applications in various areas including chip optical circuitry, optical quantum computing, and optical manipulation.