Spin-to-orbital angular momentum conversion in focusing, scattering, and imaging systems

Polarization-Addressable Optical Movement of Plasmonic Nanoparticles and Hotspot Spin Vortices

Spin-orbit coupling in nanoscale optical fields leads to the emergence of a nontrivial spin angular momentum component, transverse to the orbital momentum. In this study, we initially investigate how this spin-orbit coupling effect influences the dynamics in gold monomers. We observe that localized surface plasmon resonance induces self-generated transverse spin, affecting the trajectory of the nanoparticles as a function of the incident polarization. Furthermore, we investigate the spin-orbit coupling in gold dimers. The resonant spin momentum distribution is characterized by the unique formation of vortex and anti-vortex spin angular momentum pairs on opposite surfaces of the nanoparticles, also affecting the particle motion. These findings hold promise for various fields, particularly for the precision control in the development of plasmonic thrusters and the development of metasurfaces and other helicity-controlled system aspects. They offer a method for the development of novel systems and applications in the realm of spin optics.

Chiral nanoparticle separation and discrimination using radially polarized circular Airy vortex beams with orbital-induced spin angular momentum

We report orbit-induced localized spin angular momentum associated with optical spin-orbit interactions in tightly focused radially polarized circular Airy vortex beams and demonstrate their potential for separation and discrimination of chiral nanoparticles. We find that variations in spin angular momentum density endow these beams with positive and negative annular optical chirality density. Utilizing these extraordinary distributions, particles having different chirality parameters can be separated and discriminated by using two degrees of freedom, i.e., radial trapping position and azimuthal rotation. We also discuss the impacts of longitudinal optical force and topological charge on manipulating chiral particles. Additionally, we conduct a comparative analysis of the optical trapping of a non-chiral particle. Our work is expected to deepen the understanding of spin-orbit interactions and provide valuable insight into vortex beam interactions with chiral particles.

Fundamental symmetry origins in the chiral interactions of optical vortices

Recently, a variety of mechanisms have been discovered that extend the range of optical techniques for identifying and characterizing molecular chirality, beyond those associated with optical polarization. It is now evident that beams of light with a twisted wavefront, known as optical vortices, can also interact with chiral matter with a specificity determined by relative handedness. Exploring this chiral sensitivity of vortex light in its interactions with matter requires careful consideration of the symmetry properties that engage in such processes. Most of the familiar measures of chirality are directly applicable to either matter, or to light itself-but only to one or the other. To elicit the principles that determine the viability of distinctly optical vortex-based forms of chiral discrimination invites a more universal approach to symmetry analysis, as is afforded by the common, fundamental physics of CPT symmetry. Taking this approach supports a comprehensive and straightforward analysis to identify the mechanistic origins of vortex chiroptical interactions. Careful inspection of selection rules for absorption also elicits the principles governing any identifiable engagement with vortex structures, providing a reliable basis to ascertain the viability of other forms of enantioselective vortex interaction.

Confined Phase Singularities Reveal the Spin-to-Orbital Angular Momentum Conversion of Sound Waves

We identify an acoustic process in which the conversion of angular momentum between its spin and orbital form takes place. The interaction between an evanescent wave propagating at the interface of two immiscible fluids and an isolated droplet is considered. The elliptical motion of the fluid supporting the incident wave is associated with a simple state of spin angular momentum, a quantity recently introduced for acoustic waves in the literature. We experimentally observe that this field predominantly forces a directional wave transport circling the droplet's interior, revealing the existence of confined phase singularities. The circulation of the phase, around a singular point, is characteristic of angular momentum in its orbital form, thereby demonstrating the conversion mechanism. The numerical and experimental observations presented in this Letter have implications for the fundamental understanding of the angular momentum of acoustic waves, and for applications such as particle manipulation with radiation forces or torques, acoustic sensing and imaging.

Spin-dependent properties of optical modes guided by adiabatic trapping potentials in photonic Dirac metasurfaces

The Dirac-like dispersion in photonic systems makes it possible to mimic the dispersion of relativistic spin-1/2 particles, which led to the development of the concept of photonic topological insulators. Despite recent demonstrations of various topological photonic phases, the full potential offered by Dirac photonic systems, specifically their ability to emulate the spin degree of freedom-referred to as pseudo-spin-beyond topological boundary modes has remained underexplored. Here we demonstrate that photonic Dirac metasurfaces with smooth one-dimensional trapping gauge potentials serve as effective waveguides with modes carrying pseudo-spin. We show that spatially varying gauge potentials act unevenly on the two pseudo-spins due to their different field distributions, which enables control of guided modes by their spin, a property that is unattainable with conventional optical waveguides. Silicon nanophotonic metasurfaces are used to experimentally confirm the properties of these guided modes and reveal their distinct spin-dependent radiative character; modes of opposite pseudo-spin exhibit disparate radiative lifetimes and couple differently to incident light. The spin-dependent field distributions and radiative lifetimes of their guided modes indicate that photonic Dirac metasurfaces could be used for spin-multiplexing, controlling the characteristics of optical guided modes, and tuning light-matter interactions with photonic pseudo-spins.

Symmetry-breaking enabled topological phase transitions in spin-orbit optics

The topological phase transitions (TPT) of light refers to a topological evolution from one type of spin-orbit interaction to another, which has been recently found in beam scattering at optical interfaces and propagation in uniaxial crystals. In this work, the focusing of off-axis and partially masked circular-polarization Gaussian beams are investigated by using of a full-wave theory. Moreover, two different types of spin-orbit interactions (i.e., spin-dependent vortex generation and photonic spin-Hall effect) in the focusing system are unified from the perspective of TPT. It is demonstrated that as the off-axis distance or the masked area increases, a TPT phenomenon in the focused optical field takes place, evolving from the spin-dependent vortex generation to the spin-Hall shift of the beam centroids. The intrinsic mechanism is attributed to the cylindrical symmetry-breaking of the system. This symmetry-breaking induced TPT based on the method of vortex mode decomposition is further examined. The main difference between the TPT phenomenon observed here and that trigged by oblique incidence at optical interfaces or oblique propagation in uniaxial crystals is also uncovered. Our findings provide fruitful insights for understanding the spin-orbit interactions in optics, providing an opportunity for unifying the TPT phenomena in various spin-orbit photonics systems.

Hall Effect at the Focus of an Optical Vortex with Linear Polarization

The tight focusing of an optical vortex with an integer topological charge (TC) and linear polarization was considered. We showed that the longitudinal components of the spin angular momentum (SAM) (it was equal to zero) and orbital angular momentum (OAM) (it was equal to the product of the beam power and the TC) vectors averaged over the beam cross-section were separately preserved during the beam propagation. This conservation led to the spin and orbital Hall effects. The spin Hall effect was expressed in the fact that the areas with different signs of the SAM longitudinal component were separated from each other. The orbital Hall effect was marked by the separation of the regions with different rotation directions of the transverse energy flow (clockwise and counterclockwise). There were only four such local regions near the optical axis for any TC. We showed that the total energy flux crossing the focus plane was less than the total beam power since part of the power propagated along the focus surface, while the other part crossed the focus plane in the opposite direction. We also showed that the longitudinal component of the angular momentum (AM) vector was not equal to the sum of the SAM and the OAM. Moreover, there was no summand SAM in the expression for the density of the AM. These quantities were independent of each other. The distributions of the AM and the SAM longitudinal components characterized the orbital and spin Hall effects at the focus, respectively.

Temporal effect of the spin-to-orbit conversion in tightly focused femtosecond optical fields

Spin and orbital angular momenta are two of the most fundamental physical quantities that describe the complex dynamic behaviors of optical fields. A strong coupling between these two quantities leads to many intriguing spatial topological phenomena, where one remarkable example is the generation of a helicity-dependent optical vortex that converts spin to orbital degrees of freedom. The spin-to-orbit conversion occurs inherently in lots of optical processes and has attracted increasing attention due to its crucial applications in spin-orbit photonics. However, current researches in this area are mainly focused on the monochromatic optical fields whose temporal properties are naturally neglected. In this work, we demonstrate an intriguing temporal evolution of the spin-to-orbit conversion induced by tightly-focused femtosecond optical fields. The results indicate that the conversion in such a polychromatic focused field obviously depends on time. This temporal effect originates from the superposition of local fields at the focus with different frequencies and is sensitive to the settings of pulse width and central wavelength. This work can provide fundamental insights into the spin-orbit dynamics within ultrafast wave packets, and possesses the potential for applications in spin-controlled manipulations of light.

Quadratic spin Hall effect of light due to phase change

The spin Hall effect (SHE) of light has brought important applications, but the involved spin states only split in one direction. Here we employ an accurate three-dimensional model of light to show that the SHE generally exhibits quadratic spin splitting, i.e., both vertical and horizontal splitting, in the presence of a fast phase change of reflection. Further, we disclose that the two splittings are actually different from each other, and that they originate from the vertical and horizontal spin momentum flows, respectively, owing to the spatial gradient of polarization in the individual direction. Finally, it is found that by tuning the incident angle and polarization of light, one can manipulate the quadratic SHE so as to realize a variety of spin splittings, such as unbalanced quadratic splitting and off-center splitting of spin states.

Stable optical lateral forces from inhomogeneities of the spin angular momentum

Transverse spin momentum related to the spin angular momentum (SAM) of light has been theoretically studied recently and predicted to generate an intriguing optical lateral force (OLF). Despite extensive studies, there is no direct experimental evidence of a stable OLF resulting from the dominant SAM rather than the ubiquitous spin-orbit interaction in a single light beam. Here, we theoretically unveil the nontrivial physics of SAM-correlated OLF, showing that the SAM is a dominant factor for the OLF on a nonabsorbing particle, while an additional force from the canonical (orbital) momentum is exhibited on an absorbing particle due to the spin-orbit interaction. Experimental results demonstrate the bidirectional movement of 5-μm-diameter particles on both sides of the beam with opposite spin momenta. The amplitude and sign of this force strongly depend on the polarization. Our optofluidic platform advances the exploitation of exotic forces in systems with a dominant SAM, facilitating the exploration of fascinating light-matter interactions.

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.

Topological spatial differentiators upon reflection of the normally incident light

We theoretically propose topological spatial differentiators by the normal-incidence reflection of light. Firstly, a three-dimensional propagation model is established for the light normally incident on the interface between two media. It is found that due to the spin-orbit interaction of light, a given circularly polarized light always induces oppositely polarized light carrying a topological charge, so the two intrinsic spin components are separated radially or azimuthally. Moreover, the normally reflected fields are approximately proportional to two kinds of second-order spatial differentiations of the input circularly and linearly polarized fields. Further results applying to the two-dimensional image processing for edge detection validate the two topological spatial differentiators.

Dark-field spin Hall effect of light

While an optical system's symmetry ensures that the spin Hall effect of light (SHEL) vanishes at normal incidence, the question of how close to the normal incidence can one reliably measure the SHEL remains open. Here we report simulation and experimental results on the measurement of SHEL at $\sim 0.12^\circ$ away from normal incidence in the Fourier plane of a weakly focused beam of light, reflected at an air-glass interface. Measurement of transverse spin-shift due to $< 0.05^\circ$ polarization variation in the beam cross section along the X- and Y-directions is achieved in the dark-field region of the reflected beam. Our ability to measure the SHEL at near-normal incidence with no moving optomechanical parts and significantly improved sensitivity to phase-polarization variations is expected to enable several applications in the retro-reflection geometry including material characterization with significant advantages.

Spin Hall effect of transversely spinning light

Light carries spin angular momentum, which, in the free space, is aligned to the direction of propagation and leads to intriguing spin Hall phenomena at an interface. Recently, it was shown that a transverse-spin (T-spin) state could exist for surface waves at an interface or for bulk waves inside a judiciously engineered metamaterial, with the spin oriented perpendicular to the propagation direction. Here, we demonstrate the spin Hall effect for transversely spinning light-a T-spin-induced beam shift at the interface of a metamaterial. It is found that the beam shift takes place in the plane of incidence, in contrast to the well-known Imbert-Fedorov shifts. The observed T-spin-induced beam shift is of geometrodynamical nature, which can be rendered positive or negative controlled by the orientation of T-spin of the photons. The unconventional spin Hall effect of light found here provides a previously unexplored mechanism for manipulating light-matter interactions at interfaces.

Spin-Orbital Conversion with the Tight Focus of an Axial Superposition of a High-Order Cylindrical Vector Beam and a Beam with Linear Polarization

In this paper, spin-orbital conversion in the tight focus of an axial superposition of a high-order (order m) cylindrical vector beam and a beam with linear polarization is theoretically and numerically considered. Although such a beam does not have a spin angular momentum in the initial plane and the third projection of its Stokes vector is equal to zero, subwavelength local regions with a transverse vortex energy flow and with the non-zero third Stokes projection (the longitudinal component of the spin angular momentum) are formed in the focal plane for an odd number m. This means that such a beam with an odd m has regions of elliptical or circular polarization with alternating directions of rotation (clockwise and counterclockwise) in the focus. For an even m, the field is linearly polarized at every point of the focal plane, and the transverse energy flux is absent. These beams can be used to create a micromachine in which two microparticles in the form of gears are captured in the focus of the beam into neighboring local areas in which the energy flow rotates in different directions, and therefore, these gears will also rotate in different directions.

Spin-orbit periodic conversion in a gradient-index fiber

The characteristics of the cylindrical vector beam (CVB) and the cylindrical vector vortex beam (CVVB) in a radial gradient-index (GRIN) fiber are analyzed on the basis of the generalized Huygens-Fresnel principle. The CVB and CVVB exhibit periodic and stable transmission characteristics in the radial GRIN fiber. In the beam with a vortex phase (CVVB), the polarization changes and the spin angular momentum (SAM) is detected at the focal plane of the radial GRIN fiber. A spin-orbit periodic conversion is observed in the radial GRIN fibers. Finally, the SAM expression of partially coherent light is deduced and verified via a simulation.

Circular Polarization Conversion in Single Plasmonic Spherical Particles

Temporal and spectral behaviors of plasmons determine their ability to enhance the characteristics of metamaterials tailored to a wide range of applications, including electric-field enhancement, hot-electron injection, sensing, as well as polarization and angular momentum manipulation. We report a dark-field (DF) polarimetry experiment on single particles with incident circularly polarized light in which gold nanoparticles scatter with opposite handedness at visible wavelengths. Remarkably, for silvered nanoporous silica microparticles, the handedness conversion occurs at longer visible wavelengths, only after adsorption of molecules on the silver. Finite element analysis (FEA) allows matching the circular polarization (CP) conversion to dominant quadrupolar contributions, determined by the specimen size and complex susceptibility. We hypothesize that the damping accompanying the adsorption of molecules on the nanostructured silver facilitates the CP conversion. These results offer new perspectives in molecule sensing and materials tunability for light polarization conversion and control of light spin angular momentum at submicroscopic scale.

Mapping the spin angular momentum distribution of focused linearly and circularly polarized vortex fields

Using the previously proposed spin-resolved near-field scanning optical microscopy (NSOM) technique, we mapped the spin angular momentum (SAM) axial component (S_z) distributions of tightly focused linearly and circularly polarized vortex beams. The system's effectiveness was confirmed in our previous article by mapping various tightly focused cylindrical vector vortex beams. The SAM of different focused vortex light fields is essential in the research of near-field spin optics and topological photonics. The SAM distributions of different orders of linearly and circularly polarized vortex beams were mapped by separating their right spin (I_RCP) and left spin component (I_LCP) using the relationship S_z∝I_RCP-I_LCP.

Spin-orbit Hall effect in the tight focusing of a radially polarized vortex beam

When the first-order radially polarized vortex beam propagates in an uniaxial crystal, the spin and the orbital angular momentum parts can be separated. It is called the optical spin-orbit Hall effect. In this study, we investigate the tight focusing of the radially polarized vortex beam theoretically and find the spatial separation of the spin and the orbital angular momentum parts occurs in the focal plane when the polarization order equals 1 and the vortex charge equals 1 (or -1). Moreover, when the initial phase of the polarization state takes π/2, the spatial separation of intensity in the focal plane corresponds to the spatial separation of the spin and the orbital angular momentum parts. This phenomenon can be considered as a manifestation of the optical spin-orbit Hall effect in the tight focusing of radially polarized vortex beam. Also, we show that, when the polarization order is greater than 1, the initial phase change of polarization state just leads to the rotation of the focal field and the spin and the orbital angular momentum density in the focal plane. Our results provide the potential application in the field of optical micro-manipulation.

Focusing a Vortex Laser Beam with Polarization Conversion

We show that when strongly focusing a linearly polarized optical vortex with the topological charge 2 (or −2) in the near-focus region, there occurs not only a reverse energy flow (where the projection of the Poynting vector is negative) but the right- (or left-) handed circular polarization of light as well. Notably, thanks to spin–orbital conversion, the on-axis polarization vector handedness is the same as that of the transverse energy flow, i.e., anticlockwise (clockwise). An absorbing spherical microparticle centered on the optical axis placed in the focus may be expected to rotate anticlockwise (clockwise) around its axis and its center of masses. We also show that in the case of sharp focusing of light with linear polarization (without an optical vortex) before and after focus, the light has an even number of local regions with left- and right-handed circular (elliptical) polarizations. Theoretical predictions are corroborated by the numerical simulation.

Spin-orbit interactions of transverse sound

Spin-orbit interactions (SOIs) endow light with intriguing properties and applications such as photonic spin-Hall effects and spin-dependent vortex generations. However, it is counterintuitive that SOIs can exist for sound, which is a longitudinal wave that carries no intrinsic spin. Here, we theoretically and experimentally demonstrate that airborne sound can possess artificial transversality in an acoustic micropolar metamaterial and thus carry both spin and orbital angular momentum. This enables the realization of acoustic SOIs with rich phenomena beyond those in conventional acoustic systems. We demonstrate that acoustic activity of the metamaterial can induce coupling between the spin and linear crystal momentum k, which leads to negative refraction of the transverse sound. In addition, we show that the scattering of the transverse sound by a dipole particle can generate spin-dependent acoustic vortices via the geometric phase effect. The acoustic SOIs can provide new perspectives and functionalities for sound manipulations beyond the conventional scalar degree of freedom and may open an avenue to the development of spin-orbit acoustics.

Symmetry and Quantum Features in Optical Vortices

Optical vortices are beams of laser light with screw symmetry in their wavefront. With a corresponding azimuthal dependence in optical phase, they convey orbital angular momentum, and their methods of production and applications have become one of the most rapidly accelerating areas in optical physics and technology. It has been established that the quantum nature of electromagnetic radiation extends to properties conveyed by each individual photon in such beams. It is therefore of interest to identify and characterize the symmetry aspects of the quantized fields of vortex radiation that relate to the beam and become manifest in its interactions with matter. Chirality is a prominent example of one such aspect; many other facets also invite attention. Fundamental CPT symmetry is satisfied throughout the field of optics, and it plays significantly into manifestations of chirality where spatial parity is broken; duality symmetry between electric and magnetic fields is also involved in the detailed representation. From more specific considerations of spatial inversion, amongst which it emerges that the topological charge has the character of a pseudoscalar, other elements of spatial symmetry, beyond simple parity inversion, prove to repay additional scrutiny. A photon-based perspective on these features enables regard to be given to the salient quantum operators, paying heed to quantum uncertainty limits of observables. The analysis supports a persistence in features of significance for the material interactions of vortex beams, which may indicate further scope for suitably tailored experimental design.

Extraordinary spin to orbital angular momentum conversion on guided zone plates

Focusing systems with high numerical aperture can be used to convert spin angular momentum into orbital angular momentum with efficiencies of 50%, while for low numerical apertures this conversion vanishes. In this paper, based on the properties of binary Fresnel zone plates, we propose a structure that is achieved by making an accurate selection of the width and the depth of the rings. This allows us to obtain a large increase in the spin to orbital angular momentum conversion of the resulting focusing fields, and it also has the special characteristic that the obtained conversion is higher for low numerical aperture structures, where standard focusing systems do not work. The ability of the system to perform this extraordinary conversion is demonstrated by FDTD methods and an analytical model developed using a combination of guided mode theory for the structure and Stratton–Chu diffraction theory.

Off-Axis Dipole Forces in Optical Tweezers by an Optical Analog of the Magnus Effect

It is shown that a circular dipole can deflect the focused laser beam that induces it and will experience a corresponding transverse force. Quantitative expressions are derived for Gaussian and angular top hat beams, while the effects vanish in the plane wave limit. The phenomena are analogous to the Magnus effect, pushing a spinning ball onto a curved trajectory. The optical case originates in the coupling of spin and orbital angular momentum of the dipole and the light. In optical tweezers the force causes off-axis displacement of the trapping position of an atom by a spin-dependent amount up to λ/2π, set by the direction of a magnetic field. This suggests direct methods to demonstrate and explore these effects, for instance, to induce spin-dependent motion.

Inversion of the axial projection of the spin angular momentum in the region of the backward energy flow in sharp focus

We show theoretically and numerically that when strongly focusing a circularly polarized optical vortex, the longitudinal component of its spin angular momentum undergoes inversion. A left-handed circularly polarized input beam is found to convert in the focus and near the optical axis to a right-handed circularly polarized beam. Thanks to this effect taking place near the strong focus, where a reverse energy flow is known to occur, the spin angular momentum inversion discovered can be utilized to detect a reverse energy flow.

Vortex generation in the spin-orbit interaction of a light beam propagating inside a uniaxial medium: origin and efficiency

It has been known that an optical vortex with a topological charge ±2 can be generated as a circularly polarized (CP) light beam propagates in a bulk uniaxial crystal, but its physical origin remains obscure which also hinders its practical applications. Here, through a rigorous full-wave analyses on the problem, we show that, as a CP beam possessing a particular spin (handedness) propagates inside a uniaxial crystal, two beams with opposite spins can be generated caused by the unique spin-sensitive light-matter interactions in the anisotropic medium. Flipping the spin can offer the light beam an vortex phase with a topological charge of ±2 owing to the Pancharatnam-Berry mechanism, with efficiency dictated by the material properties of the uniaxial medium and the topological structure of the beam itself. With its physical origin fully uncovered, we finally discuss how to improve the efficiency of such effect, and compare the mechanisms of vortex generations in different systems. Our findings not only provide deeper understandings on such an intriguing effect, but also shed light on other spin-orbit-interaction-induced effects.

Theoretical analysis on spatially structured beam induced mass transport in azo-polymer films

The radiation force from paraxial beams possessing helical phase fronts causes twists on the surface of an azobenzene polymer sample, and leads to the formation of micro-scale structures. Here, we theoretically investigate the radiation force generated by spatially structured optical beams on a dispersive-absorptive substrate. We derive an analytical expression for the radiation force from spatially structured polarized beams, including, lemon, star, monstar and vector vortex beams in the paraxial regime. Finally, we extend our calculation for non-paraxial beams - optical beams under the tight-focusing regime - and simulate the transverse radiation forces numerically at the focal plane.

Mapping the near-field spin angular momenta in the structured surface plasmon polariton field

Optical spin angular momenta in a confined electromagnetic field exhibit a remarkable difference with their free space counterparts; in particular, the optical transverse spin that is locked with the energy propagating direction lays the foundation for many intriguing physical effects such as unidirectional transportation, quantum spin Hall effects, photonic Skyrmions, etc. In order to investigate the underlying physics behind the spin-orbit interactions as well as to develop the optical spin-based applications, it is crucial to uncover the spin texture in a confined field, yet it faces challenges due to their chiral and near-field vectorial features. Here, we propose a scanning imaging technique which can map the near-field distributions of the optical spin angular momenta with an achiral dielectric nanosphere. The spin angular momentum component normal to the interface can be uncovered experimentally by employing the proposed scanning imaging technique and the three-dimensional spin vector can be reconstructed theoretically with the experimental results. The experiment is demonstrated on the example of surface plasmon polaritons excited with various vector vortex beams under a tight-focusing configuration, where the spin-orbit interaction emerges clearly. The proposed method, which can be utilized to reconstruct the photonic Skyrmion and other photonic topological structures, is straightforward and of high precision, and hence it is expected to be valuable for the study of near-field spin optics and topological photonics.

Dual Coaxial Longitudinal Polarization Vortex Structures

Carrying orbital angular momentum per photon, the optical vortex has elicited widespread interest. Here, we demonstrate that dual coaxial longitudinal polarization vortices can appear upon a nonparaxial propagation of a tightly focused Pancharatnam-Berry tailored Laguerre-Gaussian beam. Most importantly, it is capable of accessing arbitrary independent topological charges for both vortices, as well as predesigned tunable spacing distances between them.

Broadband chiral hybrid plasmon modes on nanofingernail substrates

There is significant interest in the utility of asymmetric nanoaperture arrays as substrates for the surface-enhanced detection, fluorescence, and imaging of individual molecules. This work introduces obliquely-cut, out-of-plane, coaxial layered structures on an aperture edge. We refer to these structures as nanofingernails, which emphasizes their curved, oblique, and out-of-plane features. Broadband coupling into chiral hybrid plasmon modes and helicity-dependent near-field scattering without circular dichroism are demonstrated. The unusually-broadband, multipolar modes of nanofingernail micropore structures exhibit phase retardation effects that may be useful for achieving spatial overlap at different frequencies. The nanofingernail geometry shows new potential for simultaneous polarization-enhanced hyperspectral imaging on apertured, plasmonic surfaces.

Geometric phases in 2D and 3D polarized fields: geometrical, dynamical, and topological aspects

Geometric phases are a universal concept that underpins numerous phenomena involving multi-component wave fields. These polarization-dependent phases are inherent in interference effects, spin-orbit interaction phenomena, and topological properties of vector wave fields. Geometric phases have been thoroughly studied in two-component fields, such as two-level quantum systems or paraxial optical waves. However, their description for fields with three or more components, such as generic nonparaxial optical fields routinely used in modern nano-optics, constitutes a nontrivial problem. Here we describe geometric, dynamical, and total phases calculated along a closed spatial contour in a multi-component complex field, with particular emphasis on 2D (paraxial) and 3D (nonparaxial) optical fields. We present several equivalent approaches: (i) an algebraic formalism, universal for any multi-component field; (ii) a dynamical approach using the Coriolis coupling between the spin angular momentum and reference-frame rotations; and (iii) a geometric representation, which unifies the Pancharatnam-Berry phase for the 2D polarization on the Poincaré sphere and the Majorana-sphere representation for the 3D polarized fields. Most importantly, we reveal close connections between geometric phases, angular-momentum properties of the field, and topological properties of polarization singularities in 2D and 3D fields, such as C-points and polarization Möbius strips.

Angular momentum properties of hybrid cylindrical vector vortex beams in tightly focused optical systems

Optical angular momenta (AM) have attracted tremendous research interest in recent years. In this paper we theoretically investigate the electromagnetic field and angular momentum properties of tightly focused arbitrary cylindrical vortex vector (CVV) input beams. An absorptive particle is placed in focused CVV fields to analyze the optical torques. The spin-orbit motions of the particle can be predicted and controlled when the influences of different parameters, such as the topological charge, the polarization and the initial phases, are taken into account. These findings will be helpful in optical beam shaping, optical spin-orbit interaction and practical optical manipulation.

Photonic spin Hall effect on an ellipsoidal Rayleigh particle in scattering far-field

We present the photonic spin Hall effect on an ellipsoidal Rayleigh particle, which amounts to a polarization-dependent shift in scattering far-field. Based on the dipole model, we demonstrate that such shift is unavoidable when the light incidence is inclined with respect to the main axis of the ellipsoidal Rayleigh particle. The result has general validity and can be applied to metal and dielectric materials. In addition, the photonic spin Hall effect also manifests itself in the optical force and torque exerted on the particle, which is promising for precision metrology, spin-optics devices and optical driven micro-machines. Due to wide existence of the Rayleigh particles in nature, we believe that our findings might provide a useful toolset for investigating polarization-dependent scattering of particles.

Sectoral multipole focused beams

We discuss the properties of pure multipole beams with well-defined handedness or helicity, with the beam field a simultaneous eigenvector of the squared total angular momentum and its projection along the propagation axis. Under the condition of hemispherical illumination, we show that the only possible propagating multipole beams are "sectoral" multipoles. The sectoral dipole beam is shown to be equivalent to the non-singular time-reversed field of an electric and a magnetic point dipole Huygens' source located at the beam focus. Higher order multipolar beams are vortex beams vanishing on the propagation axis. The simple analytical expressions of the electric field of sectoral multipole beams, exact solutions of Maxwell's equations, and the peculiar behaviour of the Poynting vector and spin and orbital angular momenta in the focal volume could help to understand and model light-matter interactions under strongly focused beams.

Dynamics of angular momentum-torque conversion in silicon waveguides

We present a refined theoretical analysis on the relationship between the optical total angular momenta (TAM) and the optical torque (OT) in a birefringent silicon waveguide. By using the vector angular spectrum method, we demonstrate the dynamic evolutions of the OT, TAM, spin angular momentum (SAM), and orbital angular momentum (OAM). The SAM and OAM coexist and evolve simultaneously in the propagation. The ratio between the OAM and TAM is related to the incident wavelength and the size of waveguide. Moreover, we design a three-layer waveguide structure to convert the light chirality and generate high torque. The performance of such torque-generator is analyzed numerically in detail.

Asymmetry and spin-orbit coupling of light scattered from subwavelength particles

Light scattering and spin-orbit angular momentum coupling phenomena from subwavelength objects, with electric and magnetic dipolar responses, are receiving an increasing interest. Under illumination by circularly polarized light, spin-orbit coupling effects have been shown to lead to significant shifts between the measured and actual position of particles. Here we show that the remarkable angular dependence of these "optical mirages" and those of the intensity, degree of circular polarization (DoCP), and spin and orbital angular momentum of scattered photons are all linked, and fully determined, by the dimensionless "asymmetry parameter" g, being independent of the specific optical properties of the scatterer. Interestingly, for g≠0, the maxima of the optical mirage and angular momentum exchange take place at different scattering angles. We further show that the g parameter is exactly half of the DoCP at a right-angle scattering, which opens the possibility to infer the whole angular properties of the scattered fields by a single far-field polarization measurement.

Spin to orbital light momentum conversion visualized by particle trajectory

In a tightly focused beam of light having both spin and orbital angular momentum, the beam exhibits the spin-orbit interaction phenomenon. We demonstrate here that this interaction gives rise to series of subtle, but observable, effects on the dynamics of a dielectric microsphere trapped in such a beam. In our setup, we control the strength of spin-orbit interaction with the width, polarization and vorticity of the beam and record how these parameters influence radius and orbiting frequency of the same single orbiting particle pushed by the laser beam. Using Richard and Wolf model of the non-paraxial beam focusing, we found a very good agreement between the experimental results and the theoretical model based on calculation of the optical forces using the generalized Lorenz-Mie theory extended to a non-paraxial vortex beam. Especially the radius of the particle orbit seems to be a promising parameter characterizing the spin to orbital momentum conversion independently on the trapping beam power.

Negative optical torque on a microsphere in optical tweezers

We show that the optical force field in optical tweezers with elliptically polarized beams has the opposite handedness for a wide range of particle sizes and for the most common configurations. Our method is based on the direct observation of the particle equilibrium position under the effect of a transverse Stokes drag force, and its rotation around the optical axis by the mechanical effect of the optical torque. We find overall agreement with theory, with no fitting, provided that astigmatism, which is characterized separately, is included in the theoretical description. Our work opens the way for characterization of the trapping parameters, such as the microsphere complex refractive index and the astigmatism of the optical system, from measurements of the microsphere rotation angle.

Transverse spin forces and non-equilibrium particle dynamics in a circularly polarized vacuum optical trap

We provide a vivid demonstration of the mechanical effect of transverse spin momentum in an optical beam in free space. This component of the Poynting momentum was previously thought to be virtual, and unmeasurable. Here, its effect is revealed in the inertial motion of a probe particle in a circularly polarized Gaussian trap, in vacuum. Transverse spin forces combine with thermal fluctuations to induce a striking range of non-equilibrium phenomena. With increasing beam power we observe (i) growing departures from energy equipartition, (ii) the formation of coherent, thermally excited orbits and, ultimately, (iii) the ejection of the particle from the trap. As well as corroborating existing measurements of spin momentum, our results reveal its dynamic effect. We show how the under-damped motion of probe particles in structured light fields can expose the nature and morphology of optical momentum flows, and provide a testbed for elementary non-equilibrium statistical mechanics.

Here, the authors provide a vivid demonstration of the dynamic effect of transverse spin momentum in an optical beam in free space revealed by placing a dielectric bead in a counter-propagating optical beam trap in vacuum.

Singular knot bundle in light

As the size of an optical vortex knot, imprinted in a coherent light beam, is decreased, nonparaxial effects alter the structure of the knotted optical singularity. For knot structures approaching the scale of wavelength, longitudinal polarization effects become non-negligible, and the electric and magnetic fields differ, leading to intertwined knotted nodal structures in the transverse and longitudinal polarization components, which we call a knot bundle of polarization singularities. We analyze their structure using polynomial beam approximations and numerical diffraction theory. The analysis reveals features of spin-orbit effects and polarization topology in tightly focused geometry, and we propose an experiment to measure this phenomenon.

Orbit-induced localized spin angular momentum in the tight focusing of linearly polarized vortex beams

Optical spin-orbit interaction has gained much interest recently due to its universality and importance in modern photonics. In this Letter, we theoretically demonstrate that orbit-induced localized spin angular momentum (SAM) conversion can occur in the tight focusing of spin-free linearly polarized vortex beams (LPVBs). By analysis of the polarization states that are associated with the SAM density, we attribute the occurrence of such a conversion to the helical-phase-induced change of local polarization states in the focused field. In the local SAM, density can be further regulated by altering the sign and value of the orbital angular momentum in the incident LPVBs, as well as their polarization orientations. This Letter is expected to advance our understanding of optical spin-orbit coupling and benefit applications of optical microscopy and trapping.

Symmetry Protection of Photonic Entanglement in the Interaction with a Single Nanoaperture

In this work, we experimentally show that quantum entanglement can be symmetry protected in the interaction with a single subwavelength plasmonic nanoaperture, with a total volume of V∼0.2λ^{3}. In particular, we experimentally demonstrate that two-photon entanglement can be either completely preserved or completely lost after the interaction with the nanoaperture, solely depending on the relative phase between the quantum states. We achieve this effect by using specially engineered two-photon states to match the properties of the nanoaperture. In this way we can access a symmetry protected state, i.e., a state constrained by the geometry of the interaction to retain its entanglement. In spite of the small volume of interaction, we show that the symmetry protected entangled state retains its main properties. This connection between nanophotonics and quantum optics probes the fundamental limits of the phenomenon of quantum interference.

Structured spin angular momentum in highly focused cylindrical vector vortex beams for optical manipulation

We investigate the spin properties of a family of cylindrical vector vortex beams under a focusing condition. The spin-orbit interaction is demonstrated by comparing the energy flow and spin flow density of the focused field to those of the incident field. This spin-orbit interaction is analyzed to construct the desired distribution of spin angular momentum for optical manipulation. The structured spin angular momentum of the focused field can transfer to the optical torque for the non-magnetic absorptive particle. The influences of polarization topological charge, vortex topological charge and wavelength on optical torque in the hot-spot of focused field are summarized for three typical particles. Such results may be exploited in practical optical manipulation, particularly for optically induced rotations.

Design for a Nanoscale Single-Photon Spin Splitter for Modes with Orbital Angular Momentum

We propose using the effective spin-orbit coupling of light in Bragg-modulated cylindrical waveguides for the efficient separation of spin-up and spin-down photons emitted by a single photon emitter. Because of the spin and directional dependence of photonic stop bands in the waveguides, spin-up (-down) photon propagation in the negative (positive) direction along the waveguide axis is blocked while the same photon freely propagates in the opposite direction. Frequency shifts of photonic band structures induced by the spin-orbit coupling are verified by finite-difference time-domain numerical simulations.

Spin-Hall effect in the scattering of structured light from plasmonic nanowire

Spin-orbit interactions are subwavelength phenomena that can potentially lead to numerous device-related applications in nanophotonics. Here, we report the spin-Hall effect in the forward scattering of Hermite-Gaussian (HG) and Gaussian beams from a plasmonic nanowire. Asymmetric scattered radiation distribution was observed for circularly polarized beams. Asymmetry in the scattered radiation distribution changes the sign when the polarization handedness inverts. We found a significant enhancement in the spin-Hall effect for a HG beam compared to a Gaussian beam for constant input power. The difference between scattered powers perpendicular to the long axis of the plasmonic nanowire was used to quantify the enhancement. In addition, the nodal line of the HG beam acts as the marker for the spin-Hall shift. Numerical calculations corroborate experimental observations and suggest that the spin flow component of the Poynting vector associated with the circular polarization is responsible for the spin-Hall effect and its enhancement.

Topological transport of sound mediated by spin-redirection geometric phase

When a dynamic system undergoes a cyclic evolution, a geometric phase that depends only on the path traversed in parameter space can arise in addition to the normal dynamical phase. These geometric phases have profound impacts in both quantum and classical physics. In addition to the geometric phase associated with band structures in reciprocal space that has led to the discovery of topological insulators, the spin-redirection geometric phase induced by the SO(3) rotation of states in real space can also give rise to intriguing phenomena such as the photonic analog of the spin Hall effect. By exploiting the orbital angular momentum of sound vortices, we theoretically and experimentally demonstrate the spin-redirection geometric phase effects in airborne sound, which is a scalar wave without spin. We show that these effects, associated with the helical transport of sound, can be used to control the flow of sound. This finding opens new possibilities for the manipulation of scalar wave propagation by exploiting spin-redirection geometric phases.

Optical angular momentum derivation and evolution from vector field superposition

Optical intrinsic angular momentum can be regarded as derivation from spatial superposition of optical vector fields embodied by spinning or/and spiraling the electric-field vector. We employ vectorial formulation derivation to comprehensively study all angular momentum contents of optical vector fields in arbitrary superposition states, including the longitudinal and transverse, spin and orbital (SAM and OAM) components. As for the orthogonal superposition fields, there inherently exists spin-orbit shift from longitudinal SAM to OAM, and the whole local spin flow manifests local multiple-fold helical trajectories. Especially, both the spin-orbit shift and transverse SAM could become considerable in the non-paraxial condition. Our studies here provide an explicit insight into the derivation and evolution, intrinsic correlations and salient features of various types of angular momentum components.

Azo-polymer film twisted to form a helical surface relief by illumination with a circularly polarized Gaussian beam

A helical surface relief can be created in an azo-polymer film simply by illuminating circularly polarized light with spin angular momentum and without any orbital angular momentum. The helicity of the surface relief is determined by the sign of the spin angular momentum. The illumination of circularly polarized light induces orbital motion of the azo-polymer to shape the helical surface relief as an intermediate form; a subsequent transformation to a non-helical bump-shaped relief with a central peak creates a final form with additional exposure time. The mechanism for the formation of such a helical surface relief was also theoretically analyzed using the formula for the optical radiation force in a homogeneous and isotropic material.

Efficient Vortex Generation in Subwavelength Epsilon-Near-Zero Slabs

We show that a homogeneous and isotropic slab, illuminated by a circularly polarized beam with no topological charge, produces vortices of order 2 in the opposite circularly polarized components of the reflected and transmitted fields, as a consequence of the transverse magnetic and transverse electric asymmetric response of the rotationally invariant system. In addition, in the epsilon-near-zero regime, we find that vortex generation is remarkably efficient in subwavelength thick slabs up to the paraxial regime. This physically stems from the fact that a vacuum paraxial field can excite a nonparaxial field inside an epsilon-near-zero slab since it hosts slowly varying fields over physically large portions of the bulk. Our theoretical predictions indicate that epsilon-near-zero media hold great potential as nanophotonic elements for manipulating the angular momentum of the radiation, since they are available without resorting to complicated micro- or nanofabrication processes and can operate even at very small (ultraviolet) wavelengths.