Optical nanoprobing via spin-orbit interaction of light

Highly efficient vortex generation at the nanoscale

Control of the angular momentum of light at the nanoscale is critical for many applications of subwavelength photonics, such as high-capacity optical communications devices, super-resolution imaging and optical trapping. However, conventional approaches to generate optical vortices suffer from either low efficiency or relatively large device footprints. Here we show a new strategy for vortex generation at the nanoscale that surpasses single-pixel phase control. We reveal that interaction between neighbouring nanopillars of a meta-quadrumer can tailor both the intensity and phase of the transmitted light. Consequently, a subwavelength nanopillar quadrumer is sufficient to cover a 2lπ phase change, thus efficiently converting incident light into high-purity optical vortices with different topological charges l. Benefiting from the nanoscale footprint of the meta-quadrumers, we demonstrate high-density vortex beam arrays and high-dimensional information encryption, bringing a new degree of freedom to many designs of meta-devices.

Spin-Direction-Spin Coupling of Quasiguided Modes in Plasmonic Crystals

We report an unusual spin-direction-spin coupling phenomenon of light using the leaky quasiguided modes of a waveguided plasmonic crystal. This is demonstrated as simultaneous input spin-dependent directional guiding of waves (spin-direction coupling) and wave-vector-dependent spin acquisition (direction-spin coupling) of the scattered light. These effects, manifested as the forward and the inverse spin Hall effect of light in the far field, and other accompanying spin-orbit interaction effects are observed and analyzed using a momentum (k) domain polarization Mueller matrix. Resonance-enabled enhancement of these effects is also demonstrated by utilizing the spectral Fano resonance of the hybridized modes. The fundamental origin and the unconventional manifestation of the spin-direction-spin coupling phenomenon from a relatively simple system, ability to probe and interpret the resulting spin-orbit phenomena in the far field through momentum-domain polarization analysis, and their regulated control in plasmonic-photonic crystals open up exciting avenues in spin-orbit-photonic research.

Polarization-Dependent Forces and Torques at Resonance in a Microfiber-Microcavity System

Spin-orbit interactions in evanescent fields have recently attracted significant interest. In particular, the transfer of the Belinfante spin momentum perpendicular to the propagation direction generates polarization-dependent lateral forces on particles. However, it is still elusive as to how the polarization-dependent resonances of large particles synergize with the incident light's helicity and resultant lateral forces. Here, we investigate these polarization-dependent phenomena in a microfiber-microcavity system where whispering-gallery-mode resonances exist. This system allows for an intuitive understanding and unification of the polarization-dependent forces. Contrary to previous studies, the induced lateral forces at resonance are not proportional to the helicity of incident light. Instead, polarization-dependent coupling phases and resonance phases generate extra helicity contributions. We propose a generalized law for optical lateral forces and find the existence of optical lateral forces even when the helicity of incident light is zero. Our work provides new insights into these polarization-dependent phenomena and an opportunity to engineer polarization-controlled resonant optomechanical systems.

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.

Rotational dynamics of indirect optical bound particle assembly under a single tightly focused laser

The optical binding of many particles has the potential to achieve the wide-area formation of a "crystal" of small materials. Unlike conventional optical binding, where the entire assembly of targeted particles is directly irradiated with light, if remote particles can be indirectly manipulated using a single trapped particle through optical binding, the degrees of freedom to create ordered structures can be enhanced. In this study, we theoretically investigate the dynamics of the assembly of gold nanoparticles that are manipulated using a single trapped particle by a focused laser. We demonstrate the rotational motion of particles through an indirect optical force and analyze it in terms of spin-orbit coupling and the angular momentum generation of light. The rotational direction of bound particles can be switched by the numerical aperture. These results pave the way for creating and manipulating ordered structures with a wide area and controlling local properties using scanning laser beams.

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.

Recent Progress on Optical Micro/Nanomanipulations: Structured Forces, Structured Particles, and Synergetic Applications

Optical manipulation has achieved great success in the fields of biology, micro/nano robotics and physical sciences in the past few decades. To date, the optical manipulation is still witnessing substantial progress powered by the growing accessibility of the complex light field, advanced nanofabrication and developed understandings of light-matter interactions. In this perspective, we highlight recent advancements of optical micro/nanomanipulations in cutting-edge applications, which can be fostered by structured optical forces enabled with diverse auxiliary multiphysical field/forces and structured particles. We conclude with our vision of ongoing and futuristic directions, including heat-avoided and heat-utilized manipulation, nonlinearity-mediated trapping and manipulation, metasurface/two-dimensional material based optical manipulation, as well as interface-based optical manipulation.

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.

Detecting the transverse spin density of light via electromagnetically induced transparency

For light that is transversely confined, its field vector spins in a plane not orthogonal to the propagation direction, leading to the presence of transverse spin, which plays a fundamental role in the field of chiral quantum optics. Here, we theoretically propose a scheme to detect the transverse spin density (TSD) of light by utilizing a multilevel atomic medium. The scheme is based on the electromagnetically induced transparency effect, which enables the TSD-dependent modulation of the susceptibility of the atomic medium by using a coupling field whose TSD is to be detected. The modulated susceptibility results in a spin-dependent absorption for a probe beam passing through the atomic medium. We show that there exists a corresponding relationship between the TSD distribution of the coupling field and the polarization distribution of the transmitted probe beam through a theoretical study of two typical cases, in which the coupling field is provided by a tightly focused field and a two-beam interference field, respectively. Based on this relationship, the key features of the TSD of the coupling field, such as the spatial distribution, the symmetry property, and the spin-momentum locking, can be inferred from the transmitted probe beam. Benefiting from the fast response of the atomic medium to the variation of the coupling field, the present scheme is capable of detecting the TSD in real time, offering new possibilities for developing transverse-spin-based techniques.

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.

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.

Synthesis of multiple longitudinal polarization vortex structures and its application in sorting chiral nanoparticles

As the essential properties of organisms, detection and characterization of chirality are of supreme importance in physiology and pharmacology. In this work, we propose an optical technique to sort chiral materials by use of longitudinal polarization vortex (LPV) structures, which is generated with tightly focusing Pancharatnam-Berry tailored Laguerre-Gaussian beam. The nonparaxial propagation of the focusing field leads to the creation of multiple pairs of dual LPV structures with arbitrary topological charge and location, which can be independently controlled by the spatial phase modulation applied on the illumination. More importantly, the opposite spin angular momentums carried by each pair of dual foci lead to different energy flow directions, making it suitable to sort nanoparticles by their handedness. In addition, the LPV structures would also bring different dynamic behaviors to the enantiomers, providing a feasible route toward all-optical enantiopure chemical syntheses and enantiomer separations in pharmaceuticals.

Enhanced and unidirectional photonic spin Hall effect in a plasmonic metasurface with S4 symmetry

In this Letter, we report the significant enhancement of the photonic spin Hall effect (SHE) in a plasmonic metasurface with ${\rm S}_4$ symmetry. We find that an enhanced SHE of reflected light can occur in both horizontally and vertically polarized incident beams, and the maximum transverse displacement can approach half of the beam waist. Such a large displacement is caused by the non-resonant and near-zero pseudo-Brewster angles in the plasmonic metasurface. Owing to ${\rm S}_4$ symmetry, a unidirectional SHE is obtained in the metasurface, i.e., large and tiny transverse displacements are realized for a linearly polarized beam incident from the opposite side. This Letter provides a new, to the best of our knowledge, way to achieve an enhanced photonic SHE and offers more opportunities for designing spin-based nanophotonic devices.

Angular momentum separation in focused fractional vector beams for optical manipulation

The generation, propagation, and applications of different types of integer vector beams have been extensively investigated. However, little attention focuses on the photophysical and photomechanical properties of the fractional vector beam (FVB). Herein, we theoretically and experimentally investigate the spin angular momentum (SAM) separation and propagation characteristics of weakly focused FVBs. It is demonstrated that such a beam carrying no SAM leads to both the transverse separation of SAM and the special intensity patterns in the focal region. Furthermore, we study the intensity, SAM, and orbital angular momentum (OAM) distributions of the tightly focused FVBs. It is shown that both three-dimensional SAM and OAM are spatially separated in the focal region of tightly focused FVBs. We investigate the optical forces, spin torques, and orbital torques on a dielectric Rayleigh particle produced by the focused FVBs. The results reveal that asymmetrical spinning and orbiting motions of optically trapped particles can be realized by manipulating FVBs.

Enhanced spin Hall effect due to the redshift gaps of photonic hypercrystals

We proposed a method for enhancing the spin Hall effect (SHE) of light in the photonic hypercrystal (PHC). PHC is a periodic structure that combines the properties of hyperbolic metamaterials (HMMs) and conventional one-dimensional-photonic crystals (1DPCs). The proposed PHC is composed of Ti₃O₅ and HMMs, which alternatively consist of Ag and Ti₃O₅. The giant ratio of reflection coefficients of TE/TM polarizations can be realized due to the redshift gaps of the PHCs, where the band edge of TE polarization shifts toward short wavelengths but the band edge of TM polarization moves toward long wavelengths. It will eventually lead to the enhancement of SHE in this PHC with the redshift gaps. The maximum transverse shift can be close to 15 µm with the optimum thickness and incident angle. The enhancing SHE provides us an opportunity to expand the corresponding applications in the field of optics.

Optical Spin Hall Effect in Closed Elliptical Plasmonic Nanoslit with Noncircular Symmetry

We investigated the optical spin Hall effect (OSHE) of the light field from a closed elliptical metallic curvilinear nanoslit instead of the usual truncated curvilinear nanoslit. By making use of the characteristic bright spots in the light field formed by the noncircular symmetry of the elliptical slit and by introducing a method to separate the incident spin component (ISC) and converted spin component (CSC) of the output field, the OSHE manifested in the spot shifts in the CSC was more clearly observable and easily measurable. The slope of the elliptical slit, which was inverse along the principal axes, provided a geometric phase gradient to yield the opposite shifts of the characteristic spots in centrosymmetry, with a double shift achieved between the spots. Regarding the mechanism of this phenomenon, the flip of the spin angular momentum (SAM) of CSC gave rise to an extrinsic orbital angular momentum corresponding to the shifts of the wavelet profiles of slit elements in the same rotational direction to satisfy the conservation law. The analytical calculation and simulation of finite-difference time domain were performed for both the slit element and the whole slit ellipse, and the evolutions of the spot shifts as well as the underlying OSHE with the parameters of the ellipse were achieved. Experimental demonstrations were conducted and had consistent results. This study could be of great significance for subjects related to the applications of the OSHE.

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.

Quantized Circulation of Anomalous Shift in Interface Reflection

A particle beam may undergo an anomalous spatial shift when it is reflected at an interface. The shift forms a vector field defined in the two-dimensional interface momentum space. We show that, although the shift vector at individual momentum is typically sensitive to the system details, its integral along a close loop, i.e., its circulation, could yield a robust quantized number under certain conditions of interest. Particularly, this is the case when the beam is incident from a trivial medium, then the quantized circulation of anomalous shift (CAS) directly manifests the topological character of the other medium. We demonstrate that the topological charge of a Weyl medium as well as the unconventional pair potentials of a superconductor can be captured and distinguished by CAS. Our work unveils a hidden quantized feature in a ubiquitous physical process, which may also offer a new approach for probing topological media.

Topologically-tuned spin Hall shift around Fano resonance

The topological magnetoelectric effect is associated with the photonic spin-orbit interaction. However, due to the proportionate fine structure constant of the topological term, the topological magnetoelectric effect is usually weak. In this paper, we demonstrate that the axion term enables manipulation of the spin Hall shift of light around Fano resonance. And, the excited surface plasmon near the nanoparticle's interface could enhance the topological magnetoelectric effect for several orders. Numerical simulation of near field and far-field scattering confirms our theoretical results. Our work may pave the way to exploit the topological magnetoelectric effect in practical applications, such as optical sensing and nanoprobing.

Cross-coupling effect induced beam shifts for polarized vortex beam at two-dimensional anisotropic monolayer graphene surface

We investigated beam shifts for an arbitrarily polarized vortex beam reflected and transmitted at two-dimensional (2D) anisotropic monolayer graphene surface. And generalized expressions are theoretically derived for calculating beam shifts of vortex beam. Then, we presented the beam shifts associated with the self-isotropic (SI) effect, self-anisotropic (SA) effect and cross-coupling (XC) effect originated from self-isotropic interaction, self-anisotropic interaction and cross-coupling interaction between isotropic and anisotropic of two-dimensional media, respectively. More importantly, novel optical phenomena resulting from the XC effect are flexibly shown by manipulation OAM. We believe that our results can be extensively extended to 2D anisotropic Dirac semimetals and Weyl semimetals, and expect the results to be significant and contribute to the understanding of the spin and orbit Hall effect of the light.

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.

Spin-dependent directional emission from a quantum dot ensemble embedded in an asymmetric waveguide

In this study, we examine a photonic wire waveguide embedded with an ensemble of quantum dots (QDs) that directionally emits into the waveguide depending on the spin state of the ensemble. The directional emission is facilitated by the spin-orbit interaction of light. The waveguide has a two-step stair-like cross section and QDs are embedded only in the upper step, such that the circular polarization of emission from the spin-polarized QDs controls the direction of the radiation. We numerically verify that more than 70% of the radiation from the ensemble emitter is toward a specific direction in the waveguide. We also examine a microdisk resonator with a stair-like edge, which supports selective coupling of the QD ensemble radiation into a whispering gallery mode that rotates unidirectionally. Our study provides a foundation for spin-dependent optoelectronic devices.

Emission of circularly polarized light by a linear dipole

Controlling the polarization state and the propagation direction of photons is a fundamental prerequisite for many nanophotonic devices and a precursor for future on-chip communication, where the emission properties of individual emitters are particularly relevant. Here, we report on the emission of partially circularly polarized photons by a linear dipole. The underlying effect is linked to the near-field part of the angular spectrum of the dipole, and it occurs in any type of linear dipole emitter, ranging from atoms and quantum dots to molecules and dipole-like antennas. We experimentally observe it by near-field to far-field transformation at a planar dielectric interface and numerically demonstrate the utility of this phenomenon by coupling the circularly polarized light to the individual paths of crossing waveguides.

Generating a plasmonic vortex field with arbitrary topological charges and positions by meta-nanoslits

A novel plasmonic vortex lens (PVL) consisting of an array of gold film nanoslits for vortex-field generation with arbitrary topological charges and positions is proposed. The performance of the PVL is analyzed theoretically and demonstrated numerically by the finite-element method. By utilizing a symmetric and antisymmetric phase, the plasmonic vortex generated at the center of the PVL can carry arbitrary topological charges (integer or fraction). Two circularly polarized illuminations with opposite spins can excite a composite plasmonic vortex field with symmetry-breaking distribution, in which the breaking point rotates with the phase difference between two spins. In addition, we can shift the center of the plasmonic vortex to any desired position such that a flexible location manipulation of the plasmonic vortex is achieved. The designed PVL can also work as a miniaturized polarimeter for characterizing the state of polarization of the incident light.

Weak Measurement Enhanced Spin Hall Effect of Light for Particle Displacement Sensing

A spherical nanoparticle can scatter tightly focused optical beams in a spin-segmented manner, meaning that the far field of the scattered light exhibits laterally separated left- and right-handed circularly polarized components. This effect, commonly referred to as giant spin Hall effect of light, strongly depends on the position of the scatterer in the focal volume. Here, a scheme that utilizes an optical weak measurement in a cylindrical polarization basis is put forward to drastically enhance the spin-segmentation and, therefore, the sensitivity to small displacements of a scatterer. In particular, we experimentally achieve a change of the spin-splitting signal of 5% per nanometer displacement.

Wavelength-scale errors in optical localization due to spin-orbit coupling of light

Far-field optical imaging techniques allow the determination of the position of point-like emitters and scatterers [1-3]. Although the optical wavelength sets a fundamental limit to the image resolution of unknown objects, the position of an individual emitter can in principle be estimated from the image with arbitrary precision. This is used for example in the determination of stars position [4] or in optical super-resolution microscopy [5]. Furthermore, precise position determination is an experimental prerequisite for the manipulation and measurement of individual quantum systems, such as atoms, ions, and solid-state-based quantum emitters [6-8]. Here we demonstrate that spin-orbit coupling of light in the emission of elliptically polarized emitters can lead to systematic, wavelength-scale errors in the estimation of the emitters position. Imaging a single trapped atom as well as a single sub-wavelength-diameter gold nanoparticle, we demonstrate a shift between the emitters measured and actual positions which is comparable to the optical wavelength. For certain settings, the expected shift can become arbitrarily large. Beyond optical imaging techniques, our findings could be relevant for the localization of objects using any type of wave that carries orbital angular momentum relative to the emitters position with a component orthogonal to the direction of observation.

Weak Measurement of Elliptical Dipole Moments by C-Point Splitting

We investigate points of circular polarization in the far field of elliptically polarized dipoles and establish a relation between the angular position and helicity of these C points and the dipole moment. In the case of highly eccentric dipoles, the C points of opposite handedness exhibit only a small angular separation and occur in the low intensity region of the emission pattern. In this regard, we introduce an optical weak measurement approach that utilizes the transverse electric (azimuthal) and transverse magnetic (radial) far-field polarization basis. Projecting the far field onto a spatially varying postselected polarization state reveals the angular separation and the helicity of the C points. We demonstrate the applicability of this approach and determine the elliptical dipole moment of a particle sitting on an interface by measuring the C points in its far field.

Diffraction-limited near-spherical focal spot with controllable arbitrary polarization using single objective lens

We report a time-reversal method based on the Richards-Wolf vectorial diffraction theory to generate a diffraction-limited near-spherical focal spot with arbitrary three-dimensional state of polarization using single objective lens. Three orthogonal dipole antennae are positioned above a flat mirror at a prescribed distance and an aplanatic objective lens is utilized to collect all the radiation fields emitted by the dipole antennae. The optical field in the pupil plane is calculated in a time-reversal manner and the vectorial Debye integral is used to verify the spatial intensity and polarization distributions in the focal region. The ability to confine the optical power within a subwavelength near-spherical volume with controllable three-dimensional polarization with single objective lens may be exploited in high-resolution imaging, high-density data storage, laser direct writing, lithography, spin-directional coupling, anisotropic particle trapping and manipulation.

Sensitivity of displacement detection for a particle levitated in the doughnut beam

Displacement detection of a spherical particle in focused laser beams with a quadrant photodetector provides a fast and high precision way to determine the particle location. In contrast to the traditional Gaussian beams, the sensitivity of displacement detection using various doughnut beams is investigated. The sensitivity improvement for large spherical particles along the longitudinal direction is reported. With appropriate vortex charge l of the doughnut beams, they can outperform the Gaussian beam to get more than one order of magnitude higher sensitivity and, thus, have potential applications in various high-precision measurements. By using the levitating doughnut beam to detect the particle displacement, the result will also facilitate the recent proposal of levitating a particle in doughnut beams to suppress the light absorption.

Quantifying single plasmonic nanostructure far-fields with interferometric and polarimetric k-space microscopy

Optically resonant nanoantennae are key building blocks for metasurfaces, nanosensors, and nanophotonic light sources due to their ability to control the amplitude, phase, directivity, and polarization of scattered light. Here, we report an experimental technique for the full recovery of all degrees of freedom encoded in the far-field radiated by a single nanostructure using a high-NA Fourier microscope equipped with digital off-axis holography. This method enables full decomposition of antenna-physics in its multipole contributions and gives full access to the orbital and spin angular momentum properties of light scattered by single nano-objects. Our results demonstrate these capabilities through a quantitative assessment of the purity of the "selection rules" for orbital angular momentum transfer by plasmonic spiral nanostructures.

Probing spin density at the nanoscale using spin-orbital coupling in light scattering

We propose a scattering-type nano-polarimeter for probing the local spin density with subwavelength spatial resolution via the spin-orbital interactions at the nanoscale. The nano-polarimeter is simple to operate and can be applied to a variety of asymmetric nanoprobes, allowing direct data retrieval using two point detectors. Moreover, this technique is not limited to the spin-density detection but can also be used for the measurement of any given polarization states of light, no matter whether it is a free-space propagating wave or nonpropagating wave bound in the near-field region of nanostructures.

Retrieving the Size of Deep-Subwavelength Objects via Tunable Optical Spin-Orbit Coupling

We propose a scheme to retrieve the size parameters of a nanoparticle on a glass substrate at a scale much smaller than the wavelength. This is achieved by illuminating the particle using two plane waves to create rich and nontrivial local polarization distributions, and observing the far-field scattering pattern into the substrate. By using this illumination to control the induced complex dipole moment, the exponential decay of power radiated into the supercritical region, as well as directional scattering due to spin-orbit coupling can be exploited to retrieve the particle's shape, size, and position directly from the far-field scattering with high sensitivity and without the need for a complicated and time-consuming optimization algorithm. Our method brings about a far-field superresolution nanometrology scheme based on the interaction of vectorial light with nanoparticles.

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.

Spin-orbit interaction of light induced by transverse spin angular momentum engineering

The investigations on optical angular momenta and their interactions have broadened our knowledge of light's behavior at sub-wavelength scales. Recent studies further unveil the extraordinary characteristics of transverse spin angular momentum in confined light fields and orbital angular momentum in optical vortices. Here we demonstrate a direct interaction between these two intrinsic quantities of light. By engineering the transverse spin in the evanescent wave of a whispering-gallery-mode-based optical vortex emitter, a spin-orbit interaction is observed in generated vortex beams. Inversely, this unconventional spin-orbit interplay further gives rise to an enhanced spin-direction locking effect in which waveguide modes are unidirectionally excited, with the directionality jointly controlled by the spin and orbital angular momenta states of light. The identification of this previously unknown pathway between the polarization and spatial degrees of freedom of light enriches the spin-orbit interaction phenomena, and can enable various functionalities in applications such as communications and quantum information processing.

Directing Nanoscale Optical Flows by Coupling Photon Spin to Plasmon Extrinsic Angular Momentum

As any physical particle or object, light undergoing a circular trajectory features a constant extrinsic angular momentum. Within strong curvatures, this angular momentum can match the spin momentum of a photon, thus providing the opportunity of a strong spin-orbit interaction. Using this effect, we demonstrate tunable symmetry breaking in the coupling of light into a curved nanoscale plasmonic waveguide. The helicity of the impinging optical wave controls the power distribution between the two counter-propagating subwavelength guided modes including unidirectional waveguiding. We found experimentally that up to 95% of the incoupled light can be selectively directed into one of the two propagation directions of a nanoscale waveguide. This approach offers new degrees of freedom in the manipulation of subdiffraction optical modes and thus appealing new prospects for the development of advanced, deeply subwavelength optical functionalities.

Magnetic spin-orbit interaction of light

We study the directional excitation of optical surface waves controlled by the magnetic field of light. We theoretically predict that a spinning magnetic dipole develops a tunable unidirectional coupling of light to transverse electric (TE) polarized Bloch surface waves (BSWs). Experimentally, we show that the helicity of light projected onto a subwavelength groove milled into the top layer of a 1D photonic crystal (PC) controls the power distribution between two TE-polarized BSWs excited on both sides of the groove. Such a phenomenon is shown to be solely mediated by the helicity of the magnetic optical field, thus revealing a magnetic spin-orbit interaction of light. Remarkably, this magnetic optical effect is clearly observed via a near-field coupler governed by an electric dipole moment: it is of the same order of magnitude as the electric optical effects involved in the coupling. This opens up new degrees of freedom for the manipulation of light and offers desirable and novel opportunities for the development of integrated optical functionalities.

Topological Phase Transitions in the Photonic Spin Hall Effect

The recent synthesis of two-dimensional staggered materials opens up burgeoning opportunities to study optical spin-orbit interactions in semiconducting Dirac-like systems. We unveil topological phase transitions in the photonic spin Hall effect in the graphene family materials. It is shown that an external static electric field and a high frequency circularly polarized laser allow for active on-demand manipulation of electromagnetic beam shifts. The spin Hall effect of light presents a rich dependence with radiation degrees of freedom, and material properties, and features nontrivial topological properties. We discover that photonic Hall shifts are sensitive to spin and valley properties of the charge carriers, providing an unprecedented pathway to investigate spintronics and valleytronics in staggered 2D semiconductors.

Tightly focused optical field with controllable photonic spin orientation

The spin angular momentum of photons offers a robust, scalable and high-bandwidth toolbox for many promising applications based upon spin-controlled manipulations of light. In this work, we develop a method to achieve controllable photonic spin orientation within a diffraction limited optical focal spot produced by a high numerical aperture objective lens. The required pupil field is found analytically through reversing the radiation patterns from two electric dipoles located at the focal point of the lens with orthogonal oscillation directions and quadrature phase. The calculated pupil fields are experimentally generated with a vectorial optical field generator. The produced photonic spin orientations are quantitatively evaluated by their spin densities according to the tightly focused electric fields calculated by Richard-Wolf vectorial diffraction theory to demonstrate the validity and capability of the proposed technique.

Recent advances in the spin Hall effect of light

The spin Hall effect (SHE) of light, as an analogue of the SHE in electronic systems, is a promising candidate for investigating the SHE in semiconductor spintronics/valleytronics, high-energy physics and condensed matter physics, owing to their similar topological nature in the spin-orbit interaction. The SHE of light exhibits unique potential for exploring the physical properties of nanostructures, such as determining the optical thickness, and the material properties of metallic and magnetic thin films and even atomically thin two-dimensional materials. More importantly, it opens a possible pathway for controlling the spin states of photons and developing next-generation photonic spin Hall devices as a fundamental constituent of the emerging spinoptics. In this review, based on the viewpoint of the geometric phase gradient, we give a detailed presentation of the recent advances in the SHE of light and its applications in precision metrology and future spin-based photonics.

On-Chip Optimal Stokes Nanopolarimetry Based on Spin-Orbit Interaction of Light

Full measurement of the polarization of light at the nanoscale is expected to be crucial in many scientific and technological disciplines. Ideally, such measurements will require miniaturized Stokes polarimeters able to determine polarization nondestructively, locally, and in real time. For maximum robustness in measurement, the polarimeters should also operate optimally. Recent approaches making use of plasmonic nanostructures or metasurfaces are not able to fulfill all these requirements simultaneously. Here, we propose and demonstrate a method for subwavelength-footprint Stokes nanopolarimetry based on spin-orbit interaction of light. The method, which basically consists on a subwavelength scatterer coupled to a (set of) multimode waveguide(s), can fully determine the state of polarization satisfying all the previous features. Remarkably, the nanopolarimetry technique can operate optimally (we design a nanopolarimeter whose polarization basis spans 99.7% of the maximum tetrahedron volume inside the Poincaré sphere) over a broad bandwidth. Although here experimentally demonstrated on a silicon chip at telecom wavelengths, spin-orbit interaction-based nanopolarimetry is a universal concept to be applied in any wavelength regime or technological platform.

Experimental generation of complex optical fields for diffraction limited optical focus with purely transverse spin angular momentum

We demonstrate a method to generate complex optical fields at the pupil plane of a high numerical aperture (NA) objective lens for the creation of diffraction limited optical focus with purely transverse spin angular momentum. The complex optical fields are analytically deduced through reversing the radiated patterns from two electric dipoles, which are located at the focal point of the high NA lens and oscillate respectively in x- and z- directions with phase difference of π/2. The derived fields can be experimentally created with a vectorial optical field generator. Using the Richard-Wolf vectorial diffraction theory, the electric fields within the focal region are calculated to evaluate the intensities and polarization distributions of the tightly focused beams corresponding to both the theoretical and experimentally generated pupil fields and the results clearly demonstrate the validity of the proposed technique.

Coherent Control of Optical Spin-to-Orbital Angular Momentum Conversion in Metasurface

Efficient control over the conversion of optical angular momentum from spin to orbital form in a metasurface system is achieved. Under coherent symmetric incidence, it can support nearly 100% conversion and unitary output, while it can support 50% conversion with 25% transmittance under one beam incidence.

Tunable Spin dependent beam shift by simultaneously tailoring geometric and dynamical phases of light in inhomogeneous anisotropic medium

Spin orbit interaction and the resulting Spin Hall effect of light are under recent intensive investigations because of their fundamental nature and potential applications. Here, we report an interesting manifestation of spin Hall effect of light and demonstrate its tunability in an inhomogeneous anisotropic medium exhibiting spatially varying retardance level. In our system, the beam shift occurs only for one circular polarization mode keeping the other orthogonal mode unaffected, which is shown to arise due to the combined spatial gradients of the geometric phase and the dynamical phase of light. The constituent two orthogonal circular polarization modes of an input linearly polarized light evolve in different trajectories, eventually manifesting as a large and tunable spin separation. The spin dependent beam shift and the demonstrated principle of simultaneously tailoring space-varying geometric and dynamical phase of light for achieving its tunability (of both magnitude and direction), may provide an attractive route towards development of spin-optical devices.

Accurate Feeding of Nanoantenna by Singular Optics for Nanoscale Translational and Rotational Displacement Sensing

Identifying subwavelength objects and displacements is of crucial importance in optical nanometrology. We show in this Letter that nanoantennas with subwavelength structures can be excited precisely by incident beams with singularity. This accurate feeding beyond the diffraction limit can lead to dynamic control of the unidirectional scattering in the far field. The combination of the field discontinuity of the incoming singular beam with the rapid phase variation near the antenna leads to remarkable sensitivity of the far-field scattering to the displacement at a scale much smaller than the wavelength. This Letter introduces a far-field deep subwavelength position detection method based on the interaction of singular optics with nanoantennas.

Lateral spin transport in paraxial beams of light

We investigate the lateral transport of (longitudinal) spin angular momentum in a special polarization tailored light beam composed of a superposition of a y-polarized zero-order and an x-polarized first-order Hermite-Gaussian mode. This phenomenon is linked to the relative Gouy phase shift between the individual modes upon propagation, but can also be interpreted as a geometric phase effect. Experimentally, we demonstrate the implementation of such a mode and measure the spin density upon propagation.