Direct Observation of Spin-Orbit Interaction of Light via Chiroptical Responses.

The spin-orbit interaction of light is a fundamental manifestation of controlling its angular momenta with numerous applications in photonic spin Hall effects and chiral quantum optics. However, observation of an optical spin Hall effect, which is normally very weak with subwavelength displacements, needs quantum weak measurements or sophisticated metasurfaces. Here, we theoretically and experimentally demonstrate the spin-orbit interaction of light in the form of strong chiroptical responses by breaking the in-plane inversion symmetry of a dielectric substrate. The chiroptical signal is observed at the boundary of a microdisk illuminated by circularly polarized vortex beams at normal incidence. The generated chiroptical spectra are tunable for different photonic orbital angular momenta and microdisk diameters. Our findings, correlating photonic spin-orbit interaction with chiroptical responses, may provide a route for exploiting optical information processing, enantioselective sensing, and chiral metrology.

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.

Nonlinear Metasurface for Simultaneous Control of Spin and Orbital Angular Momentum in Second Harmonic Generation.

The spin and orbital angular momentum (SAM and OAM) of light is providing a new gateway toward high capacity and robust optical communications. While the generation of light with angular momentum is well studied in linear optics, its further integration into nonlinear optical devices will open new avenues for increasing the capacity of optical communications through additional information channels at new frequencies. However, it has been challenging to manipulate the both SAM and OAM of nonlinear signals in harmonic generation processes with conventional nonlinear materials. Here, we report the generation of spin-controlled OAM of light in harmonic generations by using ultrathin photonic metasurfaces. The spin manipulation of OAM mode of harmonic waves is experimentally verified by using second harmonic generation (SHG) from gold meta-atom with 3-fold rotational symmetry. By introducing nonlinear phase singularity into the metasurface devices, we successfully generate and measure the topological charges of spin-controlled OAM mode of SHG through an on-chip metasurface interferometer. The nonlinear photonic metasurface proposed in this work not only opens new avenues for manipulating the OAM of nonlinear optical signals but also benefits the understanding of the nonlinear spin-orbit interaction of light in nanoscale devices.

Structuring Light by Concentric-Ring Patterned Magnetic Metamaterial Cavities.

Ultracompact and tunable beam converters pose a significant potential for modern optical technologies ranging from classical and quantum communication to optical manipulation. Here we design and demonstrate concentric-ring patterned structures of magnetic metamaterial cavities capable of tailoring both polarization and phase of light by converting circularly polarized light into a vector beam with an orbital angular momentum. We experimentally illustrate the realization of both radially and azimuthally polarized vortex beams using such concentric-ring patterned magnetic metamaterials. These results contribute to the advanced complex light manipulation with optical metamaterials, making it one step closer to realizing the simultaneous control of polarization and orbital angular momentum of light on a chip.

Optomechanical motions of gold dimer's spin, rotation and revolution manipulated by bessel beam.

The optomechanical motion of a gold nanoparticle (GNP) dimer-a pair of optically bound GNPs-in fluid, manipulated by a Bessel beam, is theoretically studied using the multiple multipole (MMP) method. Since a Bessel beam possesses orbital angular momentum (OAM) and spin angular momentum (SAM) simultaneously, complicated rigid-body motions of the dimer can be induced. The mechanism involves the equilibrium between the optical force with the reactive drag force exerted by the fluid. Our results demonstrate that the dimer rotates around its center of mass (COM), while the COM performs an orbital revolution around the optical axis. Additionally, each individual GNP undergoes spinning. The directions of the GNPs' spin and the orbital revolution of COM depend on the handedness and the order (topological charge) of Bessel beam, respectively. Nevertheless, the rotation direction of the dimer depends on the size of GNP. In the case of a smaller dimer, the direction of dimer's rotation with respect to the COM is consistent with the handedness of the light. Conversely, a larger dimer performs a reverse rotation, accompanied by a precession during the orbital revolution. There are multiple turning points in the radius of the GNP for the alternating rotation of the dimer caused by positive or negative optical torque. Our finding may provide an insight to the optomechanical manipulation of optical vortexes on the motions of GNP clusters.

SU(N) symmetry of coherent photons controlled by rotated waveplates.

The coherent state from a laser source has spin and orbital degrees of freedom, which allow an arbitrary superposition state among orthogonal states with varying amplitudes and phases. Here, we theoretically show coherent photons with SU(N) symmetry are characterised by expectation values of angular momentum shown on a hypersphere in SO( N 2 - 1 ) space. To demonstrate expected unitary transformations in experiments, we have constructed generators of transformations in the Lie group simply by combining widely available optical components such as waveplates and vortex lenses. We show a superposition state between twisted and Gaussian states is characterised by the dynamics of the topological charge upon the transformation in SU(3) states. We also realised photonic singlet and triplet states corresponding to SU(4) states, which were projected to SU(2)×SU(2) states upon passing through a rotated polariser.

Dirac equation for photons in a fibre: Origin of polarisation.

Spin is a fundamental degree of freedom, which was discovered by Dirac for an electron in his relativistic quantum mechanics, known as the Dirac equation. The origin of spin for a photon is unclear because Maxwell's equations in a vacuum are Lorentz invariant without introducing the concept of spin. Here, the propagation of coherent rays of photons in a graded-index optical fibre is considered to discuss the origin of polarisation for photons using exact solutions of the Laguerre-Gauss and Hermite-Gauss modes. The energy spectrum is massive, and the effective mass is a function of the confinement and orbital angular momentum. The propagation is described by the one-dimensional (1D) non-relativistic Schrödinger equation, which is equivalent to the 2D space-time Klein-Gordon equation by a unitary transformation. The probabilistic interpretation and the conservation law require the factorisation of the Klein-Gordon equation, leading to the 2D Dirac equation with spin. The spin expectation values of photons correspond to the polarisation state on the Poincaré sphere. As an application of the theory, a polarisation interferometer is proposed, whose energy spectrum shows a Dirac cone in the Stokes parameter space.

Enhancing the Spin Hall Effect of Cylindrically Polarized Beams.

Two linked gear wheels in a micromachine can be simultaneously rotated in opposite directions by using a laser beam that has in its section areas the spin angular momentum (SAM) of the opposite sign. However, for instance, a cylindrical vector beam has zero SAM in the focus. We alter a cylindrical vector beam so as to generate areas in its focus where the SAM is of opposite signs. The first alteration is adding to the cylindrical vector beam a linearly polarized beam. Thus, we study superposition of two rotationally symmetric beams: those with cylindrical and linear polarization. We obtain an expression for the SAM and prove two of its properties. The first property is that changing superposition coefficients does not change the shape of the SAM density distribution, whereas the intensity changes. The second property is that maximal SAM density is achieved when both beams in the superposition have the same energy. The second perturbation is adding a spatial carrier frequency. We study the SAM density of a cylindrical vector beam with a spatial carrier frequency. Due to periodic modulation, upon propagation in space, such a beam is split into two beams, having left and right elliptic polarization. Thus, in the beam transverse section, areas with the spin of different signs are separated in space, which is a manifestation of the spin Hall effect. We demonstrate that such light beams can be generated by metasurfaces, with the transmittance depending periodically on one coordinate.

Spin-Manipulated Photonic Skyrmion-Pair for Pico-Metric Displacement Sensing.

Photonic spin skyrmions with deep-subwavelength features have aroused considerable interest in recent years. However, the manipulation of spin structure in the skyrmions in a desired manner is still a challenge, while this is crucial for developing the skyrmion-based applications. Here, an approach of optical spin manipulation by utilizing the spin-momentum equation is proposed to investigate the spin texture in a photonic skyrmion-pair. With the benefit of the proposed approach, a unique spin texture with spin angular momentum varying linearly along the line connecting the two skyrmion centers is theoretically designed and experimentally verified. The optimized spin texture is then applied in a displacement-sensing system, which is capable of attaining pico-metric sensitivity. Compared with the conventional polarization and phase schemes, the spin-based manipulation mechanism provides a new pathway for optical modulation, which is of great value in nanophotonics from both fundamental and application.

Multichannel Single-Photon Emissions with On-Demand Momentums by Using Anisotropic Quantum Metasurfaces.

Photon momentums and their control are important for carrying quantum information and increasing information capacities. It is a great challenge to freely control multiple momentums of single photons based on only phase-dependent schemes in isotropic metasurfaces because exact manipulations of interference phases and precise alignments between quantum emitters and metasurfaces are involved. Here, an anisotropic metasurface, in which anisotropic rather than isotropic nanoscatterers are arranged anisotropically, is proposed to freely control multiple momentums of single photons. In the metasurfaces, the phase-independent and phase-dependent schemes are used to independently control spin angular momentums (SAMs) and linear momentums (LMs), respectively. The phase-independent scheme allows robust alignment between quantum emitters and metasurfaces. The anisotropic design amends geometrical phases for oblique emissions, providing larger ranges (up to 53°) for tailoring LMs. In experiments, three-channel single-photon emissions with independent SAMs and LMs are demonstrated. The introduction of anisotropic nanoscatterers and anisotropic arrangements of nanoscatterers is a more general design method for metasurfaces, and it could provide more flexibility to freely and efficiently tailor single-photon emissions.

Spin Hall Effect in Paraxial Vectorial Light Beams with an Infinite Number of Polarization Singularities.

Elements of micromachines can be driven by light, including structured light with phase and/or polarization singularities. We investigate here a paraxial vector Gaussian beam with an infinite number of polarization singularities residing evenly on a straight line. The intensity distribution is derived analytically and the polarization singularities are shown to exist only in the initial plane and in the far field. The azimuthal angle of the polarization singularities is shown to increase in the far field by π/2. We obtain the longitudinal component of the spin angular momentum (SAM) density and show that it is independent of the azimuthal angle of the polarization singularities. Upon propagation in free space, an infinite number of C-points is generated, where polarization is circular. We show that the SAM density distribution has a shape of four spots, two with left and two with right elliptic polarization. The distance to the transverse plane with the maximal SAM density decreases with decreasing distance between the polarization singularities in the initial plane. Generating such alternating areas with positive and negative SAM density, despite linear polarization in the initial plane, manifests the optical spin Hall effect. Application areas of the obtained results include designing micromachines with optically driven elements.

Spin Hall Effect in the Paraxial Light Beams with Multiple Polarization Singularities.

Elements of micromachines can be driven by light, including structured light with phase and/or polarization singularities. We investigate a paraxial vectorial Gaussian beam with multiple polarization singularities residing on a circle. Such a beam is a superposition of a cylindrically polarized Laguerre-Gaussian beam with a linearly polarized Gaussian beam. We demonstrate that, despite linear polarization in the initial plane, on propagation in space, alternating areas are generated with a spin angular momentum (SAM) density of opposite sign, that manifest about the spin Hall effect. We derive that in each transverse plane, maximal SAM magnitude is on a certain-radius circle. We obtain an approximate expression for the distance to the transverse plane with the maximal SAM density. Besides, we define the singularities circle radius, for which the achievable SAM density is maximal. It turns out that in this case the energies of the Laguerre-Gaussian and of the Gaussian beams are equal. We obtain an expression for the orbital angular momentum density and find that it is equal to the SAM density, multiplied by -m/2 with m being the order of the Laguerre-Gaussian beam, equal to the number of the polarization singularities. We consider an analogy with plane waves and find that the spin Hall affect arises due to the different divergence between the linearly polarized Gaussian beam and cylindrically polarized Laguerre-Gaussian beam. Application areas of the obtained results are designing micromachines with optically driven elements.

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.

Spin Hall Effect of Double-Index Cylindrical Vector Beams in a Tight Focus.

We investigate the spin angular momentum (SAM) of double-index cylindrical vector beams in tight focus. Such a set of beams is a generalization of the conventional cylindrical vector beams since the polarization order is different for the different transverse field components. Based on the Richards-Wolf theory, we obtain an expression for the SAM distribution and show that if the polarization orders are of different parity, then the spin Hall effect occurs in the tight focus, which is there are alternating areas with positive and negative spin angular momentum, despite linear polarization of the initial field. We also analyze the orbital angular momentum spectrum of all the components of the focused light field and determine the overwhelming angular harmonics. Neglecting the weak harmonics, we predict the SAM distribution and demonstrate the ability to generate the focal distribution where the areas with the positive and negative spin angular momentum reside on a ring and are alternating in pairs, or separated in different semicircles. Application areas of the obtained results are designing micromachines with optically driven elements.

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.

Active Manipulation of The Spin and Orbital Angular Momentums in a Terahertz Graphene-Based Hybrid Plasmonic Waveguide.

Angular momentums (AMs) of photons are crucial physical properties exploited in many fields such as optical communication, optical imaging, and quantum information processing. However, the active manipulation (generation, switching, and conversion) of AMs of light on a photonic chip remains a challenge. Here, we propose and numerically demonstrate a reconfigurable graphene-based hybrid plasmonic waveguide (GHPW) with multiple functions for on-chip AMs manipulation. Its physical mechanism lies in creating a switchable phase delay of ±π/2 between the two orthogonal and decomposed linear-polarized waveguide modes and the spin-orbit coupling in the GHPW. For the linear-polarized input light with a fixed polarization angle of 45°, we can simultaneously switch the chirality (with -ћ/+ћ) of the transverse component and the spirality (topological charge ℓ = -1/+1) of the longitudinal component of the output terahertz (THz) light. With a switchable phase delay of ±π in the GHPW, we also developed the function of simultaneous conversion of the charity and spirality for the circular-polarized input light. In addition, a selective linear polarization filtering with a high extinction ratio can be realized. With the above multiple functions, our proposed GHPWs are a promising platform in AMs generation, switching, conversion, and polarization filtering, which will greatly expand its applications in the THz photonic integrated circuits.

Control of the Spin Angular Momentum and Orbital Angular Momentum of a Reflected Wave by Multifunctional Graphene Metasurfaces.

Three kinds of multifunctional graphene metasurfaces based on Pancharatnam⁻Berry (PB) phase cells are proposed and numerically demonstrated to control a reflected wave’s spin angular momentum (SAM) and orbital angular momentum (OAM) in the terahertz (THz) regime. Each proposed metasurface structure is composed of an array of graphene strips with different deviation angles and a back-grounded quartz substrate. In order to further help readers have a deeper insight into the graphene-based metasurfaces, a detailed design strategy is also provided. With the aid of the designed graphene elements, the proposed metasurfaces can achieve the full 360° range of phase coverage and provide manipulation of SAM and OAM of a circularly polarized (CP) wave at will. More importantly, simultaneous control of these two momentums can also be realized, and in order to demonstrate this function, a THz spin-controlled OAM beam generator with diverse topological charges is created, which can provide one more degree of freedom to improve the channel capability without increasing the bandwidth compared to a linearly polarized (LP) OAM beam. Numerical results verify the proposed graphene metasurfaces, which pave the way for generating spin OAM vortex waves for THz communication systems.

Rotational Dynamics and Heating of Trapped Nanovaterite Particles.

We synthesize, optically trap, and rotate individual nanovaterite crystals with a mean particle radius of 423 nm. Rotation rates of up to 4.9 kHz in heavy water are recorded. Laser-induced heating due to residual absorption of the nanovaterite particle results in the superlinear behavior of the rotation rate as a function of trap power. A finite element method based on the Navier-Stokes model for the system allows us to determine the residual optical absorption coefficient for a trapped nanovaterite particle. This is further confirmed by the theoretical model. Our data show that the translational Stokes drag force and rotational Stokes drag torque need to be modified with appropriate correction factors to account for the power dissipated by the nanoparticle.

Optomechanical measurement of photon spin angular momentum and optical torque in integrated photonic devices.

Photons carry linear momentum and spin angular momentum when circularly or elliptically polarized. During light-matter interaction, transfer of linear momentum leads to optical forces, whereas transfer of angular momentum induces optical torque. Optical forces including radiation pressure and gradient forces have long been used in optical tweezers and laser cooling. In nanophotonic devices, optical forces can be significantly enhanced, leading to unprecedented optomechanical effects in both classical and quantum regimes. In contrast, to date, the angular momentum of light and the optical torque effect have only been used in optical tweezers but remain unexplored in integrated photonics. We demonstrate the measurement of the spin angular momentum of photons propagating in a birefringent waveguide and the use of optical torque to actuate rotational motion of an optomechanical device. We show that the sign and magnitude of the optical torque are determined by the photon polarization states that are synthesized on the chip. Our study reveals the mechanical effect of photon's polarization degree of freedom and demonstrates its control in integrated photonic devices. Exploiting optical torque and optomechanical interaction with photon angular momentum can lead to torsional cavity optomechanics and optomechanical photon spin-orbit coupling, as well as applications such as optomechanical gyroscopes and torsional magnetometry.

Catenary optics for achromatic generation of perfect optical angular momentum.

The catenary is the curve that a free-hanging chain assumes under its own weight, and thought to be a "true mathematical and mechanical form" in architecture by Robert Hooke in the 1670s, with nevertheless no significant phenomena observed in optics. We show that the optical catenary can serve as a unique building block of metasurfaces to produce continuous and linear phase shift covering [0, 2π], a mission that is extremely difficult if not impossible for state-of-the-art technology. Via catenary arrays, planar optical devices are designed and experimentally characterized to generate various kinds of beams carrying orbital angular momentum (OAM). These devices can operate in an ultra-broadband spectrum because the anisotropic modes associated with the spin-orbit interaction are almost independent of the incident light frequency. By combining the optical and topological characteristics, our approach would allow the complete control of photons within a single nanometric layer.