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

A circularly polarized electromagnetic plane wave carries an electric field that rotates clockwise or counterclockwise around the propagation direction of the wave. According to the handedness of this rotation, its longitudinal spin angular momentum (AM) density is either parallel or antiparallel to the propagation of light. However, there are also light waves that are not simply plane and carry an electric field that rotates around an axis perpendicular to the propagation direction, thus yielding transverse spin AM density. Electric field configurations of this kind have been suggestively dubbed ‘photonic wheels’. It has been recently shown that photonic wheels are commonplace in optics as they occur in electromagnetic fields confined by waveguides, in strongly focused beams, in plasmonic and evanescent waves. In this work we establish a general theory of electromagnetic waves propagating along a well defined direction, and carrying transverse spin AM density. We show that depending on the shape of these waves, the spin density may be either perpendicular to the mean linear momentum (globally transverse spin) or to the linear momentum density (locally transverse spin). We find that the latter case generically occurs only for non-diffracting beams, such as the Bessel beams. Moreover, we introduce the concept of meridional Stokes parameters to operationally quantify the transverse spin density. To illustrate our theory, we apply it to the exemplary cases of Bessel beams and evanescent waves. These results open a new and accessible route to the understanding, generation and manipulation of optical beams with transverse spin AM density.

The spin‐orbit interaction (SOI) of light generated by tight focusing in optical tweezers is regularly employed in generating angular momentum ‐ both spin and orbital ‐ the effects being extensively observed in trapped mesoscopic particles. Specifically, the transverse spin angular momentum (TSAM), which arises due to the longitudinal component of the electromagnetic field generated by tight focusing is of special interest, both in terms of fundamental studies and associated applications. This study provides an effective and optimal strategy for generating TSAM in optical tweezers by tightly focusing first‐order radially and azimuthally polarized vector beams with no intrinsic angular momentum (AM) into a refractive index stratified medium. The choice of such input fields ensures that the longitudinal spin angular momentum (LSAM) arising from the electric (magnetic) field for the radial (azimuthal) polarization is zero. As a result, the effects of the electric and magnetic TSAM are exclusively observed separately in the case of input first‐order radially and azimuthally polarized vector beams on single optically trapped birefringent particles. This research opens up new and simple avenues for exotic and complex particle manipulation in optical tweezers.

Light carries both longitudinal and transverse spin angular momentum. The spin can couple with its orbital counterpart, known as the spin-orbit interaction (SOI) of light. Complementary to the longitudinal SOI known previously, here we show that transverse SOI of light is inherent in the Helmholtz equation when transverse spinning light propagates in curved paths. It lifts the degeneracy of dispersion relations of light for opposite transverse spin states, analogous to the Dresselhaus effect. Transverse SOI is ubiquitous in nanophotonic systems where transverse spin and optical path bending are inevitable. It can explain anomalous effects like the dispersion relation of surface plasmon polaritons on curved paths and the energy level of whispering gallery modes. Our results reveal the analogies of spin photonics and spintronics and offer a new degree of freedom for integrated photonics, spin photonics, and astrophysics.

Optical vortex beams, carrying orbital angular momentum (OAM), are of great interest for applications in optical communications, particle manipulation, and quantum information processing. However, achieving high‐efficiency generation and manipulation of vortex beams with a single compact element, particularly in the visible range, remains challenging. Here, we demonstrate laser‐written geometric phase fork gratings in silica glass that enable simultaneous generation and propagation control of vortex beams with an efficiency up to 98.4% at 515 nm. By tailoring the phase‐gradient period and topological charge ( l = 1–100), we achieve tunable control over the vortex beam's topological charge, diameter, and diffraction position. The fabricated gratings maintain high efficiency across a broad spectral range from 450 to 690 nm. Furthermore, we demonstrate spin–orbit coupling between incident vortices and fork gratings, verifying that the output OAM values follow the expected addition rule l out = l in ± l fork . In addition, the fork gratings exhibit excellent thermal stability (up to 800°C) and optical damage threshold (close to pristine silica glass). These results establish nanopore‐based geometric‐phase fork gratings as a scalable, broadband, high‐performance platform with outstanding thermal and optical tolerance for next‐generation OAM photonics.

Optical vortices carrying orbital angular momentum (OAM) have attracted extensive attention in recent decades because of their interesting applications in optical trapping, optical machining, optical communication, quantum information, and optical microscopy. Intriguing effects induced by OAMs, such as angular momentum conversion, spin Hall effect of light (SHEL), and spin–orbital interaction, have also gained increasing interest. In this article, we provide an overview of the modulations of OAMs on the propagation dynamics of scalar and vector fields in free space. First, we introduce the evolution of canonical and noncanonical optical vortices and analyze the modulations by means of local spatial frequency. Second, we review the Pancharatnam–Berry (PB) phases arising from spin–orbital interaction and reveal the control of beam evolution referring to novel behavior such as spindependent splitting and polarization singularity conversion. Finally, we discuss the propagation and focusing properties of azimuthally broken vector vortex beams.

Light orbital angular momentum (OAM) has been recognized as a new promising resource for classical and quantum information applications. In contrast to the spin angular momentum, the OAM is an inherently multidimensional. Thus, the information can be encoded in the higher-dimensional OAM alphabets. Recently, Marrucci et al. have invented a new device named q-plate (QP), made of liquid crystal cell patterned in such a way to introduce a topological charge q at the transverse plane, which is able to generate a well-defined values of photon OAM. My research has been aimed at investigating the physics of the QP, of the optical fields that it generates and of its possible applications for optical communication and quantum information. We studied both theoretically and experimentally a novel set of non-orthogonal but over-complete paraxial modes, named Hypergeometric-Gaussian modes, that is typically associated with OAM-carrying optical fields. We have also found the light propagation kernel inside the QP and we have shown analytically that if small losses due to reflection, absorption, and scattering are neglected, the QP can convert the photon spin into OAM with up to 100 \% efficiency. We implemented a technique to control the QP optical retardation by tuning the QP temperature. At the optimal temperature, the QP can generate a beam with up to 97\% efficiency. Moreover, the OAM state generated by QP can be rotated easily in the 2D OAM Hilbert space by proper manipulation of the input polarization state, a fact which opens a new way of beam shape controlling in MHz scale. We also performed a novel way to encode and read two bits information on the 4D OAM space by using only one QP. Finally, we experimentally demonstrated the transfer of quantum information from spin to OAM and vice versa, including the case of bi-photon states having quantum correlations. Furthermore, by exploiting these quantum information transfer devices, we demonstrated the Hong-Ou-Mandel effect and the optimal quantum cloning with OAM-carrying photons.

Twisted light with orbital angular momentum (OAM) has been extensively studied for applications in quantum and classical communications, microscopy, and optical micromanipulation. Ejecting high angular momentum states of a whispering gallery mode (WGM) microresonator through a grating-assisted mechanism provides a scalable, chip-integrated solution for OAM generation. However, demonstrated OAM microresonators have exhibited a much lower quality factor (Q) than conventional WGM resonators (by >100×), and an understanding of the limits on Q has been lacking. This is crucial given the importance of Q in enhancing light-matter interactions. Moreover, though high-OAM states are often desirable, the limits on what is achievable in a microresonator are not well understood. Here, we provide insight on these two questions, through understanding OAM from the perspective of mode coupling in a photonic crystal ring and linking it to coherent backscattering between counter-propagating WGMs. In addition to demonstrating high-Q (105 to 106), a high estimated upper bound on OAM ejection efficiency (up to 90%), and high-OAM number (up to l = 60), our empirical model is supported by experiments and provides a quantitative explanation for the behavior of Q and the upper bound of OAM ejection efficiency with l. The state-of-the-art performance and understanding of microresonator OAM generation opens opportunities for OAM applications using chip-integrated technologies.

Optical vortices usually carry integer orbital angular momentum (OAM) of light. Recently, optical vortices with rational-order OAMs have also been created continuously for entangling the super-position OAM states of monochromatic light in a single device. Here, we report the broadband generation of such rational-order optical vortex beams by using a bilateral meta-grating. The meta-grating contains two oblique gratings that encode two sign-opposite linear phase profiles in two symmetric sides, thus leading to phase dislocation along the symmetric axis. We reveal that the encoded phase profiles are valid in a range of wavelengths due to the broadband response of the meta-grating. The measured phase, intensity and tilting angles match perfectly with theoretical prediction, suggesting the bilateral meta-grating as a powerful device to create broadband and continuous OAM of light for various applications such as optical micro-manipulation, optical communication, quantum physics, and super-resolution imaging.

Optical vortices are a new kind of laser beam and receiving more and more attention currently.The complex amplitudes of optical vortices comprise a helical term exp (il),with l being the topological charge and the azimuthal angle.Each photon in optical vortices carries the orbital angular momentum (OAM) with a value of lħ,where ħ is the Planck's constant divided by 2.The topological charge l is the eigenvalue of optical vortices,and determines the helical wavefront distribution,thus also known as OAM state.Moreover,such an OAM state can be an infinite integer state. And vortices with various OAM states are orthogonal to each other,making it possible to be employed in high capacity data-transmission system.In addition,the above unique features contribute to their widely applications in lots of areas such as optical tweezers and spanners,rotation detection,quantum entanglement,etc.In these applications,detecting OAM states is basic,and greatly significant.Recently researchers have developed lots of approaches to detecting the OAM states,including the methods of interference,diffraction gratings,metasurface,etc.Of such approaches,the scheme of diffraction gratings is the simplest and most widely used,where one or more diffraction gratings are employed. When optical vortices propagate through such gratings,the OAM states are acquired immediately through capturing and analyzing the distinct OAM-related diffraction patterns.In this review,we focus on the techniques of detecting OAM states through diffraction gratings,which have been demonstrated by our group and other researchers.Some of the main detection gratings,including double-slit,triangle aperture and slit,angular slit,cylindrical lens,graduallychanging-period grating,annular grating,are introduced.In addition,schemes like composite fork grating,Dammann vortex grating and integrated Dammann grating,are presented to detect the OAM state for coaxial multiplexed vortices. Besides diagnosing OAM state,measuring the intensity proportion of each OAM channel,known as OAM spectrum, in multiplexed vortices is also necessary in some cases.Therefore we also introduce the ways to measure the OAM spectrum,e.g.the OAM mode sorter,the gray-scale algorithm.

We experimentally demonstrate and evaluate the performance of an analog signal transmission system with photonic integrated optical vortex emitter and 3.6-km few-mode fiber (FMF) link using orbital angular momentum (OAM) modes. The fabricated photonic integrated device is capable of emitting vector optical vortices carrying well-defined and quantized OAM modes with topological charge l=-2 and 2. After propagating through 3.6-km FMF, we measure and assess the spurious free dynamic range of the second-order harmonic distortion. Moreover, we study the impact of nonlinearity-induced resonance wavelength shift of the optical vortex emitter on the analog link performance as increasing the input optical power.

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

We study the energy ow pattern in the superposition of two off-axis optical vortices with orthogonal polarization states. This system presents a rich structure of polarization singularities, which allows us to study the transverse spin and orbital angular momentum of different polarization morphologies, which includes C points (stars, lemons and monstars) and L lines. We perform numerical simulations of the optical forces acting on submicron particles and show interesting configurations. We provide the set of control parameters to unambiguously distinguish between the spin and orbital ow contributions.

Transverse spin angular momentum, which appears locally in the structured optical fields, has attracted much attention, owing to its extraordinary properties and potential applications. We show theoretically that, by highly focusing a vector vortex beam with azimuthally varied polarization, it is possible to trap multiple particles simultaneously and manipulate the particles' spin along the azimuthal direction. Both the direction and the magnitude of the spin angular momentum, so the spin torque on the particle, can be varied by changing the state of the input beams. Moreover, the magnitude of the spin torque can be manipulated further by changing the characteristics of the particles. Such results may be exploited in practical optical manipulation, especially for optically induced rotations.

Light beams carrying both spin (polarization) and orbital angular momentum (OAM) can be represented by mapping the total angular momentum onto a higher-order Poincaré sphere [1]. Due to the non-separability of the polarization and OAM degrees-of-freedom, these beams, commonly known as vector vortex beams, find varieties of applications in scientific and technological fields including photon entanglement [2], material processing [3] and microscopy [4]. Such beams are commonly generated using q-plates [5] and liquid crystal based spatial light modulators [6]. However, the limitation of low power handling and restricted wavelength coverage of such techniques can be addressed through the vector vortex beam generation using nonlinear parametric processes. Unfortunately, the dependence of phase-matching of the parametric processes on the polarization of the interacting beams puts the major hindrance to the nonlinear generation of vector vortex beams. Here we report a novel experimental scheme to generate vector vortex beams using single pass second harmonic generation (SHG) of ultrafast higher order vector vortex beams.

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