Vortex beam nanofocusing and optical skyrmion generation via hyperbolic metamaterials

Spin and orbital angular momenta (AM) are of fundamental importance in physics. Acoustic waves, as typical longitudinal waves, are often perceived as spin-0 waves. Although spin AM density has been found in acoustics, the total longitudinal spin AM is, however, often vanishing. Here, from a self-consistent theoretical frame, we establish the spin, orbital, and total AM of acoustic vortex beams, and discover that a non-zero integral longitudinal spin AM is carried by the propagating acoustic field. With the longitudinal acoustic spin, we unveil a new mechanism of spin-orbit interaction emerging when a vortex beam is compressed or expanded. Moreover, we reveal the connection and distinction between the acoustic canonical-Minkowski and kinetic-Abraham AM, and prove that only the former is conserved under the corresponding symmetry. Our discovery elucidates new fundamental aspects of spin and orbital AM as well as their interplay in acoustics, which can be extended to other classical waves and may open up new ways for AM-based applications in these systems.

We present a study of the properties of the transversal "spin angular momentum" and "orbital angular momentum" operators. We show that the "spin angular momentum" operators are generators of spatial translations which depend on helicity and frequency and that the "orbital angular momentum" operators generate transformations which are a sequence of this kind of translations and rotations. We give some examples of the use of these operators in light matter interaction problems. Their relationship with the helicity operator allows to involve the electromagnetic duality symmetry in the analysis. We also find that simultaneous eigenstates of the three "spin" operators and parity define a type of standing modes which has been recently singled out for the interaction of light with chiral molecules. With respect to the relationship between "spin angular momentum", polarization, and total angular momentum, we show that, except for the case of a single plane wave, the total angular momentum of the field is decoupled from its vectorial degrees of freedom even in the regime where the paraxial approximation holds. Finally, we point out a relationship between the three "spin" operators and the spatial part of the Pauli-Lubanski four vector.

We present an approach to separating the angular momentum (AM) flux of monochromatic light into its spin and orbital parts based on a symmetrized AM tensor When considering the AM flux for a light beam through its cross section and that for an outgoing wave through a spherical surface in the far-field zone, the separation gives the desired results: the spin/orbital AM flux equals the integral of spin/orbital AM density times some weighting factor accounting for energy flux. When applied to Bessel beams, the obtained spin and orbital AM fluxes are exactly the same as those given by the paper (2014 New J. Phys. 16 093037) based on the canonical AM tensor separation. Furthermore, from the spin AM flux integral, the divergence-free spin AM tensor can be identified. We define the orbital AM tensor to be the difference between the total AM tensor and Since is divergence-free, the integral for either spin and orbital AM flux, can be made on any closed surface.

Light with nonzero orbital angular momentum (OAM) or twisted light is promising for quantum communication applications such as OAM-entangled photonic qubits. Methods and devices for the conversion of the photonic OAM to photonic spin angular momentum (SAM), as well as for the photonic SAM to electronic SAM transformation are known but the direct conversion between the photonic OAM and electronic SAM is not available within a single device. Here, we propose a scheme which converts photonic OAM to electronic SAM and vice versa within a single nanophotonic device. We employed a photonic crystal nanocavity with an embedded quantum dot (QD) which confines an electron spin as a stationary qubit. The confined spin-polarized electrons could recombine with holes to give circularly polarized emission, which could drive the rotation of the nanocavity modes via the strong optical spin-orbit interaction. The rotating modes then radiate light with nonzero OAM, allowing this device to serve as a transmitter. As this can be a unitary process, the time-reversed case enables the device to function as a receiver. This scheme could be generalized to other systems with a resonator and quantum emitters such as a microdisk and defects in diamond for example. Our scheme shows the potential for realizing an (ultra)compact electronic SAM-photonic OAM interface to accommodate OAM as an additional degree of freedom for quantum information purposes.

Spin and orbital angular momenta (AM) of light are well studied for free-space electromagnetic fields, even nonparaxial. One of the important applications of these concepts is the information transfer using AM modes, often via optical fibers and other guiding systems. However, the self-consistent description of the spin and orbital AM of light in optical media (including dispersive and metallic cases) was provided only recently [K.Y. Bliokh et al., Phys. Rev. Lett. 119, 073901 (2017)]. Here we present the first accurate calculations, both analytical and numerical, of the spin and orbital AM, as well as the helicity and other properties, for the full-vector eigenmodes of cylindrical dielectric and metallic (nanowire) waveguides. We find remarkable fundamental relations, such as the quantization of the canonical total AM of cylindrical guided modes in the general nonparaxial case. This quantization, as well as the noninteger values of the spin and orbital AM, are determined by the generalized geometric and dynamical phases in the mode fields. Moreover, we show that the spin AM of metallic-wire modes is determined, in the geometrical-optics approximation, by the transverse spin of surface plasmon-polaritons propagating along helical trajectories on the wire surface. Our work provides a solid platform for future studies and applications of the AM and helicity properties of guided optical and plasmonic waves.

We consider the evolution of a binary system interacting due to tidal effects without restriction on the orientation of the orbital, and where significant, spin angular momenta, and orbital eccentricity. We work in the low tidal forcing frequency regime in the equilibrium tide approximation. Internal degrees of freedom are fully taken into account for one component, the primary. In the case of the companion the spin angular momentum is assumed small enough to be neglected but internal energy dissipation is allowed for as this can be significant for orbital circularization in the case of planetary companions. We obtain a set of equations governing the evolution of the orbit resulting from tidal effects. These depend on the masses and radii of the binary components, the form and orientation of the orbit, and for each involved component, the spin rate, the Coriolis force, the normalized rate of energy dissipation associated with the equilibrium tide due to radiative processes and viscosity, and the classical apsidal motion constant, k2. These depend on stellar parameters with no need of additional assumptions or a phenomenological approach as has been invoked in the past. They can be used to determine the evolution of systems with initial significant misalignment of spin and orbital angular momenta as hypothesized for systems containing Hot Jupiters. The inclusion of the Coriolis force may lead to evolution of the inclination between orbital and spin angular momenta and precession of the orbital plane which may have observational consequences.

Structured light with inhomogeneous phase, amplitude, and polarization spatial distributions that represent an infinite-dimensional space of eigenstates for light as the ideal carrier can provide a structured combination of photonic spin and orbital angular momentum (OAM). Photonic spin angular momentum (SAM) interactions with matter have long been studied, whereas the photonic OAM has only recently been discovered, receiving attention in the past three decades. Although controlling polarization (i.e., SAM) alone can provide useful information about the media with which the light interacts, light fields carrying both OAM and SAM may provide additional information, permitting new sensing mechanisms and light–matter interactions. We summarize recent developments in controlling photonic angular momentum (AM) using complex structured optical fields. Arbitrarily oriented photonic SAM and OAM states may be generated through careful engineering of the spatial and temporal structures of optical fields. Moreover, we discuss potential applications of specifically engineered photonic AM states in optical tweezers, directional coupling, and optical information transmission and processing.

We present a theoretical framework for analyzing the loss of optical angular momentum (AM), including spin AM (SAM) and orbital AM (OAM) components, in light-matter interactions. Conventional SAM and OAM conservation laws rely on transverse field components, neglecting longitudinal fields and limiting applicability to a vacuum. Our approach defines optical AM using time derivatives of the electric and magnetic fields, yielding a gauge-invariant formulation that includes both transverse and longitudinal components and explicitly incorporates charge and current densities into SAM and OAM conservation laws. This enables a more complete description of AM dissipation in materials. We apply this framework to analyze spin-orbit conversion (SOC) in two scenarios: the scattering of circularly polarized (CP) Gaussian beams by a gold nanoparticle and focusing of CP Gaussian beams and linearly polarized optical vortex beams by a lens. The results show that SOC depends on particle size and polarization, with notable OAM loss in larger particles and CP Gaussian beam focusing. This framework enables the evaluation of previously overlooked SAM and OAM losses, providing a powerful tool for studying systems in which the analysis of AM losses is intrinsically important, such as chiral materials, as well as for designing photonic devices and exploring light-matter interactions at the nanoscale. Published by the American Physical Society 2025

We review and re-examine the description and separation of the spin and orbital angular momenta (AM) of an electromagnetic field in free space. While the spin and orbital AM of light are not separately meaningful physical quantities in orthodox quantum mechanics or classical field theory, these quantities are routinely measured and used for applications in optics. A meaningful quantum description of the spin and orbital AM of light was recently provided by several authors, which describes separately conserved and measurable integral values of these quantities. However, the electromagnetic field theory still lacks corresponding locally conserved spin and orbital AM currents. In this paper, we construct these missing spin and orbital AM densities and fluxes that satisfy the proper continuity equations. We show that these are physically measurable and conserved quantities. These are, however, not Lorentz-covariant, so only make sense in the single laboratory reference frame of the measurement probe. The fluxes we derive improve the canonical (nonconserved) spin and orbital AM fluxes, and include a ‘spin–orbit’ term that describes the spin–orbit interaction effects observed in nonparaxial optical fields. We also consider both standard and dual-symmetric versions of the electromagnetic field theory. Applying the general theory to nonparaxial optical vortex beams validates our results and allows us to discriminate between earlier approaches to the problem. Our treatment yields the complete and consistent description of the spin and orbital AM of free Maxwell fields in both quantum-mechanical and field-theory approaches.

Based on the Richards-Wolf formalism, we obtain two different exact expressions for the angular momentum (AM) density in the focus of a vortex beam with the topological charge n and with right circular polarization. One expression for the AM density is derived as the cross product of the position vector and the Poynting vector and has a nonzero value at the focus for an arbitrary integer number n. The other expression for the AM density is deduced as a sum of the orbital angular momentum (OAM) and the spin angular momentum (SAM). We reveal that at the focus of the light field under analysis, the latter turns zero at n = –1. While both these expressions are not equal to each other at each point of space, 3D integrals thereof are equal. Thus, exact expressions are obtained for densities of AM, SAM and OAM at the focus of a vortex beam with right-hand circular polarization and the identity for the densities AM = SAM + OAM is shown to be violated. Besides, it is shown that the expressions for the strength vectors of the electric and magnetic fields near the sharp focus, obtained by adopting the Richards-Wolf formalism, are exact solutions of the Maxwell's equations. Thus, Richards–Wolf theory exactly describes the behavior of light near the sharp focus in free space.

In recent times the spin angular momentum (SAM) and orbital angular momentum (OAM) of light have gained prominence because of their significance in optical communication systems, micromanipulation, and sub‐wavelength position sensing. To this end, simultaneous detection of SAM and OAM of light beam is one of the important topics of research from both application and fundamental spin‐orbit interaction (SOI) point of view. While interferometry and metasurface based approaches have been able to detect the states, the presented approach involves elastic scattering from a monocrystalline silver nanowire for the simultaneous detection of SAM and OAM state of a circularly polarized Laguerre–Gaussian beam. By employing Fourier plane (FP) microscopy, the transmitted scattered light intensity distribution in the FP is analyzed to reconstruct the SAM and OAM state unambiguously. The SAM and OAM induced transverse energy flow as well as the polarization dependent scattering characteristics of the nanowire is investigated to understand the detection mechanism. This method is devoid of complex nanofabrication techniques and to the authors' knowledge, is a first example of single nano‐object based simultaneous SAM and OAM detection. The study will further the understanding of SOI effects and can be useful for on‐chip optical detection and manipulation.

Electrons confined in quantum-disk structures exhibit an intrinsic spin vortex state with spin angular momentum (SAM) and orbital angular momentum (OAM) [Phys. Rev. B79(15), 155450 (2009)10.1103/PhysRevB.79.155450]. A higher-order electron state, which is a SAM - OAM entangled state expressed by superposition of spin-vortex states, has a spatial spin structure and can be represented as a higher-order Bloch vector on a higher-order Bloch sphere [Optica Quantum2(4), 245 (2024)10.1364/OPTICAQ.527615]. In this study, we analyzed the Rabi oscillation of higher-order electron states in a quantum disk structure driven by higher-order photons possessing both SAM and OAM, with the aim of manipulating SAM - OAM entangled electron states. The higher-order Bloch vector precesses about the Stokes vector of the higher-order photon-driven field, and its precession behavior can be controlled by the state of the driving photon field, pulse width, and intensity. These results will lead to the realization of high-dimensional quantum computations and high-dimensional quantum interfaces using SAM and OAM of electrons and photons.

The angular momentum of light is a useful resource for many applications. In specific physical architectures it can be considered as the sum of two independent terms, the spin and the orbital components, in analogy to particle systems. The spin angular momentum is related to the polarization of the optical beam, that is the direction of the oscillating electric field, whereas the orbital angular momentum is associated with the spatial distribution of the field. Being independent, spin and orbital angular momenta have been discovered and explored in separate contexts for many years, while only recently it has been considered the possibility to address both quantities on the same beam (or individual photons). The interaction between these two quantities gives rise to complex structures of the electromagnetic field, or to the so called classical entanglement in the domain of single photons. The research presented in this work aimed to show that combining spin and orbital angular momenta in light beams or single photons may be a useful tool for a variety of applications, with particular interest to the case of architectures characterized by spin-orbit interaction. This concept was made concrete through the design and the realization of several experiments, in the framework of singular optics, foundations of quantum mechanics, quantum information theory and quantum simulation.

The angular momentum of light is present in two different forms: spin angular momentum (SAM), related to the field's polarization, and orbital angular momentum (OAM), associated with the spatial profile of the phase of the electromagnetic wave. While these properties have been long studied and exploited in the visible/infrared regions, recent developments have extended SAM [1,2] and OAM [3,4] control into the EUV/soft x-ray regions. However, to date it has not been possible to generate coherent EUV beams with fully controlled SAM and OAM.

We theoretically and experimentally investigate a method of exciting multipole plasmons, including terahertz dark spoof localized surface plasmon (Spoof-LSP) modes, by using normally incident terahertz vortex beam. The vortex beam with angular intensity profile and phase singularities, has well-defined angular momentum which can be decomposed into the polarization-state-related spin angular momentum (SAM) for characterizing the spin feature of photon, and the helical-wavefront-related orbital angular momentum (OAM) that is characterized by an integer <inline-formula><tex-math id="Z-20200915102424-1">\begin{document}$ (l) $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20200695_Z-20200915102424-1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20200695_Z-20200915102424-1.png"/></alternatives></inline-formula>, called the topological charge. By illuminating terahertz vortex beam on the metallic disk with periodic subwavelength grooves normally, we find that the terahertz dark multipole plasmons can be excited by the terahertz vortex beam carrying different OAM and SAM. We analyze the correspondence between the spin and orbital angular momentum of vortex beam and the excited dark multipolar plasmon modes. In the experiment, a terahertz stepped spiral phase plate (SPP) with high transmission and low dispersion based on the Tsurupica olefin polymer is developed and the stepped SPP can generate a terahertz vortex beam having a topological charge of 1. Then, we further study the excitation of dark multipolar Spoof-LSPs by utilizing the stepped SPP in combination with the near-field scanning terahertz microscopy. The collimated terahertz wave, which is radiated from a 100 fs (<i>λ</i> = 780 nm) laser pulse pumped photoconductive antenna emitter, is converted into terahertz circular polarized light (CPL) which can carry SAM by the combination of the quarter wave plate and the polarizer, and then terahertz CPL impinges on the stepped SPP, producing the terahertz vortex beam which can carry OAM. The spatial two-dimensional electric field distribution is collected in steps of 0.02 mm along the <i>x</i>-direction and <i>y</i>-direction by a commercial terahertz near-field probe which is located close (≈ 10 μm) to the one side of polyimide film by three-dimensional electric translation stage and a microscope (FORTUNE TECHPLOGY FT-FH1080). The experimental results are in good agreement with simulations. We believe that our method will open the way for detailed research on the terahertz physics, plasma and imaging fields.