Extrinsic Orbital Angular Momentum Research Articles

Spatial-temporal optical vortex pendulum on a curved surface.

Spatial-temporal optical vortices (STOVs) have recently become the focus of newly structured optical fields. In this paper, their propagation on a 2D curved surface named the constant Gaussian curvature surface (CGCS) is studied. Using the matrix optics approach, we provide the analytical solution of the STOV propagation under the paraxial approximation on the CGCS with positive curvature. One method of creating timers is made possible by the spatiotemporal distribution direction of STOV light intensity, which swings like a pendulum throughout the evolution, in contrast to propagation on a flat surface. This swing, however, stops when the curved surface's curvature radius matches the light's Rayleigh distance. Besides, the transverse orbital angular momentum of STOV is deduced, and we find that the intrinsic and extrinsic OAM periodically exchange, but the total transverse OAM is always zero during the propagation on CGCS. It aids in controlling the transverse extrinsic orbital angular momentum of STOV in nontrivial space.

Momentum-dependent Pancharatnam-Berry phase enabled in- and out-of-plane photonic spin-Hall shifts

The photonic spin-Hall effect (PSHE) is a result of the interaction of spin and orbital angular momentum (OAM). However, previous research on the PSHE has primarily focused on out-of-plane (transverse) shifts. In fact, it encompasses both out-of-plane shifts and relatively weaker in-plane shifts, and the latter of which plays a crucial role in controlling the direction of spin separation. Here, we investigate the in- and out-of-plane shifts of the PSHE based on a full-wave theory, revealing that they have the same physical mechanism. The in- and out-of-plane displacements of the PSHE are determined by a momentum-dependent Pancharatnam-Berry (PB) phase, where the in-plane wavevector kx-dependent phase gradient determines the in-plane shift, and the transverse wavevector ky-dependent phase gradient dictates the out-of-plane shift. We discover that the intrinsic OAM (IOAM) and extrinsic OAM (EOAM) carried by incident off-axis vortex beams can respectively convert into the EOAM and IOAM of abnormal modes in the transmitted beam. The OAM generated during the spin-reversal process, together with the OAM carried by the incident beam, collectively determines the in- and out-of-plane displacements. When off-axis vortex beams are incident, the competition between the IOAM and EOAM is more complex than in those without OAM. Our study unifies in- and out-of-plane shifts into a single theoretical framework, which offers an alternative perspective on the spin–orbit interaction of light.

Revisiting physical mechanism of longitudinal photonic spin splitting and Goos-Hänchen shift

The intrinsic connection between the transverse photonic spin Hall effect (PSHE) and the Imbert–Fedorov shift has been well characterized. However, physical insights into the longitudinal photonic spin splitting associated with the Goos-Hänchen (GH) shift remain elusive. This paper aims to expand the theory of the PSHE generation mechanism from the transverse to the longitudinal case by examining the reflection of each spin component from an arbitrarily linearly polarized incident Gaussian beam on the air-dielectric interface. Unlike the transverse case, both spin-maintained and spin-flipped modes exhibit non-zero longitudinal displacements, with the latter being affected by the second-order expansion term of the Fresnel reflection coefficient with respect to the in-plane wave-vector component. Meanwhile, the polarization angle plays a crucial role in determining the longitudinal PSHE since each reflected total spin component is a coherent superposition of these two corresponding modes. Remarkably, the imaginary part of the relative permittivity of the dielectric significantly affects the symmetry of the longitudinal PSHE. Furthermore, the GH shift results from a superposition of individual spin states’ longitudinal displacements, taking into account their energy weights. By incorporating the corresponding extrinsic orbital angular momentum, we explore the generation mechanism of the symmetric/asymmetric longitudinal PSHE. The unified physical framework elucidating the longitudinal photonic spin splitting and GH shift provides a comprehensive understanding of the fundamental origin of the PSHE and beam shifts, paving the way for potential applications in spin-controlled nanophotonics.

Spin-orbital angular momentum degeneracy breaking in nanoplasmonic metachain.

The spin and orbital angular momentum (namely SAM and OAM) mode division provides a promising solution to surmount exhausted available degrees of freedom in conventional optical communications. Nevertheless, SAM and OAM are often subjected to the degeneracy of total angular momentum (AM) because they both have integer variables of quantum eigenstates, which inevitably brings about the shortcomings specific to limited signal channels and multiplexing cross talk. Herein, we present a nanoplasmonic metachain that can discriminatively couple any input SAM and OAM components to an extrinsic orbital AM, corresponding to the chirality and topological charge of incident light. Importantly, the unambiguous measurement has a prominent advantage of detecting the arbitrary AM component rather than the total AM. The miniature metadevice offers the possibility of harnessing AM division on chip or in fiber and holds great promise to delve the spin-orbit interactions for topological photonics and quantum cryptography.

Topological circular dichroism for asymmetric converging light beams

Light beams possess three types of angular momentum. They are the spin angular momentum, the extrinsic orbital angular momentum, and the intrinsic orbital angular momentum. Interaction of these momenta due to translational or cylindrical symmetry breaking leads to effects of the spin-orbit interaction of light, including topological effects. Topological optical activity or topological circular phase anisotropy, known as Rytov-Vladimirsky-Berry-Chao-Tomita plane polarization rotation, is the result of the extrinsic orbital angular momentum influence on the spin angular momentum. The effect manifests under linear polarized light propagation along a curved trajectory when the translational symmetry is breaking. We predict a new topological effect under the cylindrical symmetry breaking. This effect is the result of the extrinsic orbital angular momentum influence on the spin angular momentum in the converging asymmetrical light beam. It manifests as the transformation of linear polarized light into elliptically polarized one when an asymmetrical in the vertical direction beam passes through the left or right half of the focal plane. We have estimated the value of the ellipticity and proposed an experimental setup. We successfully observed the ellipticity change of 10(−3) using our method of small ellipticity determination. We have considered this transformation as the topological circular dichroism (topological circular amplitude anisotropy). We have demonstrated the connection of the ellipticity change with the value of the topological circular amplitude anisotropy R. The measured value of the topological circular amplitude anisotropy R turned out to be R=±(0.60±0.08)×10−3. This new effect of the spin-orbit interaction of light contributes to our understanding of the nature of light. It can be used to develop new sensors in optics, including nano and quantum optics.

Ultrafast Time Dynamics of Plasmonic Fractional Orbital Angular Momentum.

The creation and manipulation of optical vortices, both in free space and in two-dimensional systems such as surface plasmon polaritons (SPPs), has attracted widespread attention in nano-optics due to their robust topological structure. Coupled with strong spatial confinement in the case of SPPs, these plasmonic vortices and their underlying orbital angular momentum (OAM) have promise in novel light-matter interactions on the nanoscale with applications ranging from on-chip particle manipulation to tailored control of plasmonic quasiparticles. Until now, predominantly integer OAM values have been investigated. Here, we measure and analyze the time evolution of fractional OAM SPPs using time-resolved two-photon photoemission electron microscopy and near-field optical microscopy. We experimentally show the field's complex rotational dynamics and observe the beating of integer OAM eigenmodes at fractional OAM excitations. With our ability to access the ultrafast time dynamics of the electric field, we can follow the buildup of the plasmonic fractional OAM during the interference of the converging surface plasmons. By adiabatically increasing the phase discontinuity at the excitation boundary, we track the total OAM, leading to plateaus around integer OAM values that arise from the interplay between intrinsic and extrinsic OAM.

Quantum commutation relationship for photonic orbital angular momentum

Orbital Angular Momentum (OAM) of photons are ubiquitously used for numerous applications. However, there is a fundamental question whether photonic OAM operators satisfy standard quantum mechanical commutation relationship or not; this also poses a serious concern on the interpretation of an optical vortex as a fundamental quantum degree of freedom. Here, we examined canonical angular momentum operators defined in cylindrical coordinates, and applied them to Laguerre-Gauss (LG) modes in a graded index (GRIN) fibre. We confirmed the validity of commutation relationship for the LG modes and found that ladder operators also work properly with the increment or the decrement in units of the Dirac constant (ℏ). With those operators, we calculated the quantum-mechanical expectation value of the magnitude of angular momentum, which includes contributions from both intrinsic and extrinsic OAM. The obtained results suggest that OAM characterised by the LG modes exhibits a well-defined quantum degree of freedom.

Time-Varying Optical Spin-Orbit Interactions in Tight Focusing of Self-Torqued 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.

Revisiting the photonic orbital Hall effect with the vortex mode decomposition

The photonic orbital Hall effect (POHE) refers to the vortex-dependent beam shifts, which is generally believed to result from the conversion of intrinsic orbital angular momentum (IOAM) to extrinsic orbital angular momentum (EOAM). However, the physical mechanism of the POHE, such as how the IOAM is converted to the EOAM, remains further elucidation. In this paper, we re-examine the POHE of a vortex beam with additional IOAM illuminating at an optically thin slab by means of vortex mode decomposition. By considering the competition and coupling between the radial and azimuthal vortex harmonics of the abnormal mode in the transmitted beam, it is found that the underlying mechanism of the POHE is in fact a spin-to-orbital angular momentum (OAM) conversion process. And the IOAM carried by the incident beam is directly superimposed on the OAM obtained during the conversion. Our findings not only offer an alternative perspective for understanding the POHE, but also exhibit application potential in orbit–orbit and spin–orbit optical components.

Role of in-plane shift in reconstructing the photonic spin Hall effect

The photonic spin Hall effect (SHE) manifests itself as in-plane and transverse spin-dependent shifts of left- and right-handed circularly polarized (LCP, RCP) components and originates from the spin-orbit interaction (SOI) of light, where extrinsic orbital angular momentum (EOAM) can induce these shifts. However, previous studies mainly focus on the SOI corresponding to transverse shifts and generally consider the paraxial approximation case. In this Letter, we reconstruct a more general theory of the photonic SHE in the non-paraxial case and reveal that the induction of an in-plane shift mainly relies on the EOAM of the y direction, supplemented by the EOAM of the x and z directions under the laboratory coordinate system. In addition, the EOAM in the x and z directions completely determine the transverse shift. Moreover, the angular momentum conversion between the LCP and RCP components results in the angular momentum of the LCP (RCP) component of the incident Gaussian beam not being equal to the sum of the angular momentum of the LCP (RCP) component of the reflected and transmitted light. These findings explore the influence of in-plane shifts on the SOI of light and provide an in-depth understanding of the photonic SHE.

Linear polarization splitting and circular polarization accumulation in a weakly focused linear polarized Gaussian light beam

A weakly focused light beam is studied numerically in the focal plane, to observe the linear polarization separation and circular polarization accumulation in the beam cross section. This is an example of spin-orbit interaction of light, where the extrinsic orbital angular momentum of light encountered due to focusing is converted into spin angular momentum and causes circular polarization generation and linear polarization separation in different parts of the beam cross section. This effect is studied by evaluating the polarization vector and Stokes vector and angle parameters in the beam cross section in detail. Because of the lens’s spherical geometry and origination of geometric phase, the accumulation of the spin component in the beam cross section is observed to be circularly symmetric, while the linear polarization shows splitting into orthogonal polarization components in the beam cross section. The underlying results may have an important role for understanding the spin-orbit interaction in a weakly focused system at a fundamental level and can be useful in many applications of nanophotonics.

Determination of the beam waist position for the spin-orbit interaction effect observation

The spin angular momentum and the extrinsic orbital angular momentum of light are associated with the polarization of light and the light propagation trajectory, respectively. Those momenta are interdependent not only in an inhomogeneous or anisotropic medium but even in free space. This interaction is called the spin-orbit interaction of light. The effects of the spin-orbit interaction of light manifest themselves in a small transverse shift of the beam field longitudinal component from the beam propagation axis in the waist region under the circular polarization sign change. They can be observed both for Gaussian beams and for structured beams. The effects of the spin-orbit interaction of light should be taken into account when nanophotonics devices are created, but the detailed investigation of the effect had not been performed yet due to the low intensity noise image of the beam waist. Precise measurements of the focal waist centerline are needed to determine the transverse shift of the beam field longitudinal component of the asymmetric converging beam's waist under the circular polarization sign change. We propose methods for determining the transverse and longitudinal positions of the beam waist. Computer image processing methods made it possible to obtain the value of the beam waist's transverse position with an accuracy of 0.1 mkm. These methods will allow further testing of the shifts' theoretical predictions, the values of which are the order of 1 mkm. The results obtained can also be used for laser processing of materials by polarized light and precise positioning of the beam's focal spot at a surface.

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.

Dragging of inertial frames in the composed black-hole-particle system and the weak cosmic censorship conjecture

We analyze a gedanken experiment in which a spinning particle that also possesses an extrinsic orbital angular momentum is captured by a spinning Kerr black hole. The gravitational spin-orbit interaction decreases the energy of the particle, thus allowing one to test the validity of the Penrose weak cosmic censorship conjecture in extreme situations that have not been analyzed thus far. It is explicitly shown that, to leading order in the black-hole-particle interactions, the linearized test particle can over-spin the black hole, thus exposing its inner spacetime singularity to external observers. However, we prove that the general relativistic effect of dragging of inertial frames by the orbiting particle contributes to the energy budget of the system a non-linear black-hole-particle interaction term that ultimately ensures the validity of the Penrose cosmic censorship conjecture in this type of gedanken experiments.

Geometric Phase and Intensity-Controlled Extrinsic Orbital Angular Momentum of Off-Axis Vortex Beams

Smooth control of the intrinsic orbital angular momentum (OAM) carried by a beam of light is important for $e.g.$ optical tweezers, communication, and quantum information processing, while control of extrinsic OAM is useful for $e.g.$ super-resolution microscopy and light-matter interaction with atoms, molecules, and condensates. This study presents a technique to control intrinsic and extrinsic OAM in a single-path configuration that is free from mechanical errors. By managing the relative intensity and Pancharatnam-Berry phase difference between two orthogonal spatial modes with orthogonal polarizations, one may tune the net transverse linear momentum to yield variable extrinsic OAM.

Gouy phase-assisted topological transformation of vortex beams from fractional fork holograms.

The topological transformation of optical vortex beams from fractional fork holograms induced by the modulation of controlled Gouy phase (GP) is demonstrated. The GP change is tuned by varying the wavefront curvature of the input beam on the plane of the fractional phase generating optic. The locus of the point of singularity traces a semi-circle about the beam axis for maximum possible change of the associated GP. The morphology parameters describing the anisotropic vortex phases of generated optical vortices are tuned in the experiment by varying the input wavefront curvature. Through the transformation of the transverse Poynting vector of the fractional vortex beams, control of the extrinsic orbital angular momentum is demonstrated for the first time, to the best of our knowledge. This could enable better manipulation of an optically trapped micro-particle and be used in optically driven micro-machines.

Near-field imaging of surface-plasmon vortex-modes around a single elliptical nanohole in a gold film

We present scanning near-field images of surface plasmon modes around a single elliptical nanohole in 88 nm thick Au film. We find that rotating surface plasmon vortex modes carrying extrinsic orbital angular momentum can be induced under linearly polarized illumination. The vortex modes are obtained only when the incident polarization direction differs from one of the ellipse axes. Such a direct observation of the vortex modes is possible thanks to the ability of the SNOM technique to obtain information on both the amplitude and the phase of the near-field. The presence of the vortex mode is determined by the rotational symmetry breaking of the system. Finite element method calculations show that such a vorticity originates from the presence of nodal points where the phase of the field is undefined, leading to a circulation of the energy flow. The configuration producing vortex modes corresponds to a nonzero total topological charge (+1).

Demonstration of spin and extrinsic orbital-angular-momentum interaction using a few-mode optical fiber

We demonstrate the spin and extrinsic orbital-angular-momentum interaction of light in a few-mode fiber. The interaction of spin and extrinsic orbital angular momentum splits the degeneracy of a degenerate subspace of the higher-order solution of Maxwell's equation and creates correction to the propagating constants of its degenerate eigenmodes that results in the formation of transmitting-length-dependent beat along the propagating trajectory. We examine the interaction of spin and extrinsic orbital angular momentum by the observation of the rotation of the polarization or intensity pattern of the propagating modes which are the combinations of these degenerate eigenmodes when altering the length of this transmitting-length-dependent beat. In experiment, the length of this transmitting-length-dependent beat is altered by the alteration of the pitch of a fiber helix which is made for the production of the extrinsic angular momentum and where the space inversion or mirror symmetry of the mode is broken and the interaction between the spin and extrinsic orbital angular momentum is realized. We demonstrate that the spin and extrinsic orbital-angular-momentum interaction induce the rotation of the polarization or intensity pattern of propagating modes in a way related with the order index of spin and orbital angular momentum carried by their constituent eigencomponents, which are circular vortex modes. This work may contribute to understanding the physical mechanism underlying the evolution of the modes in few-mode fiber or other complex systems for their various applications.

Electromagnetic wave propagating along a space curve

Using the thin-layer approach, we derive the effective equation for the electromagnetic wave propagating along a space curve. We find intrinsic spin-orbit, extrinsic spin-orbit and extrinsic orbital angular momentum and intrinsic orbital angular momentum couplings induced by torsion, which can lead to geometric phase, spin and orbital Hall effects. And we show the helicity inversion induced by curvature that can convert the right-handed circularly polarized electromagnetic wave into left-handed polarized one, vice verse. Finally, we demonstrate that the gauge invariance of the effective dynamics is protected by the geometrically induced gauge potential.

Photonic spin Hall effect by the spin-orbit interaction in a metasurface with elliptical nano-structures

The metasurface with elliptical nano-structures containing doubly degenerate geometrical charge is designed to investigate the enhanced spin-orbit optical interactions, numerically as well as experimentally. It is found that localized surface plasmon (LSP) resonance with orbital angular momentum (i.e., rotating SP vortex mode carrying extrinsic orbital angular momentum) can be induced under linearly polarized illumination. On the contrary, the LSP resonance without orbital angular momentum is formed under circularly polarized illumination. Moreover, based on the different LSP modes as results of spin-orbit interaction with alternative geometrical charge, directional propagations of surface plasmon polariton in two orthogonal trajectories depending on spin states of the incident light are presented with experimental demonstration, a phenomenon called photonic spin Hall effect.