Spin Angular Momentum Density Research Articles

Acoustic versus electromagnetic field theory: scalar, vector, spinor representations and the emergence of acoustic spin

We construct a novel Lagrangian representation of acoustic field theory that describes the local vector properties of longitudinal (curl-free) acoustic fields. In particular, this approach accounts for the recently-discovered nonzero spin angular momentum density in inhomogeneous sound fields in fluids or gases. The traditional acoustic Lagrangian representation with a scalar potential is unable to describe such vector properties of acoustic fields adequately, which are however observable via local radiation forces and torques on small probe particles. By introducing a displacement vector potential analogous to the electromagnetic vector potential, we derive the appropriate canonical momentum and spin densities as conserved Noether currents. The results are consistent with recent theoretical analyses and experiments. Furthermore, by an analogy with dual-symmetric electromagnetic field theory that combines electric- and magnetic-potential representations, we put forward an acoustic spinor representation combining the scalar and vector representations. This approach also includes naturally coupling to sources. The strong analogies between electromagnetism and acoustics suggest further productive inquiry, particularly regarding the nature of the apparent spacetime symmetries inherent to acoustic fields.

Spin angular momentum density in the tight focus of a light field with phase and polarization singularities

For a light field with both phase and polarization singularities at its center, expressions are obtained that describe the distribution of the spin angular momentum (SAM) density in the sharp focal spot of an aplanatic system. These expressions include the radial, azimuthal, and longitudinal SAM components. As special cases, focusing of optical vortices with radial, azimuthal, and saddle polarizations is studied. Using the Bessel beam as an example, it is shown that in some areas in the focal plane the longitudinal SAM component is zero (resulting in a photonic wheel), while in others it is an order of magnitude less than the transverse component.

Acoustic Radiation Force and Torque on Small Particles as Measures of the Canonical Momentum and Spin Densities.

We examine acoustic radiation force and torque on a small (subwavelength) absorbing isotropic particle immersed in a monochromatic (but generally inhomogeneous) sound-wave field. We show that by introducing the monopole and dipole polarizabilities of the particle, the problem can be treated in a way similar to the well-studied optical forces and torques on dipole Rayleigh particles. We derive simple analytical expressions for the acoustic force (including both the gradient and scattering forces) and torque. Importantly, these expressions reveal intimate relations to the fundamental field properties introduced recently for acoustic fields: the canonical momentum and spin angular momentum densities. We compare our analytical results with previous calculations and exact numerical simulations. We also consider an important example of a particle in an evanescent acoustic wave, which exhibits the mutually orthogonal scattering (radiation-pressure) force, gradient force, and torque from the transverse spin of the field.

Observation of spin-polarized directive coupling of light at bound states in the continuum

Spin-polarized directive coupling of light associated with the photonic quantum spin-Hall effect (QSHE) is a nanoscale phenomenon based on strong spin–orbit interaction that has recently attracted significant attention. Herein, we discuss the experimental manifestation of QSHE intrinsic in the Bloch waves associated with a bound state in the continuum (BIC) of a dielectric photonic crystal metasurface (PhCM). We show numerically that BICs in nanoscale PhCMs have photonic spin angular momentum density transverse to the orbital momentum not only at the interfaces but also inside the confining dielectric medium. Then, we experimentally demonstrate that the fundamental Bloch waves of the BIC mode, macroscopically amplified on resonance, propagate along the symmetry axes of the PhCM obeying spin-momentum locking also at normal incidence, i.e., with no symmetry breaking. This BIC-enhanced spin-directive coupling of light may enable versatile implementations of spin-optical structures, paving the way for novel photonic spin multiplatform devices.

Spin angular momentum density and transverse energy flow of tightly focused kaleidoscope-structured vector optical fields

We propose a novel scheme for designing and generating kaleidoscope-structured vector optical fields (KS-VOFs) by analogy with the principle of multiple mirror reflection in a kaleidoscope. For KS-VOFs with symmetric polarization states, we show the symmetry properties of the focal fields with various shapes for different applications. The redistributing symmetric local spin angular momentum (SAM) density indicates that the design method of the KS-VOFs plays a role as a catalyst to the redistribution process of polarization states and local SAM conversion in the tight focusing process. Meanwhile, the controllable transverse energy flow in the focal plane can be used to transport multiple absorptive particles and then to be fixed at certain locations. Our results may find applications in optical machining, trapping, and manipulation.

Symmetry of electric spin angular momentum density in the tight focusing of linearly polarized vortex beams.

Symmetry of electric spin angular momentum (SAM) density in the tight focusing of linearly polarized vortex beams is investigated in this paper. By calculating analytic expressions of SAM density, reflection symmetry and rotation symmetry of SAM density are found in the focal region. The vortex phase can break some symmetry, leading to non-zero longitudinal SAM. When the vortex phase vanishes, more symmetry will occur. It is proved that longitudinal SAM is zero when the topological charge is zero, and that transverse SAM is always zero. This paper is expected to advance our understanding of distribution of SAM density and optical spin-orbit coupling.

Spin and orbital angular momenta of acoustic beams

We analyze spin and orbital angular momenta in monochromatic acoustic wave fields in a homogeneous medium. Despite being purely longitudinal (curl-free), inhomogeneous acoustic waves generically possess nonzero spin angular momentum density caused by the local rotation of the vector velocity field. We show that the integral spin of a localized acoustic wave vanishes in agreement with the spin-0 nature of longitudinal phonons. We also show that the helicity or chirality density vanishes identically in acoustic fields. As an example, we consider nonparaxial acoustic Bessel beams carrying well-defined integer orbital angular momentum, as well as nonzero local spin density, with both transverse and longitudinal components. We describe the nontrivial polarization structure in acoustic Bessel beams and indicate a number of observable phenomena, such as nonzero energy density and purely-circular transverse polarization in the center of the first-order vortex beams.

Spin Angular Momentum of a Nonlinear Surface Wave at the Interface between Ordinary and Topological Insulators

The surface waves that propagate along the interface of a dielectric with nonlinear susceptibility of the third order and topological insulator have been considered. The optical nonlinearity of the dielectric ensures the existence of a surface wave. The density of the spin angular momentum of a surface wave has been determined for dielectrics with positive or negative linear permittivity. It has been shown that the spin angular momentum vector has a projection on the normal to the interface, which is different from the usual surface polaritons or plasmon polaritons. The discrete nature of the topological number manifests itself in the discreteness of the values of the normal and tangential components of the spin angular momentum density. The increase in the intensity of the electric field of the wave at the interface of the media changes the value of the spin angular momentum and can lead to its disappearance.

Transverse spin and surface waves in acoustic metamaterials

We consider spin angular momentum density in inhomogeneous acoustic fields: evanescent waves and surface waves at interfaces with negative-density metamaterials. Despite being purely longitudinal (curl-free), acoustic waves possess intrinsic vector properties described by the velocity field. Motivated by the recent description and observation of the spin properties in elastic and acoustic waves, we compare these properties with their well-known electromagnetic counterparts. Surprisingly, both the transverse spin of evanescent waves and the parameters of surface waves are very similar in electromagnetism and acoustics. We also briefly analyze the important role of dispersion in the description of the energy and spin densities in acoustic metamaterials.

Спиновый угловой момент нелинейной поверхностной волны на границе раздела обычного и топологического изоляторов

AbstractThe surface waves that propagate along the interface of a dielectric with nonlinear susceptibility of the third order and topological insulator have been considered. The optical nonlinearity of the dielectric ensures the existence of a surface wave. The density of the spin angular momentum of a surface wave has been determined for dielectrics with positive or negative linear permittivity. It has been shown that the spin angular momentum vector has a projection on the normal to the interface, which is different from the usual surface polaritons or plasmon polaritons. The discrete nature of the topological number manifests itself in the discreteness of the values of the normal and tangential components of the spin angular momentum density. The increase in the intensity of the electric field of the wave at the interface of the media changes the value of the spin angular momentum and can lead to its disappearance.

Orbit-induced localized spin angular momentum in the tight focusing of linearly polarized vortex beams.

Optical spin-orbit interaction has gained much interest recently due to its universality and importance in modern photonics. In this Letter, we theoretically demonstrate that orbit-induced localized spin angular momentum (SAM) conversion can occur in the tight focusing of spin-free linearly polarized vortex beams (LPVBs). By analysis of the polarization states that are associated with the SAM density, we attribute the occurrence of such a conversion to the helical-phase-induced change of local polarization states in the focused field. In the local SAM, density can be further regulated by altering the sign and value of the orbital angular momentum in the incident LPVBs, as well as their polarization orientations. This Letter is expected to advance our understanding of optical spin-orbit coupling and benefit applications of optical microscopy and trapping.

Transverse spin in the scattering of focused radially and azimuthally polarized vector beams

We study the effect of focusing of the radially and azimuthally polarized vector beams on the spin angular momentum (SAM) density and Poynting vector of scattered waves from a Mie particle. Remarkably, the study reveals that the SAM density of the scattered field is solely transverse in nature for radially and azimuthally polarized incident vector beams; however the Poynting vector shows usual longitudinal character. We also demonstrate that the transverse SAM density can further be tuned with wavelength and focusing of the incident beam by exploiting the interference of different scattering modes. These results may stimulate further experimental technique of detecting the transverse spin and Belinfante's spin-momentum densities.

Generation of a sub-half-wavelength focal spot with purely transverse spin angular momentum

We theoretically demonstrate that optical focus fields with purely transverse spin angular momentum (SAM) can be obtained when a kind of special incident fields is focused by a high numerical aperture (NA) aplanatic lens (AL). When the incident pupil fields are refracted by an AL, two transverse Cartesian components of the electric fields at the exit pupil plane do not have the same order of sinusoidal or cosinoidal components, resulting in zero longitudinal SAMs of the focal fields. An incident field satisfying above conditions is then proposed. Using the Richard–Wolf vectorial diffraction theory, the energy density and SAM density distributions of the tightly focused beam are calculated and the results clearly validate the proposed theory. In addition, a sub-half-wavelength focal spot with purely transverse SAM can be achieved and a flattop energy density distribution parallel to z-axis can be observed around the maximum energy density point.

Optical Momentum, Spin, and Angular Momentum in Dispersive Media.

We examine the momentum, spin, and orbital angular momentum of structured monochromatic optical fields in dispersive inhomogeneous isotropic media. There are two bifurcations in this general problem: the Abraham-Minkowski dilemma and the kinetic (Poynting-like) versus canonical (spin-orbital) pictures. We show that the kinetic Abraham momentum describes the energy flux and group velocity of the wave in the medium. At the same time, we introduce novel canonical Minkowski-type momentum, spin, and orbital angular momentum densities of the field. These quantities exhibit fairly natural forms, analogous to the Brillouin energy density, as well as multiple advantages as compared with previously considered formalisms. As an example, we apply this general theory to inhomogeneous surface plasmon-polariton (SPP) waves at a metal-vacuum interface and show that SPPs carry a "supermomentum," proportional to the wave vector k_{p}>ω/c, and a transverse spin, which can change its sign depending on the frequency ω.

Transverse spin and transverse momentum in scattering of plane waves.

We study the near field to the far field evolution of spin angular momentum (SAM) density and the Poynting vector of the scattered waves from spherical scatterers. The results show that at the near field, the SAM density and the Poynting vector are dominated by their transverse components. While the former (transverse SAM) is independent of the helicity of the incident circular polarization state, the latter (transverse Poynting vector) depends upon the polarization state. It is further demonstrated that the interference of the transverse electric and transverse magnetic scattering modes enhances both the magnitudes and the spatial extent of the transverse SAM and the transverse momentum components.

Spin control of light with hyperbolic metasurfaces

Transverse spin angular momentum is an inherent feature of evanescent waves which may have applications in nanoscale optomechanics, spintronics, and quantum information technology due to the robust spin-directional coupling. Here we analyze a local spin angular momentum density of hybrid surface waves propagating along anisotropic hyperbolic metasurfaces. We reveal that, in contrast to bulk plane waves and conventional surface plasmons at isotropic interfaces, the spin of the hybrid surface waves can be engineered to have an arbitrary angle with the propagation direction. This property allows to tailor directivity of surface waves via the magnetic control of the spin projection of quantum emitters, and it can be useful for optically controlled spin transfer.

The ubiquitous photonic wheel

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.

Local physical quantities for spin based on the relativistic quantum field theory in molecular systems

Local physical quantities for spin are investigated on the basis of the four‐ and two‐component relativistic quantum theory. In the quantum field theory, local physical quantities for spin such as the spin angular momentum density, spin torque density, zeta force density, and zeta potential play important roles in spin dynamics. We discuss how to calculate these local physical quantities based on the two‐component relativistic quantum theory. Some different types of relativistic numerical calculations of local physical quantities in Li atom and C6H6 are demonstrated and compared. Local physical quantities for each orbital are also discussed, and it is seen that a total local zeta potential is given as a result of some cancellation of large contributions from each orbital. © 2016 Wiley Periodicals, Inc.

Local spin dynamics with the electron electric dipole moment

The local spin dynamics of the electron is studied from the viewpoint of the electric dipole moment (EDM) of the electron in the framework of the quantum field theory. The improvements of the computational accuracy of the effective electric field $({\mathcal{E}}_{\mathrm{eff}})$ for the EDM and the understanding of spin precession are important for the experimental determination of the upper bound of the EDM. Calculations of ${\mathcal{E}}_{\mathrm{eff}}$ in YbF $({}^{2}{\mathrm{\ensuremath{\Sigma}}}_{1/2})$, BaF $({}^{2}{\mathrm{\ensuremath{\Sigma}}}_{1/2})$, ThO $({}^{3}{\mathrm{\ensuremath{\Delta}}}_{1})$, and ${\mathrm{HF}}^{+} ({}^{2}{\mathrm{\ensuremath{\Pi}}}_{1/2})$ are performed on the basis of the restricted active space configuration interaction approach by using the four-component relativistic electronic structure calculation. The spin precession is also discussed from the viewpoint of local spin torque dynamics. We show that a contribution to the torque density for the spin is brought into by the EDM. Distributions of the local spin angular momentum density and torque densities induced by external fields in the above molecules are calculated and a property related with large ${\mathcal{E}}_{\mathrm{eff}}$ is discussed.

Plasmonic lateral forces on chiral spheres

We show that the optical force exerted on a finite size chiral sphere by a surface plasmon mode has a component along a direction perpendicular to the plasmon linear momentum. We reveal how this chiral lateral force, pointing in opposite directions for opposite enantiomers, stems from an angular-to-linear crossed momentum transfer involving the plasmon transverse spin angular momentum density and mediated by the chirality of the sphere. Our multipolar approach allows us discussing the inclusion of the recoil term in the force on a small sphere taken in the dipolar limit and observing sign inversions of the lateral chiral force when the size of the sphere increases.