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Motivated by recent progress in the generation of optical spatiotemporal vortex pulses (STVPs), there is a theoretical discussion about the transverse orbital angular momentum (OAM) carried by such pulses. Two recent works [K. Y. Bliokh, Phys. Rev. Lett. 126, 243601 (2021)] and [S. W. Hancock et al., Phys. Rev. Lett. 127, 193901 (2021)] claimed the OAM values which differ by a factor of 2 for circular STVPs. Here we resolve this controversy by showing that the result by Hancock et al. is correct for the total OAM, while the result by Bliokh describes the suitably defined intrinsic part of the OAM. The other, extrinsic part of the OAM originates from the fact that plane waves of the same amplitude but different frequencies in the pulse spectrum contain different densities of photons, which induces a transverse vortex-dependent shift of the photon centroid even in a STVP with symmetric energy-density distribution. We describe similar peculiarities of acoustic and quantum-relativistic (Klein-Gordon and arbitrary-spin) STVPs. In all cases, only the intrinsic OAM keeps a universal form independent of the details of the problem and similar to the OAM of monochromatic vortex beams., 7 pages, 2 figures

Polarization singularities and topological polarization structures are generic features of inhomogeneous vector wave fields of any nature. However, their experimental studies mostly remain restricted to optical waves. Here, we report the observation of polarization singularities, topological Möbius-strip structures, and skyrmionic textures in 3D polarization fields of inhomogeneous sound waves. Our experiments are made in the ultrasonic domain using nonparaxial propagating fields generated by space-variant 2D acoustic sources. We also retrieve distributions of the 3D spin density in these fields. Our results open the avenue to investigations and applications of topological features and nontrivial 3D vector properties of structured sound waves.

It is well known that spin angular momentum of light, and therefore that of photons, is directly related to their circular polarization. Naturally, for totally unpolarized light, polarization is undefined and the spin vanishes. However, for nonparaxial light, the recently discovered transverse spin component, orthogonal to the main propagation direction, is largely independent of the polarization state of the wave. Here we demonstrate, both theoretically and experimentally, that this transverse spin survives even in nonparaxial fields (e.g., tightly focused or evanescent) generated from a totally unpolarized light source. This counterintuitive phenomenon is closely related to the fundamental difference between the degrees of polarization for 2D paraxial and 3D nonparaxial fields. Our results open an avenue for studies of spin-related phenomena and optical manipulation using unpolarized light., 11 pages, 3 figures

We consider reflection and transmission of 2D quantum wavepackets with phase vortices (also known in optics as spatiotemporal vortex pulses) at potential step-like, delta-function, and rectangular barriers. The presence of a vortex significantly modifies the Wigner time delays and Goos-H\"{a}nchen shifts, previously studied for Gaussian-like wavepackets. In particular, the scattered wavepackets undergo non-zero time delays and lateral shifts even for purely real scattering coefficients, when the standard Wigner and Artmann formulae vanish. We derive analytical expressions for the vortex-induced times delays and spatial shifts of 2D vortices and verify these with numerical calculations of the Schr\"{o}dinger equation. The time delays and shifts are resonantly enhanced in the vicinity of the critical-angle incidence for a step-like potential and near transmission resonances for a rectangular barrier., Comment: 16 pages, 7 figures

Recently, spatiotemporal optical vortex pulses carrying a purely transverse intrinsic orbital angular momentum were generated experimentally [{\it Optica} {\bf 6}, 1547 (2019); {\it Nat. Photon.} {\bf 14}, 350 (2020)]. However, an accurate theoretical analysis of such states and their angular-momentum properties remains elusive. Here we provide such analysis, including scalar and vector spatiotemporal Bessel-type solutions as well as descrption of their propagational, polarization, and angular-momentum properties. Most importantly, we calculate both local densities and integral values of the spin and orbital angular momenta, and predict observable spin-orbit interaction phenomena related to the coupling between the trasnverse spin and orbital angular momentum. Our analysis is readily extended to spatiotemporal vortex pulses of other natures (e.g., acoustic)., 6 pages, 5 figures, to appear in Phys. Rev. Lett

Transverse (Hall-effect) and Goos--H\"{a}nchen shifts of light beams reflected/refracted at planar interfaces are important wave phenomena, which can be significantly modified and enhanced by the presence of intrinsic orbital angular momentum (OAM) in the beam. Recently, optical spatiotemporal vortex pulses (STVPs) carrying a purely transverse intrinsic OAM were predicted theoretically and generated experimentally. Here we consider the reflection and refraction of such pulses at a planar isotropic interface. We find theoretically and confirm numerically novel types of the OAM-dependent transverse and longitudinal pulse shifts. Remarkably, the longitudinal shifts can be regarded as time delays, which appear, in contrast to the well-known Wigner time delay, without temporal dispersion of the reflection/refraction coefficients. Such time delays allow one to realize OAM-controlled slow (subluminal) and fast (superluminal) pulse propagation without medium dispersion. These results can have important implications in various problems involving scattering of localized vortex states carrying transverse OAM., Comment: 7 pages, 4 figures, to appear in Nanophotonics

The authors examine complex three-dimensional polarization in the interference of several vector waves with different commensurable frequencies. They describe knots formed by such polychromatic vector fields, as well as their spin and polarization properties.

We analyze planar electromagnetic waves confined by a slab waveguide formed by two perfect electrical conductors. Remarkably, two-dimensional (2D) Maxwell equations describing transverse electromagnetic modes in such waveguides are exactly mapped onto equations for acoustic waves in fluids or gases. We show that interfaces between two slab waveguides with opposite-sign permeabilities support 1D edge modes, analogous to surface acoustic plasmons at interfaces with opposite-sign mass densities. We analyze this type of edge mode for the cases of isotropic media and anisotropic media with tensor permeabilities (including hyperbolic media). We also take into account ``non-Hermitian'' edge modes with imaginary frequencies or/and propagation constants. Our theoretical predictions are feasible for optical and microwave experiments involving 2D metamaterials.

Angular momentum of spinning bodies leads to their remarkable interactions with fields, waves, fluids, and solids. Orbiting celestial bodies, balls in sports, liquid droplets above a hot plate, nanoparticles in optical fields, and spinning quantum particles exhibit nontrivial rotational dynamics. Here, we report self-guided propulsion of magnetic fast-spinning particles on a liquid surface in the presence of a solid boundary. Above some critical spinning frequency (higher rotational Reynolds numbers), such particles generate localized 3D vortices and form composite 'spinner-vortex' quasi-particles with nontrivial, yet robust dynamics. Such spinner-vortices are attracted and dynamically trapped near the boundaries, propagating along the wall of any shape similarly to 'liquid wheels'. The propulsion velocity and the distance to the wall are controlled by the angular velocity of the spinner via the balance between the Magnus and wall-repulsion forces. Our results offer a new type of surface vehicles and provide a powerful tool to manipulate spinning objects in fluids., 10 pages, 5 figures

Following to the recently published approach [Phys. Rev. Lett. 119, 073901 (2017); New J. Phys., 123014 (2017)], we refine and accomplish the general scheme for the unified description of the momentum and angular momentum in complex media. The equations for the canonical (orbital) and spin linear momenta, orbital and spin angular momenta in a lossless inhomogeneous dispersive medium are presented in the compact form analogous to the Brillouin's relation for the energy. The results are applied to the surface plasmon-polariton (SPP) field, and the microscopic calculations support the phenomenological expectations. The refined general scheme correctly describes the unusual SPP properties (transverse spin, magnetization momentum) and additionally predicts the singular momentum contribution sharply localized at the metal-dielectric interface, which is confirmed by the microscopic analysis. The results can be useful in optical systems employing the structured light, especially for microoptics, plasmophotonics, optical sorting and micromanipulation., Comment: 19 pages, 2 figures. Presented at the Memorial Conference dedicated to Prof. A.E. Glauberman in Odessa National University 14 - 15 November 2017. 17 Dec 2020: 2 lines are added beneath Eq. (40), and the number of Eq. (55) is corrected

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. We show that next order correction to the force is responsible for the recoil effect.

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., Comment: 7 pages, 3 figures, Supplemental Material, to appear in Phys. Rev. Lett

Geometric phases are a universal concept that underpins numerous phenomena involving multi-component wave fields. These polarization-dependent phases are inherent in interference effects, spin-orbit interaction phenomena, and topological properties of vector wave fields. Geometric phases have been thoroughly studied in two-component fields, such as two-level quantum systems or paraxial optical waves. However, their description for fields with three or more components, such as generic nonparaxial optical fields routinely used in modern nano-optics, constitutes a nontrivial problem. Here we describe geometric, dynamical, and total phases calculated along a closed spatial contour in a multi-component complex field, with particular emphasis on 2D (paraxial) and 3D (nonparaxial) optical fields. We present several equivalent approaches: (i) an algebraic formalism, universal for any multi-component field; (ii) a dynamical approach using the Coriolis coupling between the spin angular momentum and reference-frame rotations; and (iii) a geometric representation, which unifies the Pancharatnam-Berry phase for the 2D polarization on the Poincar\'e sphere and the Majorana-sphere representation for the 3D polarized fields. Most importantly, we reveal close connections between geometric phases, angular-momentum properties of the field, and topological properties of polarization singularities in 2D and 3D fields, such as C-points and polarization M\"obius strips., Comment: 21 pages, 11 figures, to appear in Rep. Prog. Phys

Recently, it was shown that surface electromagnetic waves at interfaces between continuous homogeneous media (e.g., surface plasmon-polaritons at metal-dielectric interfaces) have a topological origin [K. Y. Bliokh et al., Nat. Commun. 10, 580 (2019)]. This is explained by the nontrivial topology of the non-Hermitian photon helicity operator in the Weyl-like representation of Maxwell equations. Here we analyze another type of classical waves: longitudinal acoustic waves corresponding to spinless phonons. We show that surface acoustic waves, which appear at interfaces between media with opposite-sign densities, can be explained by similar topological features and the bulk-boundary correspondence. However, in contrast to photons, the topological properties of sound waves originate from the non-Hermitian four-momentum operator in the Klein-Gordon representation of acoustic fields., 6 pages, 2 figures, and Supplemental Material. To appear in Phys. Rev. Lett

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 ${\it scalar}$ 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 ${\it vector}$ 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 ${\it spinor}$ 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., 26 pages, 1 figure, published version

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., 15 pages, 3 figures, 1 table, to appear in Phys. Rev. B

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., 10 pages, 2 figures, 1 table, to appear in Phys. Rev. B

Maxwell's equations, formulated 150 years ago, ultimately describe properties of light, from classical electromagnetism to quantum and relativistic aspects. The latter ones result in remarkable geometric and topological phenomena related to the spin-1 massless nature of photons. By analyzing fundamental spin properties of Maxwell waves, we show that free-space light exhibits an intrinsic quantum spin Hall effect, i.e., surface modes with strong spin-momentum locking. These modes are evanescent waves that form, e.g., surface plasmon-polaritons at vacuum-metal interfaces. Our findings illuminate the unusual transverse spin in evanescent waves and explain recent experiments demonstrating the transverse spin-direction locking in the excitation of surface optical modes. This deepens our understanding of Maxwell's theory, reveals analogies with topological insulators for electrons, and offers applications for robust spin-directional optical interfaces., 8 pages, 4 figures, Supplementary Materials

Plane waves and cylindrical or spherical vortex modes are important sets of solutions of quantum and classical wave equations. These are eigenmodes of the energy-momentum and angular-momentum operators, i.e., generators of spacetime translations and spatial rotations, respectively. Here we describe another set of wave modes: eigenmodes of the "boost momentum" operator, i.e., a generator of Lorentz boosts (spatio-temporal rotations). Akin to the angular momentum, only one (say, z) component of the boost momentum can have a well-defined quantum number. The boost eigenmodes exhibit invariance with respect to the Lorentz transformations along the z-axis, leading to scale-invariant wave forms and step-like singularities moving with the speed of light. We describe basic properties of the Lorentz-boost eigenmodes and argue that these can serve as a convenient basis for problems involving causal propagation of signals., 16 pages, 4 figures, to appear in Phys. Rev. A

Optical helicity density is usually discussed for monochromatic electromagnetic fields in free space. It plays an important role in the interaction with chiral molecules or nanoparticles. Here we introduce the optical helicity density in a dispersive isotropic medium. Our definition is consistent with biorthogonal Maxwell electromagnetism in optical media, the Brillouin energy density, as well as with the recently-introduced canonical momentum and spin of light in dispersive media. We consider a number of examples, including electromagnetic waves in dielectrics, negative-index materials, and metals, as well as interactions of light in a medium with chiral and magnetoelectric molecules., Comment: to appear in Phys. Rev. Lett

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., 12 pages, 4 figures, to appear in Optica

Motivated by recent interest in relativistic electron vortex states, we revisit the spin and orbital angular momentum properties of Dirac electrons. These are uniquely determined by the choice of the position operator for a relativistic electron. We overview two main approaches discussed in the literature: (i) the projection of operators onto the positive-energy subspace, which removes the zitterbewegung effects and correctly describes spin-orbit interaction effects, and (ii) the use of Newton-Wigner-Foldy-Wouthuysen operators based on the inverse Foldy-Wouthuysen transformation. We argue that the first approach [previously described in application to Dirac vortex beams in K.Y. Bliokh et al., Phys. Rev. Lett. 107, 174802 (2011)] has a more natural physical interpretation, including spin-orbit interactions and a nonsingular zero-mass limit, than the second one [S.M. Barnett, Phys. Rev. Lett. 118, 114802 (2017)]., Comment: 10 pages, 1 table, to appear in Phys. Rev. A

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 Minkowsky-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. We apply this general theory to inhomogeneous surface plasmon-polariton (SPP) waves at a metal-vacuum interface and show that SPPs carry a "super-momentum", proportional to the wave vector $k_{p} > \omega/c$, and a transverse spin, which can change its sign depending on the frequency $\omega$., Comment: 6 pages, 2 figures, to appear in Phys. Rev. Lett

We examine the momentum and angular-momentum (AM) properties of monochromatic optical fields in dispersive and inhomogeneous isotropic media, using the Abraham- and Minkowski-type approaches, as well as the kinetic (Poynting-like) and canonical (with separate spin and orbital degrees of freedom) pictures. While the kinetic Abraham-Poynting momentum describes the energy flux and the group velocity of the wave, the Minkowski-type quantities, with proper dispersion corrections, describe the actual momentum and angular momentum carried by the wave. The kinetic Minkowski-type momentum and AM densities agree with phenomenological results derived by Philbin. Using the canonical spin-orbital decomposition, previously used for free-space fields, we find the corresponding canonical momentum, spin and orbital AM of light in a dispersive inhomogeneous medium. These acquire a very natural form analogous to the Brillouin energy density and are valid for arbitrary structured fields. The general theory is applied to a non-trivial example of a surface plasmon-polariton (SPP) wave at a metal-vacuum interface. We show that the integral momentum of the SPP per particle corresponds to the SPP wave vector, and hence exceeds the momentum of a photon in the vacuum. We also provide the first accurate calculation of the transverse spin and orbital AM of the SPP. While the intrinsic orbital AM vanishes, the transverse spin can change its sign depending on the SPP frequency. Importantly, we present both macroscopic and microscopic calculations, thereby proving the validity of the general phenomenological results. The microscopic theory also predicts a transverse magnetization in the metal (i.e., a magnetic moment for the SPP) as well as the corresponding direct magnetization current, which explains the difference between the Abraham and Minkowski momenta., 33 pages, 4 figures, 1 table, to appear in New J. Phys

We have analyzed total spin angular momentum of surface waves localized at a metasurface described within an effective conductivity approach. We show that hybrid TE-TM polarized surface waves propagating along the anisotropic metasurface provide unprecedented control over the spin angular momentum of light. The obtained results can be used in a number of photonic applications.

Both classical and quantum waves can form vortices: with helical phase fronts and azimuthal current densities. These features determine the intrinsic orbital angular momentum carried by localized vortex states. In the past 25 years, optical vortex beams have become an inherent part of modern optics, with many remarkable achievements and applications. In the past decade, it has been realized and demonstrated that such vortex beams or wavepackets can also appear in free electron waves, in particular, in electron microscopy. Interest in free-electron vortex states quickly spread over different areas of physics: from basic aspects of quantum mechanics, via applications for fine probing of matter (including individual atoms), to high-energy particle collision and radiation processes. Here we provide a comprehensive review of theoretical and experimental studies in this emerging field of research. We describe the main properties of electron vortex states, experimental achievements and possible applications within transmission electron microscopy, as well as the possible role of vortex electrons in relativistic and high-energy processes. We aim to provide a balanced description including a pedagogical introduction, solid theoretical basis, and a wide range of practical details. Special attention is paid to translate theoretical insights into suggestions for future experiments, in electron microscopy and beyond, in any situation where free electrons occur., 87 pages, 34 figures

We describe the spin-Hall effect of light (as well as the angular Goos-H\"{a}nchen effect) at a tilted linear-dichroic plate, such as a usual linear polarizer. Although the spin-Hall effect at a tilted polarizer was previous associated with the geometric spin-Hall effect of light (which was contrasted to the regular spin-Hall effect) [J. Korger et al., Phys. Rev. Lett. 112, 113902 (2014)], we show that the effect is actually an example of the regular spin-Hall effect that occurs at tilted anisotropic plates [K. Y. Bliokh et al., Optica 3, 1039 (2016)]. Moreover, our approach reveals the angular spin-Hall shift, which is absent in the "geometric" approach. We verify our theory experimentally using the method of quantum weak measurements., Comment: 4 pages, 3 figures, to appear in Opt. Lett

We demonstrate theoretically and experimentally the fine lateral circular birefringence of uniaxial crystal plates, an example of the spin — Hall effect of light. We report experimental observations this effect using polarimetric and quantum-weak-measurement techniques.

Polarization, spin, and helicity are important properties of electromagnetic waves. It is commonly believed that helicity is invariant under the Lorentz transformations. This is indeed so for plane waves and their localized superpositions. However, this is not the case for evanescent waves, which are well-defined only in a half-space, and are characterized by complex wave vectors. Here we describe transformations of evanescent electromagnetic waves and their polarization/spin/helicity properties under the Lorentz boosts along the three spatial directions., Comment: 12 pages, 4 figures, to appear in Phys. Lett. A

Laboratory optics, typically dealing with monochromatic light beams in a single reference frame, exhibits numerous spin-orbit interaction phenomena due to the coupling between the spin and orbital degrees of freedom of light. Similar phenomena appear for electrons and other spinning particles. Here we examine transformations of paraxial photon and relativistic-electron states carrying the spin and orbital angular momenta (AM) under the Lorentz boosts between different reference frames. We show that transverse boosts inevitably produce a rather nontrivial conversion from spin to orbital AM. The converted part is then separated between the intrinsic (vortex) and extrinsic (transverse shift or Hall effect) contributions. Although the spin, intrinsic-orbital, and extrinsic-orbital parts all point in different directions, such complex behavior is necessary for the proper Lorentz transformation of the total AM of the particle. Relativistic spin-orbit interactions can be important in scattering processes involving photons, electrons, and other relativistic spinning particles, as well as when studying light emitted by fast-moving bodies., Comment: 9 pages, 3 figures

We study inelastic resonant scattering of a Gaussian wave packet with the parameters close to a zero of the complex scattering coefficient. We demonstrate, both theoretically and experimentally, that such near-zero scattering can result in anomalously-large time delays and frequency shifts of the scattered wave packet. Furthermore, we reveal a close analogy of these anomalous shifts with the spatial and angular Goos-H\"anchen optical beam shifts, which are amplified via quantum weak measurements. However, in contrast to other beam-shift and weak-measurement systems, we deal with a one-dimensional scalar wave without any intrinsic degrees of freedom. It is the non-Hermitian nature of the system that produces its rich and non-trivial behaviour. Our results are generic for any scattering problem, either quantum or classical. As an example, we consider the transmission of an optical pulse through a nano-fiber with a side-coupled toroidal micro-resonator. The zero of the transmission coefficient corresponds to the critical coupling conditions. Experimental measurements of the time delays near the critical-coupling parameters verify our weak-measurement theory and demonstrate amplification of the time delay from the typical inverse resonator linewidth scale to the pulse duration scale., Comment: 14 pages, 5 figures

We provide an overview of recent theoretical and experimental studies, which revisited the basic dynamical properties of light: momentum and angular momentum. Recently, we described qualitatively new types of the spin and momentum in structured optical fields. These are: (i) the transverse spin, which is orthogonal to the wave vector and is independent of the helicity, and (ii) the anomalous transverse momentum, which depends on the helicity of light. Both of these quantities were described and measured experimentally in various optical systems, and they are currently attracting rapidly growing attention. In particular, the transverse spin in evanescent waves has found promising applications for robust spin-controlled unidirectional coupling to surface and waveguide optical modes. In turn, the transverse momentum provides a weak spin-dependent optical force, which is orthogonal to both the propagation direction and the intensity gradient in a wave field.

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., 6 pages, 3 figures

The semiclassical evolution of spinning particles has recently been re-examined in condensed matter physics, high energy physics, and optics, resulting in the prediction of the intrinsic spin Hall effect associated with the Berry phase. A fundamental nature of this effect is related to the spin-orbit interaction and topological monopoles. Here we report a unified theory and a direct observation of two mutual phenomena: a spin-dependent deflection (the spin Hall effect) of photons and the precession of the Stokes vector along the coiled ray trajectory of classical geometrical optics. Our measurements are in perfect agreement with theoretical predictions, thereby verifying the dynamical action of the topological Berry-phase monopole in the evolution of light. These results may have promising applications in nano-optics and can be immediately extrapolated to the evolution of massless particles in a variety of physical systems., Comment: 18 pages, 4 figures, to appear in Nature Photonics

Super-resolution, extraordinary transmission, total absorption, and localization of electromagnetic waves are currently attracting growing attention. These phenomena are related to different physical systems and are usually studied within the context of different, sometimes rather sophisticated, approaches. Remarkably, all these seemingly unrelated phenomena owe their origin to the same underlying physical mechanism, namely, wave interaction with an open resonator. Here we show that it is possible to describe all of these effects in a unified way, mapping each system onto a simple resonator model. Such description provides a thorough understanding of the phenomena, explains all the main features of their complex behavior, and enables one to control the system via the resonator parameters: eigenfrequencies, $Q$ factors, and coupling coefficients.

We analyze chiral topological edge modes in a non-Hermitian variant of the 2D Dirac equation. Such modes appear at interfaces between media with different "masses" and/or signs of the "non-Hermitian charge". The existence of these edge modes is intimately related to exceptional points of the bulk Hamiltonians, i.e., degeneracies in the bulk spectra of the media. We find that the topological edge modes can be divided into three families ("Hermitian-like", "non-Hermitian", and "mixed"), these are characterized by two winding numbers, describing two distinct kinds of half-integer charges carried by the exceptional points. We show that all the above types of topological edge modes can be realized in honeycomb lattices of ring resonators with asymmetric or gain/loss couplings., Comment: 6 pages, 3 figures, and Supplementary Materials, to appear in Phys. Rev. Lett

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Maxwell's equations, formulated 150 years ago, ultimately describe properties of light, from classical electromagnetism to quantum and relativistic aspects. The latter ones result in remarkable geometric and topological phenomena related to the spin-1 massless nature of photons. By analyzing fundamental spin properties of Maxwell waves, we show that free-space light exhibits an intrinsic quantum spin Hall effect—surface modes with strong spin-momentum locking. These modes are evanescent waves that form, for example, surface plasmon-polaritons at vacuum-metal interfaces. Our findings illuminate the unusual transverse spin in evanescent waves and explain recent experiments that have demonstrated the transverse spin-direction locking in the excitation of surface optical modes. This deepens our understanding of Maxwell's theory, reveals analogies with topological insulators for electrons, and offers applications for robust spin-directional optical interfaces.

Although strong localization of waves in one-dimensional random media has been well studied theoretically, most of the analytical results were obtained for lossless systems and for values averaged over ensembles of random realizations. Obviously, this does not specify the frequency spectrum and the intensity distribution within a particular sample, yet such data are essential for possible applications.

We analyze the interference field formed by two electromagnetic plane waves (with the same frequency but different wave vectors), and find that such field reveals a rich and highly non-trivial structure of the local momentum and spin densities. Despite the seemingly-planar and extensively-studied character of the two-wave system, we find that it possesses a transverse (out-of-plane) helicity-independent spin density, and also a transverse polarization-dependent momentum density with unusual physical properties. The polarization-dependent transverse momentum represents the so-called Belinfante spin momentum, which does not exert the usual optical pressure and it is considered as `virtual' in field theory. We perform analytical estimations and exact numerical simulations of the interaction of the two-wave field with probe Mie particles. The results of these calculations clearly indicate the straightforward detectability of the unusual spin and momentum properties in the two-wave field and strongly motivate their future experimental verifications., 13 pages, 4 figures, Supplementary Information, to appear in Phys. Rev. X

Nonreciprocity and one-way propagation of optical signals is crucial for modern nanophotonic technology, and is typically achieved using magneto-optical effects requiring large magnetic biases. Here we suggest a fundamentally novel approach to achieve unidirectional propagation of surface plasmon-polaritons (SPPs) at metal-dielectric interfaces. We employ a direct electric current in metals, which produces a Doppler frequency shift of SPPs due to the uniform drift of electrons. This tilts the SPP dispersion, enabling one-way propagation, as well as zero and negative group velocities. The results are demonstrated for planar interfaces and cylindrical nanowire waveguides., Comment: 4 pages, 4 figures, to appear in Opt. Lett

Exciton-polaritons are hybrid light-matter quasiparticles formed by strongly interacting photons and excitons (electron-hole pairs) in semiconductor microcavities. They have emerged as a robust solid-state platform for next-generation optoelectronic applications as well as fundamental studies of quantum many-body physics. Importantly, exciton-polaritons are a profoundly open (i.e., non-Hermitian) quantum system: it requires constant pumping of energy and continuously decays releasing coherent radiation. Thus, the exciton-polaritons always exist in a balanced potential landscape of gain and loss. However, the inherent non-Hermitian nature of this potential has so far been largely ignored in exciton-polariton physics. Here we demonstrate that non-Hermiticity dramatically modifies the structure of modes and spectral degeneracies in exciton-polariton systems, and, therefore, will affect their quantum transport, localisation, and dynamical properties. Using a spatially-structured optical pump, we create a chaotic exciton-polariton billiard. Eigenmodes of this billiard exhibit multiple non-Hermitian spectral degeneracies -- exceptional points. These are known to cause remarkable wave phenomena, such as unidirectional transport, anomalous lasing/absorption, and chiral modes. By varying parameters of the billiard, we observe crossing and anti-crossing of energy levels and reveal the nontrivial topological modal structure exclusive to non-Hermitian systems. We also observe the mode switching and topological Berry phase for a parameter loop encircling the exceptional point. Our findings pave the way for studies of non-Hermitian quantum dynamics of exciton-polaritons, which can lead to novel functionalities of polariton-based devices., Comment: 8 pages, 4 figures

Light carries spin and orbital angular momentum. These dynamical properties are determined by the polarization and spatial degrees of freedom of light. Modern nano-optics, photonics, and plasmonics, tend to explore subwavelength scales and additional degrees of freedom of structured, i.e., spatially-inhomogeneous, optical fields. In such fields, spin and orbital properties become strongly coupled with each other. We overview the fundamental origins and important applications of the main spin-orbit interaction phenomena in optics. These include: spin-Hall effects in inhomogeneous media and at optical interfaces, spin-dependent effects in nonparaxial (focused or scattered) fields, spin-controlled shaping of light using anisotropic structured interfaces (metasurfaces), as well as robust spin-directional coupling via evanescent near fields. We show that spin-orbit interactions are inherent in all basic optical processes, and they play a crucial role at subwavelength scales and structures in modern optics., Comment: 23 pages, 6 figures. Comments welcome

We review basic physics and novel types of optical angular momentum. We start with a theoretical overview of momentum and angular momentum properties of generic optical fields, and discuss methods for their experimental measurements. In particular, we describe the well-known longitudinal (i.e., aligned with the mean momentum) spin and orbital angular momenta in polarized vortex beams. Then, we focus on the transverse (i.e., orthogonal to the mean momentum) spin and orbital angular momenta, which were recently actively discussed in theory and observed in experiments. First, the recently-discovered transverse spin angular momenta appear in various structured fields: evanescent waves, interference fields, and focused beams. We show that there are several kinds of transverse spin angular momentum, which differ strongly in their origins and physical properties. We describe extraordinary features of the transverse optical spins and overview recent experiments. In particular, the helicity-independent transverse spin inherent in edge evanescent waves offers robust spin-direction coupling at optical interfaces (the quantum spin Hall effect of light). Second, we overview the transverse orbital angular momenta of light, which can be both extrinsic and intrinsic. These two types of the transverse orbital angular momentum are produced by spatial shifts of the optical beams (e.g., in the spin Hall effect of light) and their Lorentz boosts, respectively. Our review is underpinned by a unified theory of the angular momentum of light based on the canonical momentum and spin densities, which avoids complications associated with the separation of spin and orbital angular momenta in the Poynting picture. It allows us to construct comprehensive classification of all known optical angular momenta based on their key parameters and main physical properties., Comment: 56 pages, 21 figures. To appear in Physics Reports