arXiv subjects

Aleksandr Bekshaev

Publications and source records attributed to Aleksandr Bekshaev.

At least 19 recordsLinked to original sources

arXiv2024

Wigner function and intensity moments of spatio-temporal light fields

The Wigner distribution function and its spatial-angular moments (intensity-moments) are known as efficient instruments for characterization of complex quasimonochromatic light beams and their transformations. In this paper, the generalization of the WF-based approach to spatio-temporal (ST) light fields (wave packets, short pulses) is considered. It is shown that the ST intensity moments are related with the important characteristics of the wave-packet structure, especially, with the transverse orbital angular momentum (OAM) being a specific feature of the ST optical vortices (STOV). The ST moments' transformations in a paraxial optical system obey simple and unified rules involving the ray-transfer ABCD-matrix of the system. On this base, and with simple examples of the OAM-carrying optical pulses, the schemes and mechanisms of the STOV generation and transformation are presented. Examples of non-vortex ST wave packets with the transverse OAM, their possible realizations are discussed as well as the relations between the OAM and the visible pulse rotations. The regular and unified formalism, developed in this paper, can be generalized and applied to more complex situations where the ST field propagates through inhomogeneous and random (scattering) media.

physics.optics↗

arXiv2024

Bi-chromatic paraxial beam as a model of spatio-temporal light fields

Optical fields with rich and well-developed spatio-temporal structure, including ultra-short structured light pulses, are essentially non-monochromatic and contain a continuous spectrum of monochromatic constituents. However, some substantial features of such fields and physical mechanisms determining their behavior can be understood based on simplified models including only two monochromatic paraxial components. We consider examples of such model beams, their specific spatial and temporal properties as well as their descriptive abilities for the meaningful characterization of realistic spatio-temporal light fields. In particular, the proposed model enables an explicit consistent analysis of the photon-probability distributions in non-monochromatic fields, which confirms a high degree of coincidence between the "energy center" and "probability center" of the field. Simultaneously, particular features of the two-component bi-chromatic paraxial fields (periodic and rotational character of the longitudinal and temporal evolution, specific deformations of the propagating-beam transverse intensity profile, etc.) are inspected using numerical examples.

physics.optics↗

arXiv2024

Spatio-temporal optical vortices: principles of description and basic properties

This compilation represents a summary of the main physical foundations underlying the structure and properties of spatio-temporal optical vortices (STOV). The general approach to the STOV description and characterization is based on the model of scalar paraxial Gaussian wave packet. On this ground, the STOV structures of arbitrary orders are considered as superpositions of spatio-temporal Hermite-Gaussian modes. This approach enables a systematic characterization of the main STOV properties in an explicit and physically transparent form. In particular, we analyze the STOV amplitude and phase distributions, their evolution upon free propagation and in optical systems, internal energy flows and the orbital angular momentum. The topologically determined inherent asymmetry of the STOVs and the difference between the "energy center" and "probability center" [Phys. Rev. A 107, L031501 (2023)] are discussed and qualitatively interpreted. Methods for the STOV generation and diagnostics are outlined, and the main properties of non-Gaussian (Bessel-type) STOVs are briefly described. Finally, limitations of the scalar Gaussian model, accepted throughout the whole text, are considered, and possible generalizations are exposed. The whole presentation may be useful as initial introduction to the STOV-associated ideas and their extraordinary properties.

physics.optics↗

arXiv2023

Subwavelength particles in an inhomogeneous light field: Optical forces associated with the spin and orbital energy flows

We analyze the ponderomotive action experienced by a small spherical particle immersed in an optical field, in relation to the internal energy flows (optical currents) and their spin and orbital constituents. The problem is studied analytically, based on the dipole model, and numerically. Three sources of the field mechanical action - energy density gradient and the orbital and spin parts of the energy flow - differ by the ponderomotive mechanism, and their physical nature manifests itself in the optical force dependence on the particle radius a. If a is much less than the radiation wavelength, the optical force behaves as a^n and integer n can be used to classify the sources of the mechanical action. This classification correlates with the multipole representation of the field-particle interaction: The gradient force and the orbital-momentum force appear due to the electric or magnetic dipole moments per se, the spin-momentum force emerges due to interaction between the electric and magnetic dipoles or between the dipole and quadruple moments (if the particle is polarisable electrically but not magnetically or vice versa). In principle, the spin and orbital currents can be measured separately by the probe particle motion, employing the special choice of particles with necessary magnetic and/or electric properties.

physics.optics↗

arXiv2022

Inverse Faraday effect and Stokes drift in plasma

Recent theory of the light-induced medium magnetization (inverse Faraday effect, IFE) performed by a transversely-limited circularly-polarized light beam [Phys. Rev. B 91, 020411 (2015)] predicts the existence of a "demagnetization current" (DC) at the beam periphery which, apparently, acts oppositely to the light-induced rotational motion of the charge carriers inside the beam and thus reduces the IFE by the factor of 2. In this note, taking the longitudinal component of the beam into account, we show that the peripheral DC is two times higher than was calculated before. Nevertheless, this circumstance does not cancel the IFE because the DC, as a sort of Stokes-drift current in plasma [Phys. Rev. E 105, 065208 (2022)], is accompanied by the additional "magnetization current" of the opposite direction.

physics.optics↗

arXiv2021

Microscopic analysis of the energy, momentum and spin distributions in a surface plasmon-polariton wave

We analyze the electromagnetic field near a plane interface between a conductive and a dielectric media, under conditions supporting surface plasmon-polariton (SPP) propagation. The conductive medium is described by the hydrodynamic electron-gas model that enables a consistent analysis of the field-induced variations of the electron density and velocity at the interface and its nearest vicinity. The distributions of electromagnetic dynamical characteristics: energy, energy flow, spin and momentum are calculated analytically and illustrated numerically, employing silver-vacuum interface as an example. A set of the "field" and material contributions to the energy, spin and momentum are explicitly identified and classified with respect to their physical origins and properties, and the orbital (canonical) and spin (Belinfante) momentum constituents are separately examined. In this context, a procedure for the spin-orbital momentum decomposition in the presence of free charges is proposed and substantiated. The microscopic results agree with the known phenomenological data but additionally show specific nanoscale structures in the near-interface behavior of the SPP energy and momentum, which can be deliberately created, controlled and used in nanotechnology applications.

physics.optics↗

arXiv2021

Extraordinary transverse spin: Hidden vorticity of the energy flow and momentum distributions in propagating light fields

Spatially inhomogeneous fields of electromagnetic guided modes exhibit a complex of extraordinary dynamical properties such as the polarization-dependent transverse momentum, helicity-independent transverse spin, spin-associated non-reciprocity and unidirectional propagation, etc. Recently, the remarkable relationship has been established between the spin and propagation features of such fields, expressed through the spin-momentum equations [Proc. Natl. Acad. Sci. 118 (2021) e2018816118] connecting the wave spin with the curl of momentum. Here, the meaning, limitations and specific forms of this correspondence are further investigated, involving the physically transparent and consistent examples of paraxial light fields, plane-wave superpositions and evanescent waves. The conclusion is inferred that the spin-momentum equation is an attribute of guided waves with well defined direction of propagation, and it unites the helicity-independent "extraordinary" transverse spin with the spatially-inhomogeneous longitudinal field momentum (energy flow) density. Physical analogies with the layered hydrodynamic flows and possible generalizations for other wave fields are discussed. The results can be useful in optical trapping, manipulation and the data processing techniques.

physics.optics↗

arXiv2020

Non-collinear rotational Doppler effect

The frequency shift of a helical light beam experiencing the rotation near the axis deferring from its own axis (conical evolution) is studied theoretically. Both the energy and the kinematic approaches lead to a paradoxical conclusion that after a whole cycle of the system rotation the beam does not return to its initial state. Another paradox is manifested in the peculiar behavior of the beam transverse pattern rotation at different geometric parameters of the evolving system. A fundamental role of the detecting system motion is substantiated. The special "natural" observer's motion is found for which both paradoxes are eliminated. Relations of the described facts with the Hannay's geometric phase concept are discussed.

physics.optics↗

arXiv2019

Transformation of the singular skeleton in optical-vortex beams diffracted by a rectilinear phase step

Based on the Kirchhoff-Fresnel approximation, we numerically analyze spatial characteristics of the light field formed after a circular Laguerre-Gaussian beam with a single-charged optical vortex (OV) passes the transparent screen with a rectilinear phase step. The main attention is paid to the localization and interactions of the OVs, which form the singular skeleton of the transformed field. The phase-step influence depends on its value and position with respect to the beam axis. Upon "weak perturbation" (low phase step) the main effect is that the OV is shifted from the initial axial position and describes a closed loop when the phase step is monotonously translated across the beam. The "strong perturbation" (the phase step is close to pi) induces topological reactions with emergence and annihilation of additional singularities in the near-axial region of the diffracted beam cross section. These features are interpreted based on the 3D OV trajectories that show an intricate behavior with kinks and "retrograde" segments. The details of the OV migration and singular skeleton transformations reveal the fundamental helical nature and transverse energy circulation in the OV beams. The numerical results obtained in this paper show possibilities for the purposeful control of the singular skeleton characteristics within the transformed beam, and can be useful for the OV diagnostics, OV metrology and micromanipulation techniques.

physics.optics↗

arXiv2019

Electromagnetic dynamical characteristics of a surface plasmon-polariton

We consider the electromagnetic field near an interface between two media with arbitrary real frequency-dependent permittivities and permeabilities, under conditions supporting the surface plasmon-polariton (SPP) propagation. The dispersion of the electric and magnetic properties is taken into account based on the recent approach for description of the spin and momentum of electromagnetic field in complex media [Phys. Rev. Lett. 119, 073901 (2017); New J. Phys., 19, 123014 (2017)]. It involves the Minkowski momentum decomposition into the spin and orbital parts with the dispersion-modified permittivities and permeabilities. Explicit expressions are derived for spatial densities of the energy, energy flow, spin and orbital momenta and angular momenta of the transverse-magnetic (TM) SPP field. They are free from non-physical singularities; the only singular contribution describes a strictly localized surface part of the spin momentum that can be associated with the magnetization current in the conductive part of the SPP-supporting structure. On this ground, a phenomenological theory of the SPP-induced magnetization (predicted earlier based on the simplified microscopic approach) is outlined. Possible modifications and generalizations, including the transverse-electric (TE) SPP waves, are discussed.

physics.optics↗

arXiv2018

Dynamical characteristics of electromagnetic field under conditions of total reflection

The dynamical characteristics of electromagnetic fields include energy, momentum, angular momentum (spin) and helicity. We analyze their spatial distributions near the planar interface between two transparent and non-dispersive media, when the incident monochromatic plane wave with arbitrary polarization is totally reflected, and an evanescent wave is formed in the medium with lower optical density. Based on the recent arguments in favor of the Minkowski definition of the electromagnetic momentum in a material medium [Phys. Rev. A 83, 013823 (2011); 86, 055802 (2012); Phys. Rev. Lett. 119, 073901 (2017)], we derive the explicit expressions for the dynamical characteristics in both media, with special attention to their behavior at the interface. Especially, the "extraordinary" spin and momentum components orthogonal to the plane of incidence are described, and the canonical (spin - orbital) momentum decomposition is performed that contains no singular terms. The field energy, helicity, the spin momentum and orbital momentum components are everywhere regular but experience discontinuities at the interface; the spin components parallel to the interface appear to be continuous, which testifies for the consistency of the adopted Minkowski picture. The results supply a meaningful example of the electromagnetic momentum decomposition, with separation of spatial and polarization degrees of freedom, in inhomogeneous media, and can be used in engineering the structured fields designed for optical sorting, dispatching and micromanipulation.

physics.optics↗

arXiv2017

Abraham-based momentum and spin of optical fields under conditions of total reflection

This memo contains a collection of formulas describing the electromagnetic energy, momentum and spin distribution of an optical field formed in dielectric media separated by a plane interface when an incident monochromatic plane wave is totally reflected. The formulas are based on the Abraham momentum definition and include the momentum decomposition into the orbital (canonical) and spin parts as well as explicit dual-symmetric separation of the electric and magnetic contributions. This material was prepared in February 2013 but it had not been finalized and published because of the difficulties in physical interpretation of singular terms in the spin and orbital momentum expressions associated with the sharp interface. Meanwhile, it has become clear that the "naive" Abraham approach is not correct for this problem and the electromagnetic spin and momentum in inhomogeneous media are better characterized by the more elaborated relations based on the Minkowski paradigm [see, e.g., Phys. Rev. A 83, 013823 (2011); 86, 055802 (2012); arXiv:1706.05493]. In application to the total-reflection situation this Minkowski-based description was recently illustrated in arXiv:1706.06263, so the present material is mainly of historical interest. However, it seems useful to make it known for a wide audience, at least for comparison with the recent improved approaches and for suitable references. The last section, treating the ponderomotive action experienced by a Mie particle in the evanescent wave, is independent of the Abraham - Minkowski controversy. The numerical calculations preserve their validity, and association of the various force and torque components with corresponding components of the optical momentum and spin remains legal in the Minkowski pattern. The results of the last section were partly used in other published works [e.g., Nature Commun. 5, 3300 (2014)].

physics.optics↗

arXiv2017

Singular skeleton evolution and topological reactions in edge-diffracted circular optical-vortex beams

Edge diffraction of a circular optical vortex (OV) beam transforms its singular structure: a multicharged axial OV splits into the set of single-charged ones that form the 'singular skeleton' of the diffracted beam. The OV positions in the beam cross section depend on the propagation distance as well as on the edge position with respect to the incident beam axis, and the OV cores describe regular trajectories when one or both of these parameters change. However, the trajectories are not always continuous; they may be accompanied with topological reactions, including emergence of new singularities, their interaction and annihilation. Based on the Kirchhoff-Fresnel integral, we consider the singular skeleton behavior in diffracted Kummer beams and Laguerre-Gaussian beams with topological charge |m|=2 and 3. We reveal the nature of the trajectories' discontinuities and other topological events in the singular skeleton evolution that appear to be highly sensitive to the incident beam properties and to the diffraction conditions. Conditions at which the OV trajectory becomes discontinuous and mechanisms by which this is realized are discussed. The conclusions based on the numerical calculations are supported by the asymptotic analytical model of the OV beam diffraction. The results can be useful in the OV metrology and for the OV beam's diagnostics.

physics.optics↗

arXiv2017

Displacements and evolution of optical vortices in edge-diffracted Laguerre-Gaussian beams

Based on the Kirchhoff-Fresnel approximation, we consider behavior of the optical vortices (OV) upon propagation of the diffracted Laguerre-Gaussian (LG) beams with topological charge |m| = 1, 2. Under conditions of weak diffraction perturbation (i.e. the diffraction obstacle covers only the far transverse periphery of the incident LG beam), the OVs describe almost perfect 3D spirals within the diffracted beam body, which is an impressive demonstration of the helical nature of an OV beam. The far-field OV positions within the diffracted beam cross section depend on the wavefront curvature of the incident OV beam so that the input wavefront curvature is transformed into the output azimuthal OV rotation. The results can be useful in the OV metrology and for the OV beam's diagnostics.

physics.optics↗

arXiv2016

Localization and migration of phase singularities in the edge-diffracted optical-vortex beams

When a circularly-symmetric light beam with optical vortex (OV) diffracts at an opaque screen with the sharp edge, the OV core is displaced from the beam axis and, in case of the m-charged incident OV, decomposed into |m| single-charged ones. By means of numerical simulations and based on examples of incident beams with topological charges |m| =1, 2, 3 we show that, while the screen edge monotonously advances towards the beam axis, the OVs in the diffracted beam cross section move away from the incident beam axis along spiral-like trajectories. The trajectories contain fine structure details that reflect the nature and peculiar spatial configuration of the diffracting beam. For the Kummer beams' diffraction, the trajectories contain self-crossings and regions of "backward" rotation (loops); in case of Laguerre-Gaussian beams, the trajectories are smoother. The numerical results are supported by analytical approximations and conform with experiment The general shape of the trajectories and their local behavior show high sensitivity to the diffraction conditions (spatial structure of the diffracting beam, its disposition with respect to the screen edge, etc.), which can be used in diverse metrological applications.

physics.optics↗

arXiv2016

Evolution of the phase singularities in edge-diffracted optical-vortex beams

We study, both theoretically and by experiment, migration of the amplitude zeros within a fixed cross section of the edge-diffracted optical-vortex beam, when the screen edge performs permanent translation in the transverse plane from the beam periphery towards the axis. Generally, the amplitude zeros (optical-vortex cores) describe spiral-like trajectories. When the screen edge advances uniformly, the motion of the amplitude zeros is not smooth and sometimes shows anomalously high rates, which make an impression of instantaneous "jumps" from one position to another. We analyze the nature, conditions and mechanism of these jumps and show that they are associated with the "birth - annihilation" topological reactions involving the optical vortex dipoles.

physics.optics↗

arXiv2011

Transverse energy flow and the "running" behaviour of the instantaneous field distribution of a light beam

It is known that the orbital angular momentum of a paraxial beam is related to the rotational motion of the instantaneous field pattern representing the electric field optical-frequency oscillations [arXiv:0812.0888; J. Opt. A: Pure Appl. Opt 11, 094004, (2009)]. Now this conclusion is generalized: any identifiable directed motion of the instantaneous 2D pattern of the field oscillation ("running" behaviour of the instant oscillation pattern) corresponds to the transverse energy flow in the experimentally observable time-averaged field. The transverse orbital flow density can be treated as a natural geometric and kinematic characteristic of this running behaviour.

physics.optics↗

arXiv2011

Polarization-dependent transformation of a paraxial beam upon reflection and refraction: a real-space approach

We analyze the paraxial beam transformation upon reflection and refraction at a plane boundary. In contrast to the usual approach dealing with the beam angular spectrum, we apply the continuity conditions to explicit spatial representations of the electric and magnetic fields on both sides of the boundary. It is shown that the polarization-dependent distortions of the beam trajectory (in particular, the "longitudinal" Goos-Hänchen shift and the "lateral" Imbert-Fedorov shift of the beam center of gravity) are directly connected to the incident beam longitudinal component and appear due to its transformation at the boundary.

physics.optics↗