Aleksandr Bekshaev

Dual electromagnetism: helicity, spin, momentum and angular momentum

The dual symmetry between electric and magnetic fields is an important intrinsic property of Maxwell equations in free space. This symmetry underlies the conservation of optical helicity and, as we show here, is closely related to the separation of spin and orbital degrees of freedom of light (the helicity flux coincides with the spin angular momentum). However, in the standard field-theory formulation of electromagnetism, the field Lagrangian is not dual symmetric. This leads to problematic dual-asymmetric forms of the canonical energy–momentum, spin and orbital angular-momentum tensors. Moreover, we show that the components of these tensors conflict with the helicity and energy conservation laws. To resolve this discrepancy between the symmetries of the Lagrangian and Maxwell equations, we put forward a dual-symmetric Lagrangian formulation of classical electromagnetism. This dual electromagnetism preserves the form of Maxwell equations, yields meaningful canonical energy–momentum and angular-momentum tensors, and ensures a self-consistent separation of the spin and orbital degrees of freedom. This provides a rigorous derivation of the results suggested in other recent approaches. We make the Noether analysis of the dual symmetry and all the Poincare symmetries, examine both local and integral conserved quantities and show that only the dual electromagnetism naturally produces a complete self-consistent set of conservation laws. We also discuss the observability of physical quantities distinguishing the standard and dual theories, as well as relations to quantum weak measurements and various optical experiments.

Rotational transformations and transverse energy flow in paraxial light beams: linear azimuthons

Paraxial beams whose transverse structure rotates upon free propagation (spiral beams) can be treated as analogs of azimuthons recently found in nonlinear media [Phys. Rev. Lett.95, 203904 (2005)]. These linear azimuthons have essentially a nonlocalized character and can possess an almost arbitrary rotation rate independent of the angular momentum of the beam. Such beams can be assimilated into fluent mechanical bodies with intrinsic mass flows determined by transverse energy redistribution over the beam cross section.

Optical momentum and angular momentum in complex media: from the Abraham–Minkowski debate to unusual properties of surface plasmon-polaritons

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.

Transverse energy redistribution upon edge diffraction of a paraxial laser beam with optical vortex

We present the results of the numerical investigation of the transverse profile evolution for a beam obtained by the edge diffraction of a circular Laguerre-Gaussian mode. It is shown that the energy penetrates into the geometric shadow region asymmetrically, which testifies for the transverse energy circulation in the incident beam. The intensity profile shows the “overall” rotation in agreement with the energy circulation handedness. The phase profile of the diffracted beam is characterized by the system of singularities (optical vortices) that migrate over the beam cross section and participate in topological reactions of emergence and/or annihilation. In the far field, the beam profile structure is simplified and becomes symmetric with respect to the axis orthogonal to the screen edge. No matter which part of the Laguerre-Gaussian beam is stopped by the screen, the far-field profile contains the optical vortex of the same sense as the incident one.

Direct measurement of the extraordinary optical momentum using a nano-cantilever

An unexpected optical momentum and force perpendicular to the wavevector are measured using a nano-cantilever in an evanescent optical field, confirming a 75-year-old prediction.

Substrates with a periodic surface structure in grazing-exit X-ray microanalysis

Abstract The angular distribution of X-ray radiation from a point source and a small particle situated near a substrate with a periodic (diffraction grating-like) surface structure is analyzed theoretically. Due to diffraction on the surface grating, the radiation, reflected from the substrate, can be concentrated near certain directions depending on the wavelength and the grating parameters. As a result, distinct peaks appear in the X-ray signal angular dependence, whose magnitude, depending on the detector angle resolution, can exceed several times the usual value of X-ray intensity available under the same conditions of excitation with the use of a flat substrate. Different substrate structures containing amplitude as well as phase gratings with rectangular, triangular or smooth (sinusoidal) grooves are numerically investigated, predominantly for the case of low-energy characteristic X-ray radiation (O, N and C Kα lines), and the most favorable groove shapes and grating periods are revealed. The proposed method of X-ray signal enhancement is expected to be especially useful if the primary emission is relatively weak, i.e. for trace analysis, small specimens and/or analysis of low- Z elements. The angular separation of peaks for different elements forms an additional analytical advantage. The prospects for experimental realization of the method and possible further developments are discussed.

Electric-current-induced unidirectional propagation of surface plasmon-polaritons

Nonreciprocity and one-way propagation of optical signals are crucial for modern nanophotonic technology, and 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.

Spin–orbit interaction of light and diffraction of polarized beams

The edge diffraction of a homogeneously polarized light beam is studied theoretically based on the paraxial optics and Fresnel-Kirchhoff approximation, and the dependence of the diffracted beam pattern of the incident beam polarization is predicted. If the incident beam is circularly polarized, the trajectory of the diffracted beam centre of gravity experiences a small angular deviation from the geometrically expected direction. The deviation is parallel to the screen edge and reverses the sign with the polarization handedness; it is explicitly calculated for the case of a Gaussian incident beam with plane wavefront. This effect is a manifestation of the spin-orbit interaction of light and can be interpreted as a revelation of the internal spin energy flow immanent in circularly polarized beams. It also exposes the vortex character of the weak longitudinal field component associated with the circularly polarized incident beam.

Edge diffraction of optical-vortex beams formed by means of the fork hologram

We present the experimental and numerical study of the transverse profile for a beam obtained by the screen-edge diffraction of optical-vortex (OV) Kummer beams with topological charges 1, 2 and 3, generated with the help of a “fork” hologram. The main results concern the behavior of the secondary OVs formed in the diffracted beam due to splitting of the incident multicharged OV into a set of single-charged ones. When the screen edge moves across the incident beam, OVs in every cross section of the diffracted beam describe complicated spiral-like trajectories, which distinctly manifests the screw-like nature and the energy circulation in the OV beam. At certain conditions, positions of the separate OVs as well as their mutual configuration (singular skeleton of the diffracted beam) shows high sensitivity to the screen edge dislocation with respect to the incident beam axis. This can be used for remote measurements of small displacements and deformations.

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

Abstract Edge diffraction of a circular optical vortex (OV) beam transforms its singular structure: a multicharged axial OV splits into a 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 change. The trajectories are not always continuous and 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 charges 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 diffraction geometry. Conditions for the OV trajectory discontinuities and mechanisms of their realization are discussed. 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.