arXiv subjects

K. Yu. Bliokh

Publications and source records attributed to K. Yu. Bliokh.

At least 19 recordsLinked to original sources

arXiv2007

Singular polarimetry: Evolution of polarization singularities in electromagnetic waves propagating through a weakly anisotropic medium

We describe the evolution of a paraxial electromagnetic wave characterizing by a non-uniform polarization distribution with singularities and propagating in a weakly anisotropic medium. Our approach is based on the Stokes vector evolution equation applied to a non-uniform initial polarization field. In the case of a homogeneous medium, this equation is integrated analytically. This yields a 3-dimensional distribution of the polarization parameters containing singularities, i.e. C-lines of circular polarization and L-surfaces of linear polarization. The general theory is applied to specific examples of the unfolding of a vectorial vortex in birefringent and dichroic media.

physics.optics↗

arXiv2007

Semiclassical Dynamics of Electron Wave Packet States with Phase Vortices

We consider semiclassical higher-order wave packet solutions of the Schrodinger equation with phase vortices. The vortex line is aligned with the propagation direction, and the wave packet carries a well-defined orbital angular momentum (OAM) $\hbar l$ ($l$ is the vortex strength) along its main linear momentum. The probability current coils around momentum in such OAM states of electrons. In an electric field, these states evolve like massless particles with spin $l$. The magnetic-monopole Berry curvature appears in momentum space, which results in a spin-orbit-type interaction and a Berry/Magnus transverse force acting on the wave packet. This brings about the OAM Hall effect. In a magnetic field, there is a Zeeman interaction, which, can lead to more complicated dynamics.

quant-ph↗

arXiv2007

Stokes-vector evolution in a weakly anisotropic inhomogeneous medium

Equation for evolution of the four-component Stokes vector in weakly anisotropic and smoothly inhomogeneous media is derived on the basis of quasi-isotropic approximation of the geometrical optics method, which provides consequent asymptotic solution of Maxwell equations. Our equation generalizes previous results, obtained for the normal propagation of electromagnetic waves in stratified media. It is valid for curvilinear rays with torsion and is capable to describe normal modes conversion in the inhomogeneous media. Remarkably, evolution of the Stokes vector is described by the Bargmann-Michel-Telegdi equation for relativistic spin precession, whereas the equation for the three-component Stokes vector resembles the Landau-Lifshitz equation for spin precession in ferromegnetic systems. General theory is applied for analysis of polarization evolution in a magnetized plasma. We also emphasize fundamental features of the non-Abelian polarization evolution in anisotropic inhomogeneous media and illustrate them by simple examples.

physics.optics↗

arXiv2007

On spin evolution in a time-dependent magnetic field: post-adiabatic corrections and geometric phases

We examine both quantum and classical versions of the problem of spin evolution in a slowly varying magnetic field. Main attention is given to the first- and second-order adiabatic corrections in the case of in-plane variations of the magnetic field. While the first-order correction relates to the adiabatic Berry phase and Coriolis-type lateral deflection of the spin, the second-order correction is shown to be responsible for the next-order geometric phase and in-plain deflection. A comparison between different approaches, including the exact (non-adiabatic) geometric phase, is presented.

quant-ph↗

arXiv2007

Non-Abelian evolution of electromagnetic waves in a weakly anisotropic inhomogeneous medium

A theory of electromagnetic wave propagation in a weakly anisotropic smoothly inhomogeneous medium is developed, based on the quantum-mechanical diagonalization procedure applied to Maxwell equations. The equations of motion for the translational (ray) and intrinsic (polarization) degrees of freedom are derived ab initio. The ray equations take into account the optical Magnus effect (spin Hall effect of photons) as well as trajectory variations owing to the medium anisotropy. Polarization evolution is described by the precession equation for the Stokes vector. In generic case, the evolution of waves turns out to be non-Abelian: it is accompanied by mutual conversion of the normal modes and periodic oscillations of the ray trajectories analogous to electron zitterbewegung. The general theory is applied to examples of wave evolution in media with circular and linear birefringence.

physics.optics↗

arXiv2007

Polarization, transverse shifts, and angular momentum conservation laws in partial reflection and refraction of an electromagnetic wave packet

We present a solution to the problem of partial reflection and refraction of a polarized paraxial Gaussian beam at the interface between two transparent media. The Fedorov--Imbert transverse shift of the centers of gravity of the reflected and refracted beams are calculated. Our results differ in general case from ones derived previously by other authors. In particular, they obey general conservation law for the beams' total angular momentum but do not obey one-particle conservation laws for individual photons, which have been proposed by Onoda et al. [Phys. Rev. Lett. 93, 083901 (2004)]. We ascertain that these circumstances relate to the accepted in the literature artificial model for the polarized beam which does not fit to real beams. The present paper resolves the recent controversy and confirms results of our previous paper [Bliokh et al., Phys. Rev. Lett. 96, 073903 (2006)]. Besides, a diffraction effect of angular transverse shift of the reflected and refracted beams is predicted.

physics.optics↗

arXiv2006

Diffraction of Gaussian beam in a 3D smoothly inhomogeneous media: eikonal-based complex geometrical optics approach

The paper presents an ab initio account of the paraxial complex geometrical optics (CGO) in application to a scalar Gaussian beam propagation and diffraction in a 3D smoothly inhomogeneous medium. The paraxial CGO deals with quadratic expansion of the complex eikonal and reduces the wave problem to the solution of ordinary differential equations of Riccati type. This substantially simplifies description of Gaussian beams diffraction as compared to full wave or parabolic (quasi-optics) equations. For a Gaussian beam propagating in a homogeneous medium or along the symmetry axis in a lens-like medium, the CGO equations possess analytical solutions, otherwise they can be readily solved numerically. As a non-trivial example we consider Gaussian beam propagation and diffraction along a helical ray in an axially symmetric waveguide medium. It is shown that the major axis of the beam's elliptical cross-section grows unboundedly; it is oriented predominantly in azimuthal (binormal) direction and does not obey the parallel transport law.

physics.optics↗

arXiv2006

Polarization Transport of Transverse Acoustic Waves: Berry Phase and Spin Hall Effect of Phonons

We carry out a detailed analysis of the short-wave (semiclassical) approximation for the linear equations of the elasticity in a smoothly inhomogeneous isotropic medium. It is shown that the polarization properties of the transverse waves are completely analogous to those of electromagnetic waves and can be considered as spin properties of optical phonons. In particular, the Hamiltonian of the transverse waves contains an additional term of the phonon spin-orbit interaction arising from the Berry gauge potential in the momentum space. This potential is diagonal in the basis of the circularly polarized waves and corresponds to the field of two `magnetic monopoles' of opposite signs for phonons of opposite helicities. This leads to the appearance of the Berry phase in the equation for the polarization evolution and an additional ``anomalous velocity'' term in the ray equations. The anomalous velocity has the form of the `Lorentz force' caused by the Berry gauge field in momentum space and gives rise to the transverse transport of waves of opposite helicities in opposite directions. This is a manifestation of the spin Hall effect of optical phonons. The effect directly relates to the conservation of total angular momentum of phonons and also influences reflection from a sharp boundary (acoustic analogue of the transverse Ferdorov--Imbert shift).

cond-mat.other↗

arXiv2006

Localized Modes in Open One-Dimensional Dissipative Random Systems

We consider, both theoretically and experimentally, the excitation and detection of the localized quasi-modes (resonances) in an open dissipative 1D random system. We show that even though the amplitude of transmission drops dramatically so that it cannot be observed in the presence of small losses, resonances are still clearly exhibited in reflection. Surprisingly, small losses essentially improve conditions for the detection of resonances in reflection as compared with the lossless case. An algorithm is proposed and tested to retrieve sample parameters and resonances characteristics inside the random system exclusively from reflection measurements.

cond-mat.dis-nn↗

arXiv2006

Geometrical Optics of Beams with Vortices: Berry Phase and Orbital Angular Momentum Hall Effect

We consider propagation of a paraxial beam carrying the spin angular momentum (polarization) and intrinsic orbital angular momentum (IOAM) in a smoothly inhomogeneous isotropic medium. It is shown that the presence of IOAM can dramatically enhance and rearrange the topological phenomena that previously were considered solely in connection to the polarization of transverse waves. In particular, the appearance of a new-type Berry phase that describes the parallel transport of the beam structure along a curved ray is predicted. We derive the ray equations demonstrating the splitting of beams with different values of IOAM. This is the orbital angular momentum Hall effect, which resembles Magnus effect for optical vortices. Unlike the recently discovered spin Hall effect of photons, it can be much larger in magnitude and is inherent to waves of any nature. Experimental means to detect the phenomena is discussed.

physics.optics↗

arXiv2005

Comment on "Spin Transverse Force on Spin Current in an Electric Field"

Comment on S.-Q. Shen, Phys. Rev. Lett. 95, 187203 (2005) [cond-mat/0506676]. We show that the equations of motion deduced by Shen are incorrect and derive semiclassical expression for the operator of force, which also contains a term of the transverse spin force but twice as large in magnitude.

cond-mat.mes-hall↗

arXiv2005

On the Hamiltonian nature of semiclassical equations of motion in the presence of an electromagnetic field and Berry curvature

We consider the semiclassical equations of motion of a particle when both an external electromagnetic field and the Berry gauge field in the momentum space are present. It is shown that these equations are Hamiltonian and relations between the canonical and covariant variables are determined through a consistent account of all components of the Berry connection. The Jacobian of the canonical-to-covariant-variables transformation describes the nonconservation of the 'naive' phase space volume in the covariant coordinates (D.Xiao, J.Shi, and Q.Niu, Phys. Rev. Lett. 95, 137204 (2005)).

cond-mat.other↗

arXiv2005

Topological spin transport of relativistic electron

We derive the semiclassical (with accuracy of $\hbar$) motion equation for relativistic electron, which follow from the Dirac equation. We determine both the evolution equation for electron polarization, which takes the non-Abelian Berry phase into account, and Hamiltonian equations for trajectories of the particle (wave packet) center in the phase space. The equations have covariant form with respect to U(2) gauge transformations and contain topological spin terms that are connected to the Berry gauge field arising during the diagonalization of the Dirac equation. The trajectory equations obtained are substantially different from the traditional ones (for instance, those that follow from the Pauli Hamiltonian) and correspond to contemporary ideas of topological spin transport of particles.

quant-ph↗

arXiv2005

Spin Gauge Fields: from Berry Phase to Topological Spin Transport and Hall Effects

The paper examines the emergence of gauge fields during the evolution of a particle with a spin that is described by a matrix Hamiltonian with n different eigenvalues. It is shown that by introducing a spin gauge field a particle with a spin can be described as a spin multiplet of scalar particles situated in a non-Abelian pure gauge (forceless) field U(n). As the result, one can create a theory of particle evolution that is gauge invariant with regards to the group U^n(1). Due to this, in the adiabatic (Abelian) approximation the spin gauge field is an analogue of n electromagnetic fields U(1) on the extended phase space of the particle. These fields are force ones, and the forces of their action enter the particle motion equations that are derived in the paper in the general form. The motion equations describe the topological spin transport, pumping and splitting. The Berry phase is represented in this theory analogously to the Dirac phase of a particle in an electromagnetic field. Due to the analogy with the electromagnetic field, the theory becomes natural in the four-dimensional form. Besides the general theory the article considers a number of important particular examples, both known and new.

quant-ph↗

arXiv2005

On Hamiltonian approach on 3+1-dimensional space-time

The paper proposes a 4-dimensional generalization of the Hamilton equations of motion to the case of the Minkowski space-time. The approach can be applied to quantum as well as to classical, non-relativistic as well as relativistic problems.

math-ph↗

arXiv2005

Topological spin transport of photons: "magnetic monopole" gauge field in Maxwell equations and polarization splitting of rays in periodically inhomogeneous media

Topological spin transport of electromagnetic waves (photons) in stationary smoothly inhomogeneous isotropic medium is studied. By diagonalizing photon kinetic energy in Maxwell equations we derive the non-Abelian pure gauge potential in the momentum space, which in adiabatic approximation for transverse waves takes the form of two Abelian U(1) potentials corresponding to magnetic monopole-type fields. These fields act on circularly polarized waves resulting in the topological spin transport of photons. We deduce general semiclassical (geometrical optics) ray equations that take into account a Lorentz-type force of the magnetic-monopole-like gauge field. Detailed analysis of rays in 3D medium with 2D periodic inhomogeneity is presented. It is shown that rays located initially in the inhomogeneity plane experience topological deflections or splitting that move them out from this plane. The dependence of the rays' deflection on the parameters of the medium and on the direction of propagation is studied.

cond-mat.other↗

arXiv2005

Weak antilocalization of ultrarelativistic fermions

The paper discusses the Berry phase influence on the weak localization phenomenon at the adiabatic backscattering of ultrarelativistic particles in a random medium. We demonstrate that bosons that pass along a certain closed path in opposite directions come back always in phase (an example: the backscattering enhancement of electromagnetic waves), whereas fermions come exactly in antiphase. This produces a "complete weak antilocalization" of ultrarelativistic fermions: the backscattering field intensity vanishes.

physics.optics↗

arXiv2005

Spin-orbit interaction of photons and fine splitting of levels in ring dielectric resonator

We consider eigenmodes of a ring resonator made of a circular dielectric waveguide. Taking into account the polarization corrections, which are responsible for the interaction of polarization and orbital properties of electromagnetic waves (spin-orbit interaction of photons), results in fine splitting of the levels of scalar approximation. The basic features of this fine structure of the levels are similar to that of electron levels in an atom. Namely: 1) sublevels of the fine structure are defined by an additional quantum number: product of helicity of the wave and its orbital moment; 2) for a waveguide with a parabolic profile of the refractive index each level of the scalar approximation splits into N sublevels (N is the principal quantum number), while for any other profile it splits into 2 sublevels; 3) each level of the fine structure remains twice degenerated due to local axial symmetry of the waveguide. Numerical estimations show that the described fine splitting of levels may be observed in optic-fiber ring resonators.

physics.optics↗