Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium

We review the geometrical-optics evolution of an electromagnetic wave propagating along a curved ray trajectory in a gradient-index dielectric medium. A Coriolis-type term appears in Maxwell equations under transition to the rotating coordinate system accompanying the ray. This term describes the spin-orbit coupling of light which consists of (i) the Berry phase responsible for a trajectory-dependent polarization variations and (ii) the spin Hall effect representing polarization-dependent trajectory perturbations. These mutual phenomena are described within universal geometrical structures underlying the problem and are explained by the dynamics of the intrinsic angular momentum carried by the wave. Such close geometro-dynamical interrelations illuminate a dual physical nature of the phenomena.Comment: 25 pages, 4 figures, review to appear in special issue of J. Opt. A: Pure Appl. Op

Goos-H\"anchen and Imbert-Fedorov beam shifts: An overview

We consider reflection and transmission of polarized paraxial light beams at a plane dielectric interface. The field transformations taking into account a finite beam width are described based on the plane-wave representation and geometric rotations. Using geometrical-optics coordinate frames accompanying the beams, we construct an effective Jones matrix characterizing spatial-dispersion properties of the interface. This results in a unified self-consistent description of the Goos-H\"anchen and Imbert-Fedorov shifts (the latter being also known as spin-Hall effect of light). Our description reveals intimate relation of the transverse Imbert-Fedorov shift to the geometric phases between constituent waves in the beam spectrum and to the angular momentum conservation for the whole beam. Both spatial and angular shifts are considered as well as their analogues for the higher-order vortex beams carrying intrinsic orbital angular momentum. We also give a brief overview of various extensions and generalizations of the basic beam-shift phenomena and related effects.Comment: 24 pages, 6 figure, to appear in J. Opt. (special issue "Beam shifts"

Spin and orbital angular momenta of acoustic beams

We analyze spin and orbital angular momenta in monochromatic acoustic wave fields in a homogeneous medium. Despite being purely longitudinal (curl-free), inhomogeneous acoustic waves generically possess nonzero spin angular momentum density caused by the local rotation of the vector velocity field. We show that the integral spin of a localized acoustic wave vanishes in agreement with the spin-0 nature of longitudinal phonons. We also show that the helicity or chirality density vanishes identically in acoustic fields. As an example, we consider nonparaxial acoustic Bessel beams carrying well-defined integer orbital angular momentum, as well as nonzero local spin density, with both transverse and longitudinal components. We describe the nontrivial polarization structure in acoustic Bessel beams and indicate a number of observable phenomena, such as nonzero energy density and purely-circular transverse polarization in the center of the first-order vortex beams.Comment: 15 pages, 3 figures, 1 table, to appear in Phys. Rev.

Photon centroids and their subluminal propagation

We examine properties and propagation of the energy-density and photon-probability centroids of electromagnetic wavepackets in free space. In the second-order paraxial approximation, both of these centroids propagate with the same subluminal velocity because of the transverse confinement of the wavepacket and its diffraction. The tiny difference between the energy and probability centroid velocities appears only in the forth order. We consider three types of wavepackets: Gaussian, Bessel, and non-diffracting Bessel. In all these cases, the subluminal propagation is clearly visible in the intensity distributions and can be measured experimentally in both classical-light and single-photon regimes. For Gaussian wavepackets, the half-wavelength delay is accumulated after propagation over about 12 Rayleigh lengths.Comment: 10 pages, 3 figure

The Enigma of Orbital Angular Momentum of Spatiotemporal Vortex Pulses

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.Comment: 6 pages, 2 figure

Classical Field Approach to Quantum Weak Measurements

By generalizing the quantum weak measurement protocol to the case of quantum fields, we show that weak measurements probe an effective classical background field that describes the average field configuration in the spacetime region between pre- and post-selection boundary conditions. The classical field is itself a weak value of the corresponding quantum field operator and satisfies equations of motion that extremize an effective action. Weak measurements perturb this effective action, producing measurable changes to the classical field dynamics. As such, weakly measured effects always correspond to an effective classical field. This general result explains why these effects appear to be robust for pre- and post-selected ensembles, and why they can also be measured using classical field techniques that are not weak for individual excitations of the field.Comment: 6 pages, 2 figures, published versio

Transverse spin and momentum in two-wave interference

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.Comment: 13 pages, 4 figures, Supplementary Information, to appear in Phys. Rev.