Spin Hall effects and the localization of massless spinning particles
arXiv:2203.01753 · doi:10.1103/PhysRevD.105.104061
Abstract
The spin Hall effects of light represent a diverse class of polarization-dependent physical phenomena involving the dynamics of electromagnetic wave packets. In a medium with an inhomogeneous refractive index, wave packets can be effectively described by massless spinning particles following polarization-dependent trajectories. Similarly, in curved spacetime the gravitational spin Hall effect of light is represented by polarization-dependent deviations from null geodesics. In this paper, we analyze the equations of motion describing the gravitational spin Hall effect of light. We show that these equations are a special case of the Mathisson-Papapetrou equations for spinning objects in general relativity. This allows us to use several known results for the Mathisson-Papapetrou equations, and apply them to the study of electromagnetic wave packets. We derive conservation laws, we discuss the limits of validity of the spin Hall equations, and we study how the energy centroids of wave packets, effectively described as massless spinning particles, depend on the external choice of a timelike vector field, representing a family of observers. In flat spacetime, the relativistic Hall effect and the Wigner(-Souriau) translations are recovered, while our equations also provide a generalization of these effects in arbitrary spacetimes. We construct a large class of wave packets that can be described by the spin Hall equations, but also find its limits by giving examples of wave packets which are more general and are not described by the spin Hall equations. Lastly, we examine the assumption that electromagnetic wave packets are massless. While this is approximately true in many contexts, it is not exact. We show that failing to carefully account for the limitations of the massless approximation results in the appearance of unphysical centroids which are nowhere near the wave packet itself.
References in corpus (22)
- Calculating black hole shadows: Review of analytical studies
- Geometrodynamics of Spinning Light
- Role of beam propagation in Goos-Hänchen and Imbert-Fedorov shifts
- Divergence of an orbital-angular-momentum-carrying beam upon propagation
- Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium
- Geometrical Optics of Beams with Vortices: Berry Phase and Orbital Angular Momentum Hall Effect
- Frequency-dependent effects of gravitational lensing within plasma
- Gravitational Lensing in presence of Plasma: Strong Lens Systems, Black Hole Lensing and Shadow
- Modified geometrical optics of a smoothly inhomogeneous isotropic medium: the anisotropy, Berry phase, and the optical Magnus effect
- Gravitational lensing in a non-uniform plasma
- Geometrical Aspects in Optical Wavepacket Dynamics
- Berry Phase, Lorentz Covariance, and Anomalous Velocity for Dirac and Weyl Particles
- Chiral fermions as classical massless spinning particles
- Bobbing and Kicks in Electromagnetism and Gravity
- Propagation of polarized gravitational waves
- Wigner translations and the observer-dependence of the position of masslesss spinning particles
- Deflection of light rays by spherically symmetric black hole in dispersive medium
- Wigner-Souriau translations and Lorentz symmetry of chiral fermions
- Approximate spacetime symmetries and conservation laws
- Semiclassical Dynamics of Dirac particles interacting with a Static Gravitational Field
- Complete set of quasi-conserved quantities for spinning particles around Kerr
- On Conserved Quantities for the Free Motion of Particles with Spin