Gravitational spin Hall effect of light

Abstract

The propagation of electromagnetic waves in vacuum is often described within the geometrical optics approximation, which predicts that wave rays follow null geodesics. However, this model is valid only in the limit of infinitely high frequencies. At large but finite frequencies, diffraction can still be negligible, but the ray dynamics becomes affected by the evolution of the wave polarization. Hence, rays can deviate from null geodesics, which is known as the gravitational spin Hall effect of light. In the literature, this effect has been calculated ad hoc for a number for special cases, but no general description has been proposed. Here, we present a covariant WKB analysis from first principles for the propagation of light in arbitrary curved spacetimes. We obtain polarization-dependent ray equations describing the gravitational spin Hall effect of light. We also present numerical examples of polarization-dependent ray dynamics in the Schwarzschild spacetime, and the magnitude of the effect is briefly discussed. The analysis presented here is analogous to the spin Hall effect of light in inhomogeneous media, which has been experimentally verified.

Maxwell equations in a curved spacetime: Spin optics approximation

“…Recently this problem was solved. This remarkable breakthrough was achieved in paper [44]. In the present paper we present a slightly different approach to this problem.…”

“…In other words, if one found a self-dual solution of the form (43), then by taking a complex conjugation of Z in this solution one gets an anti-self-dual solution. Relations ( 43)- (44) imply that this operation is equivalent to change a ↔ ā and ω → −ω in relations ( 43)- (44). In particular, this means that when one uses the high-frequency expansion of the field equations, only the terms of the odd power in ω are sensitive to the state of polarization of the field.…”

“…Using expressions (44) for B µν and C µν , the Lorentz condition (41) and keeping the terms up to the order 1/ω one obtains…”

Gravitational Faraday and Spin-Hall Effects of Light

“…To compute the expression (46) we need the covariant form of the vorticity vector (see (25) and the text below),…”

“…A semiclassical approach to describe photon dynamics in a curved spacetime background based on the Bargmann-Wigner equations was taken in [45], and helicity-dependent photon's evolution was predicted for the Schwarzschild space-time. Spin-Hall effect of light for the Schwarzschild spacetime was also predicted in [46]. However, in these works the proper orientation and propagation of the basis representing optic axes is not discussed.…”