Spin and orbital Hall effects for diffracting optical beams in gradient-index media

TL;DR

This paper investigates how paraxial optical beams with spin and orbital angular momentum evolve in gradient-index media, revealing spin and orbital Hall effects that cause transverse beam shifts and deformations.

Contribution

It derives a parabolic equation describing beam diffraction in gradient-index media and analyzes the distinct spin and orbital Hall effects on beam propagation.

Findings

Spin Hall effect causes transverse translation of the beam.

Orbital Hall effect influences intrinsic orbital angular momentum.

Diffraction affects orbital Hall effect and beam shape.

Abstract

We examine the evolution of paraxial beams carrying intrinsic spin and orbital angular momenta (AM) in gradient-index media. A parabolic-type equation is derived which describes the beam diffraction in curvilinear coordinates accompanying the central ray. The center of gravity of the beam experiences transverse AM-dependent deflections -- the spin and orbital Hall effects. The spin Hall effect generates a transverse translation of the beam as a whole, in precise agreement with recent geometrical optics predictions. At the same time, the orbital Hall effect is significantly affected by the diffraction in the inhomogeneous medium and is accompanied by changes in the intrinsic orbital AM and deformations of the beam.