Angular momentum redirection phase of vector beams in a non-planar geometry

Abstract

An electric field propagating along a non-planar path can acquire geometric phases. Previously, geometric phases have been linked to spin redirection and independently to spatial mode transformation, resulting in the rotation of polarisation and intensity profiles, respectively. We investigate the non-planar propagation of scalar and vector light fields and demonstrate that polarisation and intensity profiles rotate by the same angle. The geometric phase acquired is proportional to j = +σ, where is the topological charge and σ is the helicity. Radial and azimuthally polarised beams with j = 0 are eigenmodes of the system and are not affected by the geometric path. The effects considered here are relevant for systems relying on photonic spin Hall effects, polarisation and vector microscopy, as well as topological optics in communication systems.

Geometric phases of light: insights from fibre bundle theory

“…Interestingly, when a path is formed on a sphere on which all modes carry the same amount of orbital angular momentum, like the second sphere of second order modes, no geometric phase is generated [15]. This would indicate that geometric phases are mediated by a variation of orbital angular momentum, in the same way as polarization transformations that generate a PB phase involve variation of the spin angular momentum [13,72,73]. While the sphere-based representation is useful as it directly relates to transformations that are easily realisable in the laboratory, it is not suitable to describe generic transformations in the state space of higher order modes.…”