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

Amy Mcwilliam,Claire Marie Cisowski,Robert Bennett,Sonja Franke-Arnold

doi:10.1515/nanoph-2021-0528

Abstract

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 = ℓ + σ, where ℓ 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.

Highlights

Throughout history, mirrors have been used for the most sacred and profane purposes, as well as for a multitude of scientific and technological purposes
We investigate the non-planar propagation of scalar and vector light fields and demonstrate that polarisation and intensity profiles rotate by the same angle
It describes a phase modulation that, unlike the dynamic phase, is independent of the optical path length but results exclusively from the geometry of the optical trajectory [22]. Such geometric phases play a crucial role in the photonic spin Hall effect [23,24,25] and its scalar equivalent, the acoustic orbital angular momentum Hall effect [26], spin–orbit transformations in general, and the closely related rotational Doppler effect [27,28,29,30]

Summary

Introduction

Throughout history, mirrors have been used for the most sacred and profane purposes, as well as for a multitude of scientific and technological purposes. When taking light via multiple mirrors along a non-planar trajectory, these successive angular momentum redirections add up, and the propagation of the electric field may be modelled as parallel transport along the beam trajectory [2, 3], resulting in a rotation of both the polarisation and intensity profile. It describes a phase modulation that, unlike the dynamic phase, is independent of the optical path length but results exclusively from the geometry of the optical trajectory [22] Such geometric phases play a crucial role in the photonic spin Hall effect [23,24,25] and its scalar equivalent, the acoustic orbital angular momentum Hall effect [26], spin–orbit transformations in general, and the closely related rotational Doppler effect [27,28,29,30].

Experimental setup

Image rotation

Polarisation rotation

Rotation of vector beams

Conclusions