Geometric phases of light: insights from fibre bundle theory

TL;DR

This paper reviews how fibre bundle theory explains the origin of geometric phases of light and explores their implications for advanced photonics and quantum communication technologies.

Contribution

It provides a comprehensive overview of fibre bundle theory's role in understanding geometric phases of light and their applications in high-dimensional state spaces.

Findings

Fibre bundle theory clarifies the origin of geometric phases in light.

Geometric phases have implications for topological photonics.

The theory supports advancements in quantum communications.

Abstract

Geometric phases are ubiquitous in physics; they act as memories of the transformation of a physical system. In optics, the most prominent examples are the Pancharatnam-Berry phase and the spin-redirection phase. Recent technological advances in phase and polarization structuring have led to the discovery of additional geometric phases of light. The underlying mechanism for all of these is provided by fibre bundle theory. In this colloquium, we review how fibre bundle theory does not only shed light on the origin of geometric phases of light, but also lays the foundations for the exploration of high dimensional state spaces, with implications for topological photonics and quantum communications.