Geometric phases of light: insights from fibre bundle theory

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.

arXiv commentSubmitted to Reviews of Modern Physics

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Cited by in corpus (20)

• Geometric descriptions for the polarization for nonparaxial optical fields: a tutorial
• Toward arbitrary spin-orbit flat optics via structured geometric phase gratings
• Wave description of geometric phase
• Spin and Orbital Angular Momentum of Coherent Photons in a Waveguide
• Quantum Commutation Relationship for Photonic Orbital Angular Momentum
• Structured Light Modal Interface via Liquid-Crystal Planar Optics
• Topological Polarisation States
• Twisted charged particles in the uniform magnetic field with broken symmetry
• Experimental measurement of the geometric phase of non-geodesic circles
• Poincaré sphere engineering of dynamical ferroelectric topological solitons
• Dirac Equation for Photons: Origin of Polarisation
• Knife-Edge Diffraction of Scalar and Vector Vortex Light
• Dynamic and Geometric Shifts in Wave Scattering
• Macroscopic Singlet, Triplet, and Colour-Charged States of Coherent Photons
• Electric-Magnetic Geometric Phase
• Exploring Weak measurements within the Einstein-Dirac Cosmological framework
• Tensor-driven geometric phase in nonlinear AlGaAs metasurfaces
• Geometric and holonomic quantum computation
• Geometric representation of higher-order optical modes
• Proposal for an experiment to verify Wigner's rotation at non-relativistic speeds with massive spin-$1/2$ particles