Photon Berry’s phase as a classical topological effect

Abstract

We discuss Berry’s phase rotation for electromagnetic radiation propagating in an optical fiber as a classical effect. We show that the evolution of the polarization vector is determined by a connection on the tangent bundle of the two-dimensional sphere. We use a topological argument to show that there exists only one rotationally invariant connection on the tangent bundle of the two sphere. The arguments apply to any classical transverse wave: for example, transverse vibrations propagating in a bent solid rod. The analogous effect in quantum electrodynamics, namely, Berry’s phase for a single photon propagating in an optical fiber, is a simple consequence of the classical effect described. We argue that this should be viewed as a classical, rather than a quantum, effect. We also comment on recent related work of Haldane and of Berry.