Interpreting the anholonomy of coiled light

Abstract

Circular birefringence of purely geometric origin was recently predicted¹ and observed² in helically coiled monomode optical fibres, and widely reported^3–5 as a successful application to photons of a general theory^6,7 for phase shifts in adiabatically transported quantum states. However, earlier similar observations^8–10 had been interpreted not by quantum mechanics but simply as a classical anholonomy, namely parallel transport of the polarization¹¹. Indeed, because the magnitude of the effect is independent of the wavelength of the light as well as Planck's constant, it might seem that 'classical' here means that not only quantum but also wave effects can be neglected. Here, I argue that these experiments, and their discrete analogues, are most appropriately described at the level of classical electromagnetism; the parallel transport law can then be derived (rather than assumed^8–11) and nonadiabatic polarization changes calculated.