The Adiabatic Phase and Pancharatnam's Phase for Polarized Light

TLDR: In this article, the existence of the phase is attributed to the non-transitivity of Pancharatnam's connection between different states of polarization, and the precise relation is established using the algebra of spinors and 2 × 2 Hermitian matrices.

Abstract: In 1955 Pancharatnam showed that a cyclic change in the state of polarization of light is accompanied by a phase shift determined by the geometry of the cycle as represented on the Poincare sphere. The phase owes its existence to the non-transitivity of Pancharatnam's connection between different states of polarization. Using the algebra of spinors and 2 × 2 Hermitian matrices, the precise relation is established between Pancharatnam's phase and the recently discovered phase change for slowly cycled quantum systems. The polarization phase is an optical analogue of the Aharonov-Bohm effect. For slow changes of polarization, the connection leading to the phase is derived from Maxwell's equations for a twisted dielectric. Pancharatnam's phase is contrasted with the phase change of circularly polarized light whose direction is cycled (e.g. when guided in a coiled optical fibre).