Berry’s Phases in Optics

Abstract

Berry’s discovery of a topological phase in quantum mechanics has led to a unified view of many seemingly disconnected topological phenomena in physics, both at the quantum and classical levels. In analogy with the wavefunction of an electron, the wavefunction of a photon can also acquire this topological phase. Here we review four recent optical manifestations of this Aharonov-Bohm-like phase. A distinction is made between classical and nonclassical Berry’s phases in optics. One example of a nonclassical phase is the one associated with a cycle of Von Neumann projections. Other nonclassical phases will be discussed. A group-theoretical analysis of classical Berry’s phases for Maxwell’s equations expressed as a Schrodinger-like equation for a six-component spinor is introduced.