Pancharatnam–Berry phase

Summary

The Pancharatnam–Berry phase is a phase that light acquires when its polarization is taken around a closed loop of states. It depends only on the loop on the Poincaré sphere, not on how fast the loop is traversed. Up to sign, it equals half the solid angle enclosed by the loop. Pancharatnam found it for polarized light in 1956, and Berry described geometric phases in general quantum systems in 1984. It is the optical case of holonomy and is used to build flat optical elements with a geometric phase.