PancharatnamBerry

PancharatnamBerry, commonly known as the Pancharatnam-Berry phase, refers to a geometric phase acquired by polarized light as its polarization state evolves. The concept combines S. Pancharatnam’s foundational work on the relative phase between polarization states (1956) with Michael Berry’s identification of a geometric phase in cyclic quantum evolution (1984). The term is often used to describe the geometric phase arising specifically from changes in polarization states on the Poincaré sphere.

Physical principle: When a beam’s polarization traces a path on the Poincaré sphere, the optical field can acquire a phase that depends only on the geometry of that path, not on the dynamical properties or optical path length. For a closed loop, the PancharatnamBerry phase γ is typically given by γ = -Ω/2, where Ω is the solid angle subtended by the loop on the Poincaré sphere. This phase is intrinsic to the polarization evolution and can arise even in the absence of conventional dynamical phase accumulation.

Realization and implementation: The geometric phase can be imparted by devices that rotate or vary the polarization state across a beam cross-section. Examples include spatially varying retarders, rotated waveplates, and birefringent metasurfaces such as q-plates or patterned half-wave plates. By engineering the spatial variation of birefringence, these elements produce a spatially dependent geometric phase that reshapes the beam’s wavefront or polarization structure without relying on path-length differences.

Applications: PancharatnamBerry phases are exploited for beam shaping, generation of vortex and other structured beams, spin-orbit light control, interferometric techniques, and compact polarization-based optical elements. The approach is valued for its robustness to certain wavelength changes and its ability to couple spin and orbital degrees of freedom in photonic systems.