Geometric phase of rotations and 3D coordinate transformations

The wave superposition model of the geometric phase shows how the addition of waves creates a shift in the resulting wave position. While previous work focused on a basis of linearly polarized light waves and the Pancharatnam–Berry phase, we show how the spin-redirection phase (Rytov–Vladimirsky–Berry phase) can also be derived from the same approach of wave superposition, using rotating vectors to represent the superposing oscillations. The result is the first derivation of the spin-redirection phase using wave superposition. We illustrate this approach with two classic examples of the geometric phase of rotations in space: a system of three fold mirrors and the helically coiled fiber.