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.