Evolution of geometric phase and explaining the geodesic rule

We use the recently developed wave model of geometric phase to track the continuous evolution of geometric phase as a wave propagates through optical elements and throughout an optical system. By working directly with the wave properties, we encounter a natural explanation of why the conventional Poincaré sphere solid angle method must use geodesic paths rather than the physical paths of the polarization state-the "geodesic rule"-and show that the existing rules for the solid angle algorithm are incomplete. Finally, we use the physical model to clarify the differences between the Pancharatnam connection and the geometric phase of a wave.