Generalized algorithm for the unified analysis and simultaneous evaluation of geometrical spin-redirection phase and Pancharatnam phase in a complex interferometric system

To permit unified analysis and simultaneous evaluation of geometrical spin-redirection phase and Pancharatnam phase, the conventional 2 x 2 Jones matrix calculation is generalized and a new scheme of 3 x 3 matrix calculation is proposed. With the proposed algorithm one can trace the polarization state changes and the geometric phase shifts caused by beam propagation along an arbitrary optical path that involves both reflection and refraction at surfaces with Fresnel shift and birefringence.