  The generation of non-Abelian geometric phases from a system of evanescently
coupled waveguides is extended towards the framework of nonorthogonal
coupled-mode theory. Here, we study an experimentally feasible tripod
arrangement of waveguides that contain dark states from which a nontrivial
U(2)-mixing can be obtained by means of an adiabatic parameter variation. We
investigate the influence of higher-order contributions beyond
nearest-neighbour coupling as well as self-coupling on the stability of a
U(3)-phase generated from an optical tetrapod setup. Our results indicate that,
despite the mode nonorthogonality, the symmetry of dark states protects the
geometric evolution of light from distortion.
