Correcting ray optics at curved dielectric microresonator interfaces: phase-space unification of Fresnel filtering and the Goos-Hänchen shift

We develop an amended ray-optics description for reflection at the curved dielectric interfaces of optical microresonators which improves the agreement with wave optics by about one order of magnitude. The corrections are separated into two contributions of similar magnitude, corresponding to ray displacement in independent quantum-phase-space directions, which can be identified with Fresnel filtering and the Goos-Hänchen shift, respectively. Hence we unify two effects which only have been studied separately in the past.