Generalized shifts and weak values for polarization components of reflected light beams

The simple reflection of a light beam of finite transverse extent from a homogeneous interface gives rise to a surprisingly large number of subtle shifts and deflections which can be seen as diffractive corrections to the laws of geometrical optics (Goos–Hänchen shifts) and manifestations of optical spin–orbit coupling (Imbert–Fedorov shifts), related to the spin Hall effect of light. We develop a unified linear algebra approach to dielectric reflection which allows for a simple calculation of all these effects and lends itself to an interpretation of beam shifts as weak values in a classical analogue to a quantum weak measurement. We present a systematic study of the shifts for the whole beam and its polarization components, finding symmetries between input and output polarizations and predicting the existence of material independent shifts.