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-Hanchen 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.