Reflections on reflected light: Classical weak measurement and singularimetry

When light beams of finite width are reflected by a mirror or dielectric surface, the reflected beam is displaced from the incident beam, and its direction is not quite equal to the angle of incidence. These effects, known as 'optical beam shifts' (including the Goos-Hänchen effect, Imbert-Fedorov effect, optical spin-Hall effect, ...) can be understood by an analogy between the finite-width light beam, and a time-evolving quantum wavepacket, for which beam shifts are precisely a classical waves analogy with quantum weak measurements introduced by Aharonov and others in the 1980s. This analogy gives insight into the meaning and interpretation of measurements in quantum mechanics.

When the light beams are structured before reflection, such as including optical singularities (vortices) on-axis (as Laguerre-Gaussian modes), the shape of the reflected light beam is also distorted, in a way that can be exactly understood using simple properties of complex functions. For incident optical vortex beams, the resulting constellation of vortices provides deep singularimetric information about the physics of reflection, which can be generalized to arbitrary weak optical scattering.