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

TL;DR

This paper develops a unified linear algebra framework to analyze polarization-dependent shifts in reflected light beams, interpreting them as weak values and revealing symmetries and material-independent effects.

Contribution

It introduces a systematic, unified approach to calculate and interpret beam shifts and polarization effects in reflection, linking classical optics with weak measurement theory.

Findings

Identifies symmetries between input and output polarizations.

Predicts the existence of material-independent shifts.

Provides a simple calculation method for all polarization-related shifts.

Abstract

The simple reflection of a light beam of finite transverse extent from a homogenous 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-H\"anchen 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 of 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.