Abstract
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.
Highlights
An elementary similarity between ray and wave theories of light is the law of specular reflection: ‘the angle of incidence equals the angle of reflection’
We have presented here a self-contained approach to optical beam shift phenomena which resulted in a simple linear algebra of 2 × 2 matrices, in which the connection between optical beams shifts and weak values is readily established
On choosing three mutually incompatible bases for the incident and analyser polarization, we have been able to study the shifts of the centre of mass and the separate polarization components algebraically in a systematic manner, which resulted in table 1
Summary
An elementary similarity between ray and wave theories of light is the law of specular reflection: ‘the angle of incidence equals the angle of reflection’. We compare the total and component shifts for three naturally incompatible bases of polarizations for the incident and reflected beam in section 4: the + basis given by the transverse electric and magnetic polarizations (i.e. the eigenpolarizations of a plane wave on the beam axis), the basis of circular polarizations and the × basis of linear polarizations diagonal to the + basis This choice of three bases (represented by three orthogonal directions on the Poincaresphere [18]) is clearly special, since each polarization is made up of equal weightings of each vector in the other two bases: for each one of these polarization states, a polarization measurement in a different basis cannot discriminate between this vector and its orthogonal partner. Readers uninterested in these derivations, but interested in their consequences, may skip to section 4
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