Abstract
We study the classical optics effects known as Goos–Hänchen and Imbert–Fedorov shifts, occurring when reflecting a bounded light beam from a planar surface, by using a quantum-mechanical formalism. This new approach allows us to naturally separate the spatial shift into two parts, one independent on orbital angular momentum (OAM) and the other one showing OAM-induced spatial-versus-angular shift mixing. In addition, within this quantum-mechanical-like formalism, it becomes apparent that the angular shift is proportional to the beams angular spread, namely to the variance of the transverse components of the wave vector. Moreover, we extend our treatment to the enhancement of beam shifts via weak measurements and relate our results to the recent experiments.
Highlights
Theoretical physics is all about describing nature in terms of mathematics
This new approach allows us to naturally separate the spatial shift into two parts, one independent on orbital angular momentum (OAM) and the other one showing OAM-induced spatial-vs-angular shift mixing. Within this quantum-mechanical-like formalism, it becomes apparent that the angular shift is proportional to the beams angular spread, namely to the variance of the transverse components of the wave vector
Following the idea of changing the perspective, in this work we propose a different treatment of beam shifts, by describing this purely classical phenomenon with the mathematical formalism of proper quantum mechanics (QM)
Summary
Theoretical physics is all about describing nature in terms of mathematics. often there is more than one way to do so. By exploiting the formal analogy between the paraxial wave equation and the two-dimensional Schrodinger equation [17] we can represent beam propagation as a “time” evolution generated by displacement operator quadratic in the “momentum” operator and, calculate both spatial and angular shifts by using a common formalism As it will be shown later, in this manner all beam shift phenomena will manifest a natural connection. There, the problem of the beam shifts is studied in terms of the quantum-mechanical formalism derived earlier, including a description of the enhancement of the beam shifts through weak measurements Figure 1. (color online) Visualization of the beam shifts occurring upon reflection of a bounded beam from a planar surface
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