Understanding interference experiments with polarized light through photon trajectories

TL;DR

This paper uses a photon trajectory framework based on a hydrodynamical formulation of electromagnetism to analyze Young-type diffraction experiments with polarized light, providing visual insights into interference effects and the Arago-Fresnel laws.

Contribution

It introduces a trajectory-based approach to visualize electromagnetic energy flow in polarized light interference, extending Bohmian mechanics concepts to photon behavior in diffraction.

Findings

Photon trajectories reveal energy flow behind slits.

Polarizer polarization affects electromagnetic energy flow.

Trajectory analysis reproduces Arago-Fresnel interference laws.

Abstract

Bohmian mechanics allows to visualize and understand the quantum-mechanical behavior of massive particles in terms of trajectories. As shown by Bialynicki-Birula, Electromagnetism also admits a hydrodynamical formulation when the existence of a wave function for photons (properly defined) is assumed. This formulation thus provides an alternative interpretation of optical phenomena in terms of photon trajectories, whose flow yields a pictorial view of the evolution of the electromagnetic energy density in configuration space. This trajectory-based theoretical framework is considered here to study and analyze the outcome from Young-type diffraction experiments within the context of the Arago-Fresnel laws. More specifically, photon trajectories in the region behind the two slits are obtained in the case where the slits are illuminated by a polarized monochromatic plane wave. Expressions to determine electromagnetic energy flow lines and photon trajectories within this scenario are provided, as well as a procedure to compute them in the particular case of gratings totally transparent inside the slits and completely absorbing outside them. As is shown, the electromagnetic energy flow lines obtained allow to monitor at each point of space the behavior of the electromagnetic energy flow and, therefore, to evaluate the effects caused on it by the presence (right behind each slit) of polarizers with the same or different polarization axes. This leads to a trajectory-based picture of the Arago-Fresnel laws for the interference of polarized light.