Position measurement and the Huygens-Fresnel principle: A quantum model of Fraunhofer diffraction for polarized pure states

TL;DR

This paper introduces a quantum model for Fraunhofer diffraction that treats the diaphragm as a measurement device for particle positions, predicting effects on polarization and intensity distribution.

Contribution

It presents a novel quantum approach to diffraction, modeling the diaphragm as a measurement process and incorporating polarization effects and wavefront interactions.

Findings

Wavelet emission from multiple wavefronts causes intensity damping.

An angular factor explains intensity decrease at large diffraction angles.

Polarization states are modified, with possible rotation of ellipse axes.

Abstract

In most theories of diffraction by a diaphragm, the amplitude of the diffracted wave, and hence the position wave function of the associated particle, is calculated directly without prior calculation of the quantum state. Few models express the state of the particle to then deduce the position and momentum wave functions related to the diffracted wave. We present a model of this type for Fraunhofer diffraction. The diaphragm is assumed to be a device for measuring the three spatial coordinates of the particles passing through the aperture. A matrix similar to the S-matrix of the scattering theory describes the process which turns out to be more complex than a simple position measurement. Some predictions can be tested. The wavelets emission involved in the Huygens-Fresnel principle occurs from several neighboring wavefronts instead of just one, causing typical damping of the diffracted wave intensity. An angular factor plausibly accounts for the decrease in intensity at large diffraction angles, unlike the obliquity factors of the wave optics theories. The position measurement modifies the polarization states and for an incident photon in an elliptically polarized pure state, the ellipse axes can undergo a rotation which depends on the diffraction angles.