Insights into the behavior of certain optical systems gleaned from Feynman's approach to quantum electrodynamics

TL;DR

This paper explores how Feynman's path integral approach can be applied to various optical systems, revealing insights and discrepancies with classical optics, and enhancing understanding of quantum optical phenomena.

Contribution

It demonstrates the application of Feynman's method to practical optical systems, highlighting its advantages and limitations compared to classical theories.

Findings

Agreement with classical optics in some cases

Discrepancies revealing quantum effects

Insights into two-photon interference phenomena

Abstract

Richard Feynman's method of path integrals is based on the fundamental assumption that a system starting at a point A and arriving at a point B takes all possible paths from A to B, with each path contributing its own (complex) probability amplitude. The sum of the amplitudes over all these paths then yields the overall probability amplitude that the system starting at A would end up at B. We apply Feynman's method to several optical systems of practical interest and discuss the nuances of the method as well as instances where the predicted outcomes agree or disagree with those of classical optical theory. Examples include the properties of beam-splitters, passage of single photons through Mach-Zehnder and Sagnac interferometers, electric and magnetic dipole scattering, reciprocity, time-reversal symmetry, the optical theorem, the Ewald-Oseen extinction theorem, far field diffraction, and the two-photon interference phenomenon known as the Hong-Ou-Mandel effect.