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

Abstract

Richard Feynman’s method of path integrals is based on the fundamental assumption that a system starting at a point 𝐴𝐴 and arriving at a point 𝐵𝐵 takes all possible paths from 𝐴𝐴 to 𝐵𝐵, 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 𝐴𝐴 would end up at 𝐵𝐵. 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.