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 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.

42 pages, 18 figures, 3 appendices, 30 references

References in corpus (7)

• Spin and Orbital Angular Momenta of Electromagnetic Waves in Free Space
• New Perspective on the Reciprocity Theorem of Classical Electrodynamics
• Fundamental properties of beam-splitters in classical and quantum optics
• New Perspective on the Optical Theorem of Classical Electrodynamics
• Ubiquity of Fourier Transformation in Optical Sciences
• Electromagnetic radiation and the self field of a spherical dipole oscillator
• Energy, linear momentum, and spin and orbital angular momenta of circularly polarized Laguerre-Gaussian wave-packets

Cited by in corpus (3)

• Linear and angular momenta of photons in the context of "which path" experiments of quantum mechanics
• On the quantum theory of light interacting with nano-materials
• Does one still need to "shut up and calculate"?