Feynman photon path integral calculations of optical reflection, diffraction, and scattering from conduction electrons

This paper describes the use of Feynman photon path integrals to compute the probability of detecting reflected, diffracted, and scattered photons at different points in space after interacting with conduction electrons. Five examples are given: (1) a thin parabolic sheet of conduction electrons (e.g. a metal mirror) that produces a sharp focus of a distant point source surrounded by the Airy diffraction pattern, (2) the loss of focusing power as the thickness of the parabolic sheet is increased and complete destructive interference for thicknesses that are an integer multiple of 1/2 the wavelength, (3) diffraction of photons entering a thin sheet from the side, (4) diffraction of photons entering the side of a sheet as its thickness is increased, and (5) the angular scattering distribution of internally generated photons in an extended volume of conduction electrons. The calculations integrated the complex probability amplitudes for photon paths from (a) a point source to (b) all points in the conduction electron volume and to (c) a point detector. At each detector position the detection probability was computed as the square of the absolute value of the integral. In general, if there is a concentration of paths that have nearly the same complex amplitude phase, reflection dominates. Otherwise, if the conduction electron volume has sharp boundaries, diffraction dominates. Isotropic scattering dominates for conduction electrons distributed throughout an extended volume, and may explain how scintillation photons in cryogenic n-type GaAs can escape total internal reflection trapping, which is essential for its high luminosity.