Photon wave-mechanical theory of single-photon diffraction from a mesoscopic hole

A quantum electrodynamical theory for single-photon diffraction of light from a mesoscopic hole in a quantum well (QW) screen with (Schrödinger) electron dynamics is established. Photon wave mechanics (PWM) is used to extend and bridge the gap between hitherto used semiclassical and quantum optical theoretical approaches for analyses of diffraction of light. An essentially complete calculation is carried out for a paradigm example: (i) a single-photon point-like electric-dipole (ED) primary source, emitting (ii) a wave packet photon toward (iii) a two-level QW screen possessing (iv) in-plane jellium electrodynamics with (v) a single mesoscopic ED hole. The PWM description is based on the, in this context attractive, Riemann-Silberstein-Oppenheimer-Bialynicki formulation. The effective size of the hole is determined on the basis of a quantum mechanical extinction theorem for the in-plane jellium electron dynamics in the vicinity of the hole. The incident electrodynamic field induced current density in the screen (with hole) allows one to obtain the single-photon probabilities for scattering from the hole and the screen. A one-photon wave train emitted by the primary ED point-like source is assumed to drive the scattering process. The far-field hole-screen diffraction pattern is calculated paying particular attention to the spectral diffraction (correlation) pattern, which illustrates the interplay between the wave-train frequency, the screen/hole local-field resonance frequency, and the Bohr frequency. Our theory shows that the ED hole polarizability is close to that of a one-dimensional single harmonic oscillator with resonance frequency coinciding with the local-field resonance in the two-level QW screen.