Quantum-mechanical linear-response theory is used to calculate the diffraction of light from a small hole in a thin flat screen. The field-induced dynamics of the charged particles (electrons) is obtained by modeling a screen without a hole as a two-level quantum well, with jellium behavior for the in-plane electron motion. Local-field corrections are calculated in a self-field approximation to a coupled-antenna theory. Particular attention is devoted to frequency resonance effects in the local field. A generalization to a screen with a hole is suggested, replicating the homogeneous jellium surface electron density by a space varying density in the vicinity of the hole. Quantum-mechanical expressions for the electric dipole moment $\mathbf{p}\left(\omega \right)$, the magnetic dipole moment $\mathbf{m}\left(\omega \right)$, and the electric quadrupole moment $\mathbf{Q}\left(\omega \right)$ of the so-called aperture current density are derived and the light scattering from these moments is studied. From the general theory results for $\mathbf{p}\left(\omega \right)$, $\mathbf{m}\left(\omega \right)$, and $\mathbf{Q}\left(\omega \right)$ in three cases are given: (i) no induced electron motion perpendicular to the plane of the screen [leading to $\mathbf{p}\left(\omega \right)=\mathit{0}]$, (ii) resonance excitation of the electron system, and (iii) a circular hole. This paper presents an extension of the quantum-mechanical diffraction theory developed in two recent papers of ours [J. Jung and O. Keller, Phys. Rev. A 90, 043830 (2014); Phys. Rev. A 92, 012122 (2015)].

• Received 25 July 2018
• Revised 20 October 2018

DOI:https://doi.org/10.1103/PhysRevA.98.053825