Microscopic theory of diffraction of light from a small hole

Abstract

On the basis of the Maxwell-Lorentz local-field equations and nonlocal linear response theory, a self-consistent microscopic Green function theory of diffraction of light from a single hole in a thin and plane metallic screen is established. By subtracting the scattering of identical incident fields from screens with and without a hole, a causal effective optical aperture response tensor is introduced. An approximate expression is derived for the aperture response tensor in the limit where the screen behaves like an electric-dipole absorber and radiator. In this limit the internal electron dynamics is that of a quantum well. For a screen so thin that its bound electron motion can be described by a single quantum level, a approach for a quantum mechanical calculation of the aperture response tensor is presented. When the linear dimensions of the hole become sufficiently small the so-called aperture field, defined as the difference between the prevailing electric field with and that without a hole, becomes identical to the field from an incident-field-induced electric dipole with anisotropic linear polarizability. Our theory is formulated in such a manner that preknowledge only of (i) the incident electromagnetic field and (ii) the light-unperturbed optical electron properties (the microscopic conductivity tensor) of the screen with the geometrically given hole is needed. Since the microscopic theory allows for the presence of an (oscillating) component of the sheet current density perpendicular to the plane of the screen, a generalization of (i) the standard jump conditions of the field across the sheet and (ii) the reflection symmetries of the various fields in the plane of the screen is worked out. As our theory deviates radically from the approach of all classical diffraction theories, which are based on the macroscopic Maxwell equations and some kind of pheno-menological expression for the screen conductivity $\ensuremath{\sigma}$ (often just $\ensuremath{\sigma}\ensuremath{\rightarrow}\ensuremath{\infty})$, we give a brief review of classical diffraction theory, formulated in such a manner that a comparison to the microscopic theory is made easier. In particular, the Bethe-Bouwkamp theory of classical diffraction from a small hole in an infinitely thin and perfectly conducting $(\ensuremath{\sigma}\ensuremath{\rightarrow}\ensuremath{\infty})$ screen is our focus. We suggest that experimental frequency and angular resolved studies of the interference of the diffracted fields from quantum wells with and without holes are undertaken to obtain detailed insight into the microscopic aperture response functions, not least in the optical near-field domain.