On optical tunneling in near-field diffraction of light from a small hole

Abstract

A quantitative theory describing optical tunneling effects related to near-field diffraction of light from a small hole in a flat screen is established. We show that in the absence of local-field corrections, optical tunneling (i.e., the possibility of detecting photons in front of the “light cone”) in near-field diffraction appears solely via the longitudinal Green tensor, GL, and the space-like part of the retarded transverse propagator, GTspace. It is demonstrated that GTspace in the space-time domain can be written as a product of an electrostatic point-dipole tensor and a time factor, which obeys microcausality and is nonvanishing only in front of a plane “light cone.” Special attention is devoted to an analysis of the tunneling of an electromagnetic pulse of finite duration through a small hole in a thin screen. In this particular case, the tunneling signal in the point of observation arises from a somewhat complicated interplay between the time interval in which the effective aperture current density is nonvanishing and the time it takes for the elementary trailing edges of the individual space-like wavelets to pass the observation point. To achieve a self-consistent description of the tunneling process, we propose to use a certain spatially nonlocal and linear constitutive equation. In this equation, which is an improved version of those used up to now in diffraction theory, only the transverse part of the electric field occurs because the induced longitudinal field is not a dynamical variable in electrodynamics. Finally, we suggest to measure the optical tunneling related to small hole diffraction via a modified frustrated total internal reflection tunneling experiment, and we indicate how it might be possible to extend the present theory to single-photon diffraction tunneling.