Relation between spatial confinement of light and optical tunneling

Abstract

With the aim of obtaining a better insight in the optical tunneling process the near-field electrodynamics of a current-density (equivalently polarization) sheet is investigated, taking as a starting point the near-field optics of a single atom, and afterwards the tunneling field of a macroscopic medium is determined integrating over a distribution of sheets. The total electric field hitherto used to study tunneling times and effective tunneling velocities is divided into a nonretarded (matter attached) longitudinal part of standing-wave character, and a retarded (detached) transverse part propagating away from the matter-vacuum interface with the vacuum speed of light. For a current-density distribution phase shifted with a wave number ${q}_{\ensuremath{\Vert}}$ along the interface, the transverse part is nonzero in the vacuum and decays exponentially with a decay constant ${q}_{\ensuremath{\Vert}}^{\ensuremath{-}1}$ as a function of the distance from the interface. Since the source domain of photons is precisely the domain of the transverse current density, the optical tunneling process attains an important contribution associated with the lack of spatial localizability of a photon in the evanescent regime. It is shown that in an observationally equivalent electromagnetic propagator description of the space-time dynamics, where the source domain of the photons is identified with the domain of the total electron current density, the retarded transverse dynamics necessarily must include spacelike couplings in the evanescent regime. Since these are destroyed with the vacuum speed of light as the light-cone coupling moves away from the matter-vacuum interface, the Einstein causality is always obeyed. The link to previous studies of the optical tunneling process is established by investigating the transverse and longitudinal dynamics in the frequency domain. Finally, it is shown that surface currents may play an important role in the optical tunneling process, in particular in cases where the incident electromagnetic field generates divergence-free currents in the bulk of the source medium.