On the quantum physical relation between photon tunnelling and near-field optics.

Abstract

The standard theory of optical tunnelling based on a mathematical analogy between the time-independent one-particle Schrödinger equation describing electron tunnelling and the Helmholtz equation for the macroscopic electric field is criticized. In a classical perspective photons are related to the dynamics of the transverse part of the electromagnetic field, and with the assumption that the electrons in a coupled photon-atom system are driven in a linear fashion by the field, a rigorous integro-differential equation for the transverse field is established. In the near-field zone of matter a transverse self-field exists and this may cause the appearance of superluminality in optical tunnelling. In the wake of a brief review of the space-time dynamics of free photons, a first-quantized description of the birth process of a single polychromatic photon in the near-field region of an active atom (molecule, mesoscopic particle) is presented, and afterwards the link between photon localizability, Einstein causality and near-field photon tunnelling is discussed. On the basis of a new one-photon quantum theory of near-field scattering from a microscopic (or mesoscopic) object, it is shown that photon tunnelling always appears in photon-atom scattering. A first-order Born approximation cannot capture the phenomenon, however. The emergence of the energy wave function of the scattered photon is followed in space and time.