Premium
On the quantum physical relation between photon tunnelling and near‐field optics
Author(s) -
Keller O.
Publication year - 2001
Publication title -
journal of microscopy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.569
H-Index - 111
eISSN - 1365-2818
pISSN - 0022-2720
DOI - 10.1046/j.1365-2818.2001.00808.x
Subject(s) - physics , photon , quantum tunnelling , quantum mechanics , field (mathematics) , mesoscopic physics , matter wave , electromagnetic field , schrödinger equation , classical mechanics , quantum electrodynamics , quantum , mathematics , pure mathematics
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.