Levy behaviour in photon tunneling through metallic thin films

摘要

In a seminal paper devoted to rare events in quantum tunneling, F.Bardou has demonstrated that small fluctuations of potential barrier width can generate very large fluctuations of quantum electron tunneling transmission. Although for low transmission, the distribution is given by a lognormal distribution which belongs to the domain of attraction of Gauss distributions for N tending to infinity, for intermediate values of N, the heavy tail characteristics of the distribution of tunneling channels can lead to effects connected with Levy flights, i.e., that tunneling may be dominated by the very few most probable tunneling paths. This property has been observed in metal-oxide layer junctions. In this paper we consider the transmission of an optical wave-packet through a metallic slab. For normal incidence and for frequencies lower than the plasmon frequency, evanescent waves are created in the metal. In the case of a Drude model, tunneling in the optical and infra-red region is formally equivalent to electron quantum tunneling. We study the conditions under which effects similar to those appearing in quantum tunneling could be also observed in photon tunneling.