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Physical Review E

Tunneling in frustrated total internal reflection: A comparison of different approaches

Anedio Ranfagni, Paolo Moretti, Ilaria Cacciari, Maria Angela Vitali

Published Oct 31, 2007• 1 citation
Publisher

Abstract

Tunneling processes in frustrated total internal reflection are reexamined in order to compare the results already obtained from adopting a procedure based on a transition-element analysis with those recently reported on the basis of a statistical method applied to a Brownian-like motion. A close agreement between the two approaches can be established, at optical and microwave scales, when suitable values of the involved parameters are adopted.

DOI
10.1103/physreve.76.047601

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Tunneling processes in frustrated total internal reflection are reexamined in order to compare the results already obtained from adopting a procedure based on a transition-element analysis with those recently reported on the basis of a statistical method applied to a Brownian-like motion. A close agreement between the two approaches can be established, at optical and microwave scales, when suitable values of the involved parameters are adopted.
We demonstrate a direct relationship between tunneling delays in a one-dimensional potential barrier and the delays observed in frustrated total internal reflection. Expressions relating the group delays in these two cases have been formulated in the past [A. M. Steinberg and R. Y. Chiao, Phys. Rev. A 49, 3283 (1994)], but only for certain limits of the normalized particle energy E/V0E/{V}_{0}E/V0​. Here, we derive a single expression relating these two group delays that is valid for arbitrary particle energy by decomposing the group delay into dwell-time and self-interference components. This decomposition also explains why the predicted delay differs in the limiting cases observed by Steinberg and Chiao.
An alternative model for near-field propagation and optical tunneling is proposed following the lines of the path-integral method developed by Feynman, and in particular by using a transition-elements analysis. Such a model was able to account for the frequency dependency of delay-time results of an experiment involving microwave propagation in the near field using two horn antennas [A. Ranfagni et al., Phys. Rev. E 66, 036111 (2002)]. Furthermore, this approach is also capable of interpreting delay-time results as a function of the barrier width in a frustrated total internal reflection experiment performed at the microwave scale and in the optical region.