Abstract

The recent experimental results by Steinberg et al.¹ imply that a single-photon Gaussian wavepacket, which "tunnels" through a periodic dielectric structure can emerge from the structure as a nearly-undistorted Gaussian wavepacket centered at a much earlier time than its twin-photon wavepacket that has propagated the same distance through air. The peak-traversal velocity of the transmitted portion of the photon in this experiment corresponded to 1.7 c. The foregoing experimental result may be viewed as an indirect proof that massive particles tunneling through potential barriers should exhibit "superluminal" traversal times, by virtue of their analogy to evanescent EM waves in dielectric structures. Such apparent superluminal features have not been explained thus far in intuitively appealing terms and continue to be viewed as partly unresolved mysteries.² Here we endeavor to elucidate the physical origin of such superluminal features by introducing a comprehensive causal description of evanescent EM wavepacket (pulse) propagation in two types of structures that have been studied experimentally: multilayered dielectric structures¹ and waveguides partly filled with a dielectric.^2,3 This description is based on an expansion of the response to an incident 8-function impulse in a series of terms corresponding to successive causal time-delays determined by the dispersion inside the structure and the number of reflections at the structure boundaries. The convolution of the incident wavepacket, e.g., a Gaussian, with the terms of this expansion yields a train of successively retarded and slightly distorted Gaussians, whose interference determines the peak-delay and shape of the transmitted wavepacket.

© 1994 IEEE