Frustrated total internal reflection and the illusion of superluminal propagation
We analyze the propagation of a pulse across a vacuum gap separating opposite flat parallel faces of two transparent dielectrics by means of an explicitly causal and retarded propagator constructed directly from the free-space wave equation. Nevertheless, our approach yields apparently superluminal propagation for the case of frustrated total internal reflection (FTIR), that is, a transmitted wave packet appears on the far side of the gap at the same time that the corresponding incident packet crosses the front one. Thus, in this example superluminality is just an illusion, being consistent with both casuality and classical electrodynamics. We study the origin of the apparent superluminality in this case, which is inherent to light pulse propagation in free space and does not depend on the particulars of light-matter interaction, and find that it is due to propagation from the lateral wings of the incident pulse to the central part of the transmitted pulse. Thus, notwithstanding their similarities, FTIR is not equivalent to 1D tunneling. We propose experiments to test our explanation of superluminality using opaque screens to block part of the wavefront, although we demonstrate that the propagation of smooth finite pulses constrained to be made up completely of evanescent Fourier components is indistinguishable from truly superluminal propagation, i.e., it may be completely accounted for using an explicitely superluminal and acausal propagator as well as the causal subluminal one.