It is shown that the time needed for light to pass through the optical barrier associated with an antiresonant quarter-wave-stack dielectric mirror, as measured by the group-delay, or phase time, asymptotically reaches a limit that is independent of the barrier thickness and hence of the number of layers. This limit, which scales as the inverse of the refractive-index difference between successive layers, is equal to the mean value of the asymptotic group delays needed for light to reflect off each side of the barrier. This superluminal transmission does not violate causality, as the transmitted intensity is always lower than the intensity that would have been transmitted in vacuum in the absence of the barrier.
© 1999 Optical Society of America
Vincent Laude and Pierre Tournois, "Superluminal asymptotic tunneling times through one-dimensional photonic bandgaps in quarter-wave-stack dielectric mirrors," J. Opt. Soc. Am. B 16, 194-198 (1999)