Ultra-fast multiple tunnelling of electromagnetic X-waves

A study is provided of the transmission of a three-dimensional electromagnetic X-wave undergoing frustrated total internal reflection on the upper surface of a multi-layered structure. The stratified structure consists of successive layers alternately allowing the transmission of evanescent and free-propagation components. It is shown that the peak of an X-wave is transmitted through these successive layers at an ultra-fast speed. Under certain conditions, the total traversal time through all successive evanescent and free-propagation sections appears to be less than zero. The peak of the transmitted pulse emerges from the stack before the incident peak reaches the front surface of the stratified structure. Conditions for the materialization of this ultra-fast multiple tunnelling of pulses are pointed out and their consequences and limitations are discussed.