Time-domain detection of superluminal group velocity for single microwave pulses

Single microwave pulses centered at 9.68 GHz with 100-MHz (full width at ha lf maximum) bandwidth are used to evanescently tunnel through a one-dimensi onal photonic crystal. In a direct time-domain measurement, it is observed that the peak of the tunneling wave packets arrives (440+/-20) ps earlier t han the companion free space (air) wave packets. Despite this superluminal behavior, Einstein causality is not violated since the earliest parts of th e signal, also known as the Sommerfeld forerunner, remain exactly luminal. The frequency of oscillations and the functional form of the Sommerfeld for erunner for any causal medium are derived.