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 half maximum) bandwidth are used to evanescently tunnel through a one-dimensional photonic crystal. In a direct time-domain measurement, it is observed that the peak of the tunneling wave packets arrives (440+/-20) ps earlier than the companion free space (air) wave packets. Despite this superluminal behavior, Einstein causality is not violated since the earliest parts of the signal, also known as the Sommerfeld forerunner, remain exactly luminal. The frequency of oscillations and the functional form of the Sommerfeld forerunner for any causal medium are derived.