Gruppengeschwindigkeit and the Homer Simpson Effect

Justin Peatross
Dept. of Physics and Astronomy
Brigham Young University

During the past century, some confusion has arisen surrounding the meaning of group velocity in situations where it exceeds the speed of light in vacuum or where it becomes negative.  This can occur when the spectrum of an electromagnetic pulse lies near an absorption or amplifying resonance line in the medium.  I will explain how group velocity, regardless of its speed, governs pulse propagation, even for broadband pulses undergoing severe distortion en route.  A linear spectral superposition of group delay tracks the center of the field energy.  In this context, group velocity always retains meaning, which is at odds with long-standing tradition.

So-called superluminal behavior is an artifact of paying attention only to the field energy while ignoring energy transferred into and out of the medium. I will explain why a causal linear dielectric must exchange energy with the front of a pulse differently than with the back, which is the reason for superluminal behavior.  The medium responds to the instantaneous spectrum of the field, that is, the spectrum experienced by the medium up to each moment in time.