Gruppengeschwindigkeit and the Homer Simpson Effect
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.