Gruppengeschwindigkeit and the Homer Simpson Effect

(Group Velocity and the Exchange of Energy in Linear Dielectrics)

Justin Peatross

Dept. of Physics and Astronomy Brigham Young University Provo, UT 84602

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. Such situations arise for narrowband pulses in the neighborhood of absorption of amplifying resonance structures where broadband pulses typically suffer severe distortion. This has led to the common perception that group velocity loses meaning near a resonance (at least for broadband pulses). We have developed a context in which group velocity always retains meaning, regardless of the spectral bandwidth of the pulse. A linear spectral superposition of group delay tracks the arrival of field energy.

So-called superluminal behavior is an artifact of paying attention only to the field energy while ignoring energy before being transferred out of or after being transferred into of the medium. The total energy in a system obeys strict luminality. A causal linear dielectric exchanges energy with the front of a pulse differently than with the back, which can lead to superluminal motion (or in other circumstances to highly subluminal motion) of the locus of field energy. The medium responds to the instantaneous spectrum of the field, that is the spectrum of the electric field pulse truncated at each new instant (as a given locale in the medium experiences the field).

©Copyright 1999 KSU Department of Physics