While ideal photonic crystals would support modes with a vanishing group velocity, state-of-the-art structures have still only provided a slow down by roughly two orders of magnitude. We find that the induced density of states caused by lifetime broadening of the electromagnetic modes results in the group velocity acquiring a finite value above zero at the band-gap edges while attaining uperluminal values within the band gap. Simple scalings of the minimum and maximum group velocities with the imaginary part of the dielectric function or, equivalently, the linewidth of the broadened states are presented. The results obtained are entirely general and may be applied to any effect which results in a broadening of the electromagnetic states, such as loss, disorder, and finite-size effects. This significantly limits the reduction in group velocity attainable via photonic crystals.
Bibliographical noteCopyright 2008 American Physical Society