Limits of slow-light in photonic crystals

TL;DR

This paper demonstrates that physical effects like loss and disorder impose fundamental limits on how slow light can be in photonic crystals, preventing ideal zero group velocity modes.

Contribution

It provides a general analysis showing that broadening of electromagnetic modes due to various effects sets a lower bound on achievable group velocities in photonic crystals.

Findings

Group velocity cannot reach zero at band edges due to mode broadening.

Superluminal group velocities can occur within the band gap.

Scaling relations link minimum and maximum group velocities to mode linewidths.

Abstract

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 superluminal 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, finite-size effects, etc. This significantly limits the reduction in group velocity attainable via photonic crystals.