Transit times of radiation through photonic bandgap materials: Pulse   reshaping of classical and quantum fields in the time domain
  We study the propagation of electromagnetic pulses through photonic bandgap materials and relate time-domain pulse reshaping to observable transit times. For layered dielectric mirrors we demonstrate how pulse reshaping of slowly varying classical fields results in transit-time delays that are equivalent to the group delay. The time-domain analysis emphasizes the causal origin of negative group delays. We also study an analogous fully-quantized model and show how the same time-domain analysis may be used to interpret observed delays of single-photon fields. 
Martin Ligare, Aaron Gee-Clough, and Charles Doersam