Propagation of optical pulses through one-dimensional photonic crystals with a dispersive and gain defect layer

The propagation of a pulse through one-dimensional photonic crystals with a dispersive and gain defect layer is discussed. The dispersion and gain of the defect layer is described by Lorentz oscillator model. It is found that the pulse peak exhibits subluminal and superluminal behaviors with varying strength of the oscillator. The Poynting vector and energy velocity can be negative, but the latter is never faster than the vacuum light speed c. The advance or delay of the pulse peak is a result of the coherent superposition of all Fourier components which experienced different phase shift and different amplification in the medium.