Group velocity, energy velocity, and superluminal propagation in finite photonic band-gap structures
We have analyzed the notions of group velocity Vg and energy velocity VE for light pulses propagating inside one-dimensional photonic band gap structures of finite length. We find that the two velocities are related through the transmission coefficient t as VE=\|t\|2Vg. It follows that VE=Vg only when the transmittance is unity (\|t\|2=1). This is due to the effective dispersive properties of finite layered structures, and it allows us to better understand a wide range of phenomena, such as superluminal pulse propagation. In fact, placing the requirement that the energy velocity should remain subluminal leads directly to the condition Vg<=c/\|t\|2. This condition places a large upper limit on the allowed group velocity of the tunneling pulse at frequencies of vanishingly small transmission.