Group velocity, energy velocity, and superluminal propagation in finite photonic band-gap structures

Abstract

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.