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

Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Mar;63(3 Pt 2):036610. doi: 10.1103/PhysRevE.63.036610. Epub 2001 Feb 23.

Abstract

We have analyzed the notions of group velocity V(g) and energy velocity V(E) 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 V(E)=/t/(2)V(g). It follows that V(E)=V(g) 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 V(g)<or=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.