Pulse propagation near highly reflective surfaces: Applications to photonic band-gap structures and the question of superluminal tunneling times

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Abstract
We address the physics of pulse propagation, energy flow, and field dynamics as described by Maxwell’s equations. After deriving the form of the Poynting vector for pulses that vary slowly in time only, we show that interference terms nontrivially affect the momentum and the energy density of an electromagnetic pulse that scatters from highly reflective materials. Inside such materials, we conclude that the magnetic- and electric-field amplitudes are strongly out of phase. We then apply our findings to the study of layered periodic structures; specifically, we examine the propagation of apparently ‘‘superluminal’’ pulses. By monitoring the local momentum and energy densities in the structure at all times, we explicitly show that the canonical energy velocity can never exceed the vacuum speed of light c at any point in the crystal.