Abstract

The concept of group velocity is critical when applied to an absorbing (or gain), homogeneous dielectric material because Vg may be greater than c, and it can even be negative in some circumstances. These topics were discussed at length in the seminal book by Brillouin [1]. Here we discuss the case in which a 1-D PBG structure displays anomalous effective index behavior, not as a result of gain or absorption, but as a result of scattering [2]. In the case of our 1-d finite geometry the energy velocity takes a form that involves both the transmittance I |t_ω|² and the imaginary part of reflectivity r_ω of the stack: where τ_ω is the tunneling time defined as: where Φ_ω is the normalized field distribution inside the structure.

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