Jm. Bendickson et al., ANALYTIC EXPRESSIONS FOR THE ELECTROMAGNETIC MODE DENSITY IN FINITE, ONE-DIMENSIONAL, PHOTONIC BAND-GAP STRUCTURES, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 53(4), 1996, pp. 4107-4121
We derive an exact expression for the electromagnetic mode density, an
d hence the group velocity, for a finite, N-period, one-dimensional, p
hotonic band-gap structure. We begin by deriving a general formula for
the mode density in terms of the complex transmission coefficient of
an arbitrary index profile. Then we develop a specific formula that gi
ves the N-period mode density in terms of the complex transmission coe
fficient of the unit cell. The special cases of mode-density enhanceme
nt and suppression at the photonic band edge and also at midgap, respe
ctively, are derived. The specific example of a quarter-wave stack is
analyzed, and applications to three-dimensional structures, spontaneou
s emission control, delay lines, band-edge lasers, and superluminal tu
nneling times are discussed.