ANALYTIC EXPRESSIONS FOR THE ELECTROMAGNETIC MODE DENSITY IN FINITE, ONE-DIMENSIONAL, PHOTONIC BAND-GAP STRUCTURES

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.