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

Citation
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
Citations number
42
Categorie Soggetti
Physycs, Mathematical","Phsycs, Fluid & Plasmas
ISSN journal
1063651X
Volume
53
Issue
4
Year of publication
1996
Part
B
Pages
4107 - 4121
Database
ISI
SICI code
1063-651X(1996)53:4<4107:AEFTEM>2.0.ZU;2-0
Abstract
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.