Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures

Abstract

We derive an exact expression for the electromagnetic mode density, and hence the group velocity, for a finite, N-period, one-dimensional, photonic 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 gives the N-period mode density in terms of the complex transmission coefficient of the unit cell. The special cases of mode-density enhancement and suppression at the photonic band edge and also at midgap, respectively, are derived. The specific example of a quarter-wave stack is analyzed, and applications to three-dimensional structures, spontaneous emission control, delay lines, band-edge lasers, and superluminal tunneling times are discussed.

Lasing Thresholds of Cholesteric Liquid Crystals Lasers

“…We have found that here , where is a fitting constant. This result is similar to that of Dowling [20], who analytically calculated the DOS as function of sample thickness in a dielectric medium with alternating refractive indices. We then write for the pump energy at lasing threshold:…”

Limits of slow light in photonic crystals

“…15,18 The limits imposed on the minimum attainable group velocity in photonic crystals have been studied in various contexts, such as, e.g., fabrication disorder, 19,20 lossy dielectrics, 21 and finitesize effects. 22 It is the aim of this Brief Report to generalize these findings and to show that they may all be presented in the context of broadening of electromagnetic modes and the resulting induced density of states ͑DOS͒.…”

Universal photonic tunneling time

“…In general, the study of electromagnetic properties of such materials is very complicated, and the dispersion relation we need to evaluate the phase time in the proposed formalism is quite involved for physical situations. This study was performed analytically in [15] where the dispersion relation (and other useful quantities) was derived starting from the complex transmission coefficient of the considered barrier. It is, then, quite a meaningless issue to get the tunnelling time from the dispersion relation obtained from the transmission coefficient, while it is easier to have directly the phase time τ from Eq.…”

“…We again assume normal incidence of the light on the photonic bandgap material. In this case the transmission coefficient T and its phase φ have the expressions as in (34) and (45), where A,B are given by (35), (36) and [15]:…”