We show here that both the Debye poles and Lorentz pole pairs are special cases of complex-conjugate pole-residue pairs, and the general form of such pairs in fact offers us a much more efficient approach of treating real dispersive media in FDTD than the usual ones that are based on Debye poles and Lorentz pole pairs. We first derive a unified formulation of the auxiliary differential equation method for arbitrary dispersive media by using these pairs. We then
use this formulation to perform several numerical experiments, including the permittivity of noble metal Ag and the electroabsorption coefficient of semiconductor quantum wells. The result of these experiments clearly demonstrates the feasibility and advantages of using these pairs in treating dispersive media in FDTD.
We use coupled optical and electronic simulations to investigate design tradeoffs in electrically pumped photonic crystal light emitting diodes. A finite-difference frequency-domain electromagnetic solver is used to calculate the spontaneous emission
enhancement factor and the extraction efficiency as a function of
frequency and of position of the emitting source. The calculated
enhancement factor is fed into an electronic simulator, which solves the coupled continuity equations for electrons and holes and Poisson's equation. We simulate a two-dimensional structure consisting of a photonic-crystal slab with a single-defect cavity, and investigate different pumping configurations for such a cavity.