Influence of fabrication disorder on the optical properties of coupled-cavity photonic crystal waveguides

Abstract

Employing a tight-binding formalism and perturbation theory, we theoretically demonstrate how weak fabrication disorder due to surface roughness dramatically reduces the band-edge performance of coupled-cavity waveguides in semiconductor photonic crystal slabs. We find that surface roughness largely affects the band-edge performance through the introduction of random variations in the individual cavity frequencies, ${\ensuremath{\Omega}}_{0}$, rather than through variations in the tight-binding coupling coefficients, $\ensuremath{\kappa}$. Using model roughness parameters comparable to state-of-the-art structures, the standard deviation of ${\ensuremath{\Omega}}_{0}$ is estimated to be ${\ensuremath{\sigma}}_{{\ensuremath{\omega}}_{0}}\ensuremath{\gtrsim}1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\text{ }{\ensuremath{\Omega}}_{0}$. High-index-contrast fabrication imperfections are found to broaden the photon density of states at the band edge with a characteristic linewidth of ${\ensuremath{\gamma}}_{e}\ensuremath{\approx}{\ensuremath{\sigma}}_{{\ensuremath{\omega}}_{0}}^{4/3}/{(2\text{ }{\ensuremath{\Omega}}_{0}\ensuremath{\kappa})}^{1/3}$. This implies a minimal band-edge group velocity of around ${v}_{g}\ensuremath{\sim}c/120$, consistent with experiments. For applications toward modified spontaneous emission, we show that the characteristic linewidth ${\ensuremath{\gamma}}_{e}$ is, unfortunately, a factor of 5 greater than the largest band-edge coupling rate for which strong photon quantum dot band-edge interactions can occur. Although large Purcell factors can still be achieved in the presence of disorder, an embedded semiconductor quantum dot then couples to a lossy (disorder-induced) propagation mode, which may limit the potential applications in coherent quantum optics.