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

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, Ω₀, rather than through variations in the tight-binding coupling coefficients, κ. Using model roughness parameters comparable to state-of-the-art structures, the standard deviation of Ω₀ is estimated to be σ_ω₀1×10^-4 Ω₀. High-index-contrast fabrication imperfections are found to broaden the photon density of states at the band edge with a characteristic linewidth of γₑ≈σ_ω₀4/3/(2 Ω₀κ)1/3. This implies a minimal band-edge group velocity of around vg~c/120, consistent with experiments. For applications toward modified spontaneous emission, we show that the characteristic linewidth γₑ 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.