Single quantum-dot Purcell factor andβfactor in a photonic crystal waveguide

A theoretical formalism to calculate the spontaneous emission rate enhancement (Purcell factor) and propagation mode β factor from single quantum dots in a planar-photonic-crystal waveguide is presented. Large Purcell factors for slow light modes, and enormous β factors ($>0.85$) over a broadband (10 THz) spectral range are subsequently predicted. The local density of photon states is found to diverge at the photonic band edge, but we discuss why this divergence will always be broadened in real samples, most notably due to structural disorder. Applications towards ``on-chip'' single photon sources are highlighted.