Two-photon correlations and Hong-Ou-Mandel visibility from an imperfect single-photon source

We study the single-photon purity of a resonantly driven single-photon source in the realistic scenario where the excitation laser pulse can leak into the detection path. We find that the duration of the excitation pulse strongly influences the quality of the single-photon source. We calculate the influence of this on the effective parameters describing the most relevant properties, including the two-photon component and Hong-Ou-Mandel visibility. Furthermore, we analyze how these properties can be strongly affected by frequency filtering of the outgoing field. Our results highlight that the relation between the two-photon component of the emission and the Hong-Ou-Mandel visibility is more complicated than typically assumed in the literature, and depends on the specific details of the source.