Single-photon sources based on incomplete binary-tree multiplexers with optimal structure

We consider novel types of spatially multiplexed single-photon sources based on output-extended incomplete binary-tree multiplexers containing general asymmetric routers where the construction of the multiplexers takes into account the total transmission efficiencies of the multiplexer arms at which a novel router can be added to the system. After selecting the multiplexer that outperforms the others, we identify the ranges of the loss parameters for which the application of the selected multiplexer leads to single-photon sources with higher single-photon probabilities and lower multiphoton noise than that can be achieved by using asymmetric multiplexers. We show that using the selected multiplexer is especially advantageous in the case of single-mode sources characterized by thermal statistics of the input photon pairs. We also reveal that the application of this multiplexer yields high performance single-photon sources even for suboptimal system sizes that is a typical situation in current experiments.