We consider periodic single-photon sources with combined multiplexing inwhich the outputs of several time-multiplexed sources are spatiallymultiplexed. We give a full statistical description of such systems in order tooptimize them with respect to maximal single-photon probability. We carry outthe optimization for a particular scenario which can be realized in bulk opticsand its expected performance is potentially the best at the present state ofthe art. We find that combined multiplexing outperforms purely spatially ortime multiplexed sources for certain parameters only, and we characterize thesecases. Combined multiplexing can have the advantages of possibly using lessnonlinear sources, achieving higher repetition rates, and the potentialapplicability for continuous pumping. We estimate an achievable single-photonprobability between 85% and 89%.
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