An optimal single-photon source should deterministically deliver one and only one photon at a time, with no trade-off between the sources efficiency and the photon indistinguishability. However, all reported solid-state sources of indistinguishable single photons had to rely on polarization filtering which reduced the efficiency by 50%, which fundamentally limited the scaling of photonic quantum technologies. Here, we overcome this final long-standing challenge by coherently driving quantum dots deterministically coupled to polarization-selective Purcell microcavities--two examples are narrowband, elliptical micropillars and broadband, elliptical Bragg gratings. A polarization-orthogonal excitation-collection scheme is designed to minimize the polarization-filtering loss under resonant excitation. We demonstrate a polarized single-photon efficiency of 0.60+/-0.02 (0.56+/-0.02), a single-photon purity of 0.975+/-0.005 (0.991+/-0.003), and an indistinguishability of 0.975+/-0.006 (0.951+/-0.005) for the micropillar (Bragg grating) device. Our work provides promising solutions for truly optimal single-photon sources combining near-unity indistinguishability and near-unity system efficiency simultaneously.
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