We theoretically investigated spectrally uncorrelated biphotons generated in a counter-propagating spontaneous parametric downconversion (CP-SPDC) from periodically poled MTiOXO4 (M = K, Rb, Cs; X = P, As) crystals. By numerical calculation, it was found that the five crystals from the KTP family can be used to generate heralded single photons with high spectral purity and wide tunability. Under the type-0 phase-matching condition, the purity at 1550 nm was between 0.91 and 0.92, and the purity can be maintained over 0.90 from 1500 nm to 2000 nm wavelength. Under the type-II phase-matching condition, the purity at 1550 nm was 0.96, 0.97, 0.97, 0.98, and 0.98 for PPKTP, PPRTP, PPKTA, PPRTA, and PPCTA, respectively; furthermore, the purity can be kept over 0.96 for more than 600 nm wavelength range. We also simulated the Hong-Ou-Mandel interference between independent photon sources for PPRTP crystals at 1550 nm, and interference visibility was 92% (97%) under type-0 (type-II) phase-matching condition. This study may provide spectrally pure narrowband single-photon sources for quantum memories and quantum networks at telecom wavelengths.
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