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. 2018 Jan 24;8:1486. doi: 10.1038/s41598-018-20035-7

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© The Author(s) 2018

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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(a) Count rates as a function of light power (average photon number per pulse) at five different I_b values. The measured points, denoted by the open circles, were fitted with straight lines in the log–log scale. The slopes of the fitting lines are 1.02 ± 0.01, 1.91 ± 0.02, 1.99 ± 0.01, 2.04 ± 0.01, and 3.05 ± 0.02, respectively. (b) Normalized PCR as a function of t_D, which is measured when the detector operated in the two-photon detection regime at I_b values of 10, 10.5, 11.5, 11.75, and 12 μA; I_b of 12.5 μA corresponding to the one-photon detection regime is also shown for comparison. The measured data were fitted with a Lorentz function. The black arrow denotes the half width at half maximum of the curve, which directly corresponds to τ_th measured at I_b = 10 μA. (c) τ_th as a function of I_b extracted from the data in (b).