## 3 Influence on Noise Suppression and Pulse Shape by Filtering System  
We measure the noise suppression by the filtering system. When the pump light was blocked and only a light pulse at 795 nm is incident into the frequency conversion module, the noise level of the leaked 795 nm field can be measured after the filtering system. The 795 nm input pulse contains 50 photons with a FWHM of 100 ns. The measurement window is 640 ns which is centered on the pulse peak. By repeating the noise collection with FPGA (repeat time of 1.56 \(\times\) 10\({}^{6}\)), we obtain a cumulative noise count lasting for 1 s, that is, noise counting rate \(N\). There is no change in noise counting rate with or without 795 nm input pulse, which means that the noise at 795 nm is completely filtered out. Next, we study the suppression of pump induced noise by the three-stage filtering system in detail. The input light at 795 nm is blocked, and only the pumping light at 1560 nm is injected into the waveguide module. In order to avoid missing counts due to the long dead time of SPD, the injected pumping light is in the form of pulses with period of 25 us and duration of 1 us. We measure the noise counts when the light is on. Figure 3 shows the noise counting rate \(N\) as a function of the pumping power \(P_{P}\) under different filtering conditions. \(P_{P}\) is the pumping power coupled into the 2 \(\times\) 1 combiner. Initially, the two etalons and F-P cavity in the three-stage filtering system are bypassed, leaving only the first-stage filter. The measured noise is shown by the blue triangles (data points on the top) in Figure 3. From the data we can see that after the first-stage filter, the noise generated by the pumping light remains at a fairly high level, such as \(N=1.36\times 10^{6}\)/s for \(P_{P}=350\) mW. Then, the second-stage filter is added in the filtering system, and the measured noise level is significantly reduced, shown by the red circles(data points in the middle). Finally, the third stage filter is also added, and the noise is further reduced as shown by the black squares (data points in the bottom). Under this condition, for \(P_{P}=350\) mW the noise counting rate is decreased to \(N=780\)/s. The noise level is related to the pumping power. We fit the noise date by using the expression [29]: \(N(P_{P})=\alpha\times P_{P}+DC\), where \(\alpha\) is the linear coefficient, and \(DC=2.5\times 10^{2}\)/s is the dark count rate of SPD. The solid lines in Figure 3 are the fitted curves, which are in good agreement with the experimental data. For the fitted lines from top to bottom, the slope \(\alpha\) is taken as \(4.5\times 10^{3}\)/mW/s, \(4.5\times 10\)/mW/s and \(1.52\)/mW/s, respectively. It is illustrated that the second-stage filter (cascaded etalons) reduces the noise level by two orders of magnitude, and the third-stage filter (F-P cavity) reduces the noise by another order of magnitude. The pump-induced noise includes the leakage of pump light at 1560 nm, SRS noise, and the SHG of strong pump at 780 nm. In order to assess the noise level at 1560 nm and 780 nm, we put another band-pass filter centered at 1621 nm behind the filtering system, which filters out most of the noise at 1560 nm and 780 nm, and remaining SRS around 1621 nm. For \(P_{P}=350\) mW, the measured noise count rate is 620/s. The addition of 1621 nm bandpass filter did not significantly reduce the noise count. The reduction in noise count is due to the transmittance loss of the inserted filter itself. This indicates that the noise at 1560 nm and 780 nm has been filtered out by the original filtering system, and the noise is mainly SRS after the filtering system. We study the influence of the filtering system on the shape of the converted pulse for different input pulse widths. Here the input pulse is taken as Gaussian shape with \(\mu_{in}=50\). The full width at half maximum (FWHM) of the input pulse is \(\Delta t_{in}=53\) ns, 112 ns and 182 ns in Figure 4a,b,c, respectively.