1. Introduction

High-speed single-photon detection (SPD) in the near-infrared has recently become a matter of interest due to the requirements of long-distance and high-bit-rate quantum communications such as in quantum key distribution (QKD). Gated-mode InGaAs/InP single-photon avalanche photodiodes (SPAD) have been well studied for near-infrared SPD [1–4]. However, the operating speed of the gated-mode SPAD is severely limited due to the after-pulsing effect [5]. After pulsing is caused by avalanche carriers trapped in the SPAD’s multiplication layer, resulting in the triggering of avalanches in subsequent gates. The after pulsing is proportional to the total number of avalanche carriers dependent on the excess bias and the gate duration applied to the SPAD.

Generally, an InGaAs/InP SPAD outputs its own oscillating capacitive response to the input gating signal. In an avalanche event, the avalanche signal is superposed on the capacitive response. In conventional gating methods that use a relatively long gating duration, the avalanche peak is high enough to be discriminated easily from the capacitive response, but the after-pulsing probability is also high due to the large avalanche carriers. Therefore, a dead-time setting is necessary for the long gating duration, which limits the operating speed of SPD [6–8]. For high-speed detection, the avalanche current should be decreased by applying a lower bias voltage. However, the weaker the avalanche current is, the more difficult it is to distinguish from the capacitive response. On the other hand, when an ultrashort gating duration is used for high-speed operation, the avalanche current is quite weak and therefore the after-pulsing effect can be significantly suppressed; however, it is very difficult to discriminate a quite weak avalanche [8]. Therefore, a technique to discriminate a weak avalanche is essential for high-speed operation and to decrease the error counts of the gated-mode SPAD.

Recently, the weak avalanche discrimination techniques of sine-wave gating (SG) [6,9] and self-differencing (SD) [7,10,11] were demonstrated for a high-speed InGaAs/InP SPAD. These techniques have been demonstrated in QKD [12–14] and photon number resolving [15]. A method that combines the SG and SD approaches was also reported [8]. The SG method uses sine-wave gating and band-elimination filters to filter out the background capacitive response, while the SD method use square-wave gating and a differencing circuit to eliminate the capacitive response. Both methods focus on eliminating the SPAD’s background capacitive response for weak avalanche discrimination. They require complicated electronics, which can be a drawback in practical application. The approach combining the two methods is also not free from electronic complexity. Moreover, because the SD and SG methods set importance on high-speed gating, they are not so practical for relatively low gating frequencies under tens of megahertz due to drawbacks such as the effective gate-width tuning in the SG method, the large time-delay setup, and the errors due to two continuous avalanche events in the SD method.

In this paper, we propose a very simple and practical method that can be used over a wide range of gating frequencies for weak avalanche discrimination in gated-mode SPD. Contrary to the SG and the SD techniques in trying to eliminate the background signal, we focus on the tuning of the background signal by using an auxiliary signal. Detection efficiency and after-pulse probability of an InGaAs/InP SPAD are investigated with a 10 MHz gating for both conventional and proposed methods. We also extend the proposed method to the SPD scheme so that the maximum count rate can approach 100 MHz.

2. Experimental setup

In our method, the SPAD output and auxiliary signals are combined through a combiner so that even a weak avalanche can be discriminated easily in the combined output. Figure 1(a) shows a schematic diagram of SPAD outputs when a weak avalanche occurs by a conventional gating; the solid line indicates the SPAD’s capacitive response; the dashed line represents a weak avalanche. As shown in Fig. 1(a), it is difficult to discriminate weak avalanches lower than the capacitive response of their amplitudes. When the background signal can be tuned so that it is at maximum when it is at the position of the weak avalanche in the time domain, then the weak avalanche can be discriminated easily. The tuning of the background signal can be done by an electric combiner that combines the capacitive and auxiliary signals. The amplitude and input timing of the auxiliary signal should be adjusted as needed to obtain a proper combiner output. Figure 1(b) shows the expected combiner output in which a weak avalanche can be discriminated easily.

 

Fig. 1 Concept of auxiliary signal method. Output signals of (a) a SPAD and (b) a combiner for a weak avalanche event.

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To verify our approach, several measurements are carried out with a 10 MHz gating frequency ($f_{\text{g}}$) using the experimental setup shown in Fig. 2 . An InGaAS/InP SPAD (Princeton Lightwave, PGA-400) is cooled to −55°C. Square-wave gating pulses of 2.5 ns (FWHM), generated by a pulse pattern generator (PPG1), are applied to the SPAD with a 10 MHz rate and ~3.8 V amplitude ($V_{\text{pp}}$) after superposition with a dc voltage ($V_{\text{dc}}$) of ~57 V through a bias tee. Auxiliary pulses of 1.5 ns (FWHM) are generated with the same rate of gating pulse through the PPG1. The amplitude and the time delay of the auxiliary signals are finely tuned to obtain proper combiner outputs.

 

Fig. 2 Experimental setup.

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When the auxiliary signals are not input to the combiner our scheme works as a conventional gating scheme. Laser pulses of 250 ps (FWHM) in 1548 nm are generated with a 100 kHz rate ($f_{\text{p}}$) for optical characterization of the SPAD, and the mean photon number (μ) of the laser pulses is set as 0.1/pulse using an optical variable attenuator (OVA). An additional PPG2 is used to synchronously trigger the laser diode (LD) and the PPG1 with rates of $f_{\text{p}}$ and $f_{\text{g}}$, respectively. Several electronic modules are used for single-photon counting analysis, including a discriminator (Phillips-708), coincidence logic (Phillips-754), a time-to-amplitude convertor (TAC, Ortec-567), and a counter card. Neither dead time nor count-off time [8] is applied for the works in this paper. An rf amplifier (Amp) is inserted when gating pulses over 3.8 V are required, which is the case for the 100 MHz gating mentioned later in this paper.

3. Experimental results

First, we observe the combiner output through an oscilloscope (OSC) for weak avalanche events. Figures 3(a) and 3(b) show the typical combiner output for the weak avalanche events accumulated for a few seconds by the OSC without and with input of the auxiliary signals, respectively. As shown in Fig. 3, the difference between the cases without and with an auxiliary signal illustrates clearly the weak avalanche discriminating capability of our scheme.

 

Fig. 3 Accumulated combiner output recorded on OSC with 10 MHz gating.

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Second, detection efficiency, dark-count, and after-pulse probabilities are investigated with and without input of the auxiliary pulses, and the results are plotted in Fig. 4 . Discrimination thresholds are set to right above the maximum values of the background signal for the cases with and without auxiliary signal input, and the threshold of the case without an auxiliary signal is about 7 mV lower than that of the case with an auxiliary signal.

 

Fig. 4 Detection efficiency vs. after-pulse and dark-count probabilities with $f_g$ = 10 MHz, $f_p$ = 100 kHz, and μ = 0.1, without dead time.

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In Fig. 4, The dark-count probability per gate ($P_{\text{dark}}$) is calculated by $P_{\text{dark}}=R_{\text{dark}}/f_{\text{g}}$, where $R_{\text{dark}}$ is the dark-count rate. The efficiency (η) and the after-pulse probability ($P_{\text{ap}}$) are calculated as [8]

Here, $R_{\text{de}}$ is the detection rate and $R_{\text{de}}^c$ is the coincidence rate between detection and laser pulses. The coincidence measurement can give information on whether the detection event is due to photon input or not. A 10 ns window is applied for coincidence counting. As shown in Fig. 4, there is a sharp decrease in the after-pulse probability obtained through the auxiliary-signal method as compared with the conventional method. Because our scheme enables the discrimination of weak avalanches, equivalent efficiency can be obtained even with lower bias input; thus, after-pulse probability can be suppressed. It is noticeable that the dark-count ratios of equivalent efficiencies show no conspicuous differences between the two methods. This is, we think, because the auxiliary-signal method can detect smaller amplitude for both signal and dark counts than the conventional method.

We extend our scheme to single photon detection with 100 MHz gating using another SPAD of the same model (PGA-400) used for the 10 MHz gating. The gate and auxiliary pulse widths and the mean photon number are same as those in the case of the 10 MHz gating, and other experimental parameters are shown in Table 1 .After fine tuning the amplitude and time delay of the auxiliary signal, we investigate the detection efficiency, the after pulse, and the dark-count probabilities varying the DC bias. Contrary to the 10 MHz gating, the after-pulse probability shows a relatively high dependence on the discrimination threshold. Therefore, we investigate the SPD parameters for three cases of the threshold, and the step of the increased threshold is 0.3 mV. To resolve neighboring gate pulses of the 100 MHz gating, a 3 ns window is applied for the coincidence counting between laser-pulse and single-photon detection in consideration of the gating period and width and the rising and falling edges of the gating pulse. As shown in Fig. 5 , for a higher threshold, a higher bias is required for equivalent detection efficiency, resulting in an increase of after-pulse probability. The after-pulse probability is 5.6%, with a detection efficiency of 10.4%, and the dark-count probability is 4.3 × 10⁻⁵ per gate. The maximum count rate of this 100 MHz gating scheme can approach up to 100 MHz because no dead time is applied.

Table 1. Experimental Parameters for 100 MHz Gating of SPAD

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Fig. 5 Detection efficiency vs. after-pulse and dark-count probabilities, with $f_g$ = 100 MHz, $f_p$ = 1 MHz, and μ = 0.1, without dead time.

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The time distribution of after-pulse probability is also investigated through a TAC and a multi-channel analyzer (MCA) at an after-pulse probability of 7.6%, as shown in Fig. 6 . In the measurement, the time range of the TAC is set as 500 ns. The start input of the TAC is the coincidence output between the laser pulse and detection; the stop input is the detection output. In Fig. 6, the dark-count contribution to the measured count is removed, and the after-pulse probability at each gating time is calculated on the assumption that the number of after-pulse events occurring after 500 ns from the photon-induced avalanche event is small enough to be disregarded. We can approximate, from Fig. 6, the expected after-pulse probability in the case of dead-time application.

 

Fig. 6 Time distribution of after-pulse probability.

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4. Conclusion

In summary, we demonstrated a practical method that can be used over a wide range of gating frequencies for weak avalanche discrimination of gated-mode single-photon detection. A sharp decrease in after-pulse probability by application of the proposed method was demonstrated with a 10 MHz gating. We have also extended the proposed method to the SPD scheme so that the maximum count rate can approach 100 MHz.