1. Introduction

Single-photon detectors (SPDs) in near infrared offer the possibility to realize the quantum key distribution (QKD) [1], as well as applications that require measurements of very weak light fields [2]. In QKD over optical fiber links [3, 4, 5, 6, 7, 8], SPDs with high quantum efficiency at the telecommunication wavelength (1550 nm) and low dark counts are required. The InGaAs/InP avalanche photodiode (APD) has been the most practical device for SPDs at telecommunication wavelength [9, 10, 11, 12]. Since a photo-excited carrier grows into a macroscopic current output via the carrier avalanche multiplication in an APD operated in the Geiger mode, a single-photon can be detected efficiently. However, fractions of the many carriers trapped in the APD are subsequently emitted, and trigger additional avalanches that cause erroneous events. The InGaAs/InP APD in Geiger mode has a particularly high probability that these so called “afterpulses” occur. Therefore, the InGaAs/InP APD is usually operated in the gated mode in which the gate duration (gate-on time) is generally set to a few nanoseconds. Then the interval between two consecutive gates is set to more than the lifetime (in orders of microseconds) of the trapped carriers so that the afterpulse is suppressed. As a result, the repetition frequency of the gate has been limited to several megahertz, which is unsuitable for applications such as the high-speed clocked QKD system.

The alternative SPDs at telecommunication wavelengths are frequency-upconversion-assisted Si-APD (upconversion detector) [13] and a superconducting single-photon detector (SSPD) [14, 15]. Although these SPDs can be operated with greater than gigahertz clock systems, they have drawbacks that make them difficult to apply to practical QKD systems. The upconversion detector suffers from background noise counts with high detection efficiency, while the SSPD requires cryogenic environment below 4 K.

Recently, the gated InGaAs/InP APD has been revived as a candidate for the high-speed SPD, since afterpulse suppression schemes by means of small avalanche signal detection were reported. We developed the sinusoidally gated InGaAs/InP APDs (SG-APD) that achieved a gate repetition frequency in range of sub-gigahertz [16]. Subsequently, the self-differential APD [17] achieved a gigahertz gate repetition frequency. These detectors have already been applied to QKD experiments and achieved key generation rates in orders of megahertz [7, 8]. In these schemes, to reduce the afterpulsing probability, the avalanche multiplication gain was limited to 10⁵~10⁶, which is two orders of magnitude lower than that in the conventional square gating scheme. In the case of the self-differencing APD, it might be difficult to further decrease the marginal gain for the avalanche signal discrimination, resulting from difficulty in improving the differencing circuit. On the other hand, in the sinusoidal gating scheme, the marginal gain is defined by the thermal noise, since the extra noise signal disturbing the small avalanche signal discrimination can be completely rejected by the cascaded passive filters. It has therefore been possible to further improve the gate repetition frequency of the SG-APD. In this paper, we show the latest progress of the SPD based on the SG-APD. Optimizing the electronics incorporated into the SPD, the undetected avalanche signals drastically decreased. As a result, our SG-APD achieved a gating frequency of 1.5 GHz with a low afterpulsing probability.

 

Fig. 1. Sinusoidally gated avalanche photodiode. (a) Diagram of the single-photon detection circuit. SG: signal generator, HP-AMP: 1 W class high-power amplifier, BPF: bandpass-filter, GPQC: Gated passive quenching circuit, BEF: Band-elimination filter, B-AMP: 3 GHz broadband inverting amplifier, LPF: low-pass-filter, CMP: comparator (discriminator). Oscilloscope trace of LPF outputs are shown in (b) and (c) (fast time-scale). In (b), the black line shows the signal when the avalanche occurred, and the gray line (30 mV offset is given) shows the signal without avalanche. The dotted line denotes the threshold voltage that is controlled by the offset voltage for the CMP.

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2. Sinusoidally gated InGaAs/InP avalanche photodiode

A diagram of our SPD is shown in Fig. 1(a). The tested InGaAs/InP APD is AGD-25-SE-1-T8 (Princeton Lightwave). The APD chip (25 μm in diameter) is mounted on a three-stage Peltier cooler, and are together housed in a TO-8 can package. The Peltier cooler is able to cool the APD chip to -60 degree Celsius (non-load). The APD module was used as the single-photon detection element after it was fiber-pigtailed. In order to supply an AC voltage superposed on the DC reverse bias voltage V_DC to the APD, we used a gated passive quenching circuit (GPQC) [11]. The sinusoidal voltage at a frequency of ω_g was produced by the signal generator (SG: Agilent N5181A) and used as the gate voltage after amplification by the 1 W class high-power amplifier (HP-AMP). Here the amplified sinusoidal voltage passed through the band-pass-filter (BPF) to reject amplified sideband noise, harmonics, and non-harmonics, which contributes to reduce the noise level of the GPQC output. The GPQC output signal passed through three band elimination filters (BEFs) whose center (elimination) frequency was set to ω_g. Then the signal was amplified by a broadband amplifier (B-AMP) whose gain and bandwidth were 40 dB and 3 GHz, respectively. The total elimination ratio of the BEFs was 100 dB at ω_g. The elimination ratio is adequate to discriminate the small avalanche signal. Indeed, the noise level after passing through the BEFs was close to the thermal noise limit. However, the BEFs with high elimination ratio distorted the avalanche pulse, since the BEFs eliminated the ω_g component and gave a large phase shift around ω_g. This distortion causes a wider time jitter in the avalanche signal discrimination. Therefore, to fix the pulse form, the avalanche signal was passed through a low-pass-filter (LPF) with a cutoff frequency of ~ 1.5 × ω_g before entering the discriminator. Figure 1(b) and (c) show the oscilloscope traces of the LPF outputs when a 23 dBm sinusoidal voltage at 1.5 GHz was used as gate. The transferred gate signal at ω_g was sufficiently rejected by the BEFs and the LPF, and the avalanche signal was distilled well. The noise level of the output from the LPF was approximately 20 mV (~ 100 μV correcting the noise figure and the gain of the B-AMP). Therefore, the threshold voltage for the avalanche signal discrimination was set to -26 mV, which indicates that avalanche signals containing only 10⁴~10⁵ electrons (before amplification) could be discriminated. The avalanche signal was discriminated by the ultra-high-speed comparator (CMP: MAXIM MAX9600) circuit that accepts subnanosecond pulses. We finally obtained the logic output in the emitter-coupled-logic (ECL) level.

3. Performances

We evaluated the SPD performance for 50 ps weak laser pulses at 1550 nm. The laser pulses were triggered by the 10 MHz standard clock signal originally given by the SG. Here, the phase of the sinusoidal gate voltage was synchronized with that of the 10 MHz standard clock. The relative delay (phase) between the sinusoidal voltage and the laser pulse was adjusted by the phase shifter (PS: see Fig. 1(a)) based on a coaxial line stretcher. In order to obtain the highest quantum efficiency, the timing (laser pulse delay) of the arrival of the optical pulses at the APD must be carefully tuned by the PS.

To evaluate the quantum efficiency η, the dark count probability P_d, and afterpulsing probability P_a of our SPD, the detection events (logic outputs from the SPD) were registered by a multi-channel scaler (MCS: ORTEC 9308) that gave the time histogram of the detection events. As described above, the repetition frequency ω_L of the laser pulses was set to 10 MHz, which was lower than the frequency ω_g of the sinusoidal gate. Therefore, there are many nonilluminated gates, and the photon detection events occur only in the illuminated gates, as shown in Fig. 2. The number of events in the illuminated gates is consequently much larger than that in the nonilluminated gates (see Histogram (a) in Fig. 2), since only dark counts and afterpulse events occur in the nonilluminated gates. The histogram of the dark counts can be easily obtained with the laser switched off (see Histogram (b) in Fig. 2). We must note that there are actually not only the dark counts but also the afterpulse events correlated with the dark count events. However, such afterpulse events were treated here as dark count events. The number of events in nonilluminated gates with the laser switched on is higher than that with the laser switched off, since afterpulse events correlated with the photon detection events occur. The afterpulsing probability P_a, defined as the ratio of the total afterpulse events to photon detection events, is given by the expression [17]

where C_NI and C_I are the number of the events per nonilluminated and illuminated gate, respectively, and C_D is the number of events per gate with the laser switched off. R is the (prescaling) ratio of the gating frequency to the laser pulse repetition frequency, and corresponds to the number of the gates that are applied to the APD during one period of the laser pulse.

 

Fig. 2. Schematic diagram of the time histogram measurements. The illuminated gates are highlighted. Histogram (a) and (b) show the time histograms of the detection events when the laser was switched on and off, respectively. C_I and C_NI denote the number of events in the illuminated and nonilluminated gates, respectively, with the laser switched on. C_D denotes the number of events per gate with the laser switched off.

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The quantum efficiency and the dark count probability are easily evaluated using the relations

where μ is the average photon number per optical pulse, and N_s is the number of the measurements using the MCS. In our experiment, μ and N_s was set to 0.1 and 10⁸, respectively.

The SPD performances were evaluated changing the V_DC in the range of 59.5 - 62.3 V. The power of the sinusoidal gate voltage was fixed at 23 and 21.5 dBm for ω_g=12 and 1.5 GHz, respectively. The APD operating temperature was set to -50 degree Celsius. Figure 3(a) shows the measured photon count rate as a function of the laser pulse delay, when the V_DC and the ω_g were fixed at 60.7 V and 1.5 GHz, respectively. When the laser pulse delay was 0.18 ns, the maximum count rate was obtained. The relationship between the count rate and the laser pulse delay exhibits the gating profile. As shown in Fig. 3(a), the effective gate width was ~ 100 ps at ω_g=1.5 GHz. Therefore, the delay adjustment and the jitter of the laser trigger time should be less than several tenths of picoseconds.

Figure 3(b) shows the measured time histogram when the experimental condition was the same as Fig. 3(a). The blue line shows the time histogram when the laser was switched off. In this case, only the dark count events were registered, and P_d was found to be 6.3 × 10^-7 from the experimental results. The red line shows the measured time histogram when the laser was switched on. The strongest peak at 150 ns corresponds to the illuminated gate. The number of the events is much larger than that in the other nonilluminated gates), resulting from a lot of photon detection events occurring in the illuminated gate. Moreover, the number of events in the nonilluminated gate is slightly higher than the dark counts, resulting from the afterpulse correlated with the photon detection events. From the experimental results, P_a and η were found to be 2.8 % and 10.8 %, respectively.

 

Fig. 3. (a) Relation between the detection rate and the laser pulse delay. (b) Time histogram of detection events. The red and blue lines show the histograms when the laser was switched on and off, respectively. The highlighted profile shows the expected jitter distribution. The inset shows the histogram in linear scale.

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We can also evaluate the jitter characteristics of the SPD from the time histogram. As shown in the inset of Fig. 3(b), the time jitter distribution has a FWHM of 300 ps, which is shorter than the gate period (0.67 ns). However, the logarithmic histogram (See Fig. 3(b)) shows that the peak associated with the illuminated gate is too broad to be separated from adjacent peaks. This fact means that a fraction of the detection events is registered in an incorrect gate, which obviously causes bit errors if the SPD is applied to a QKD system. It is difficult to accurately evaluate the amount of events registered at incorrect gate timing, since many afterpulse events are also registered in the gates subsequent to the illuminated one. Therefore, the erroneous events were estimated from the expected jitter profile that is highlighted in Fig. 3(b). In the time jitter analysis, we found that ~ 0.2 % of the detection events are registered at incorrect gate timing.

Figure 4 shows the relation between η and P_d when ω_g= 1.2 and 1.5 GHz. The relation between η and P_a is also plotted in the same figure. Here, we evaluated these SPD performances by the detection events registered within the 400 ps time window. As shown in the figure, for ω_g=1.2 GHz, P_d in orders of 10^-7 was achieved when η=10%. As regards ω_g=1.5 GHz, P_d was slightly lower, since the effective gate width was shorter. On the other hand, P_a was limited to several percent even if the quantum efficiency was high. For example Pa was only ~3 % when η=10% in both cases of ω_g =1.2 and 1.5 GHz.

We must note that P_a was measured with the 50 ns pulse pair resolution (dead time) of the MCS we used. As the sinusoidal gate voltage is continuously applied to the APD, many after-pulses are generated. However, almost all of the afterpulse events occur in the gates following to the gate in which the avalanche is triggered. Therefore, the afterpulse events could be efficiently ignored by employing the somewhat long dead time. On the other hand, the dead time limits the maximum detection rate of the SPD system. In our case, the maximum detection rate is approximately 20 MHz. However, it is not so disadvantageous to applications such as QKD systems, in which photon detection events rarely occur. Of course, we can shorten the dead time and improve the maximum detection rate, replacing our MCS with a faster one. If the dead time was shortened to 10 ns, the maximum detection rate would increase to ~100 MHz. However, in this case, the afterpulsing probability P_a would be ~1.5 times higher than that obtained with a 50 ns dead time.

 

Fig. 4. Dark count probability per gate P_d and afterpulsing probability P_a as functions of the quantum efficiency η. The closed and open circles show the relationship between P_d and η at 1.2 and 1.5 GHz, respectively. The closed and open squares show the relationship between P_a and η at 1.2 and 1.5 GHz, respectively.

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Table 1 shows a comparison of our results with the other reported high-speed SPDs. Our SPD achieved the highest gating repetition frequency for the gated APD-based SPD, and has low dark count probability per gate P_d and low afterpulsing probability P_a. Since the APD-based SPD has a high quantum efficiency, it achieved a high net detection rate. Although the SSPD and the upconversion detector can be applied to systems with higher clock speed, their low quantum efficiency spoils the net detection rate. The APD-based SPD is also polarization independent while the quantum efficiencies of the SSPD and the upconversion detector strongly depend on the polarization of incident photons. The dark count probability of our SPD is considerably lower than the other reported APD-based SPDs. However, it is still high in comparison with the SSPD. The dark count probability of the APD-based SPD strongly depends on the operating temperature. Therefore, if the APD operating temperature was decreased, the dark count probability would be lower. Although the afterpulsing probability would increase, it could be suppressed by employing a longer dead time in the discrimination.

Table 1. Comparison of the sinusoidally gated APD with the other reported high speed single-photon detectors. ω_g: gating repetition frequency or acceptable clock speed, R _max: maximum detection rate.

View Table

4. Conclusion

In conclusion, we have developed a single-photon detector at 1550-nm using a sinusoidally gated InGaAs/InP APD. A gate repetition frequency of 1.5 GHz was achieved with high quantum efficiency, low dark count probability, and low afterpulsing probability. The single-photon detector can be easily applied to gigahertz clocked QKD systems.