Single-photon detectors are essential components for many applications, such as quantum communication,^[1–4] laser ranging,^[5–9] circuit testing,^[10] and optical time-domain reflectometer (OTDR).^[11] Recently, quantum key distribution (QKD) of the long transmission distance and high key generation rate draw intense research on high-speed, near-infrared single-photon detectors.^[12–15] Two main candidates are superconducting nanowire single-photon detectors (SSPDs) and InGaAs/InP single-photon avalanche photodiodes (SPADs). SSPDs provide outstanding performance in low dark count rate, high detection efficiency, and low timing jitter, especially in the near-infrared wavelength. In spite of these preferable advantages, SSPDs have drawbacks for many practical applications: requirement of cryogenic temperatures (< 4 K) to keep the superconducting state.^[15] Refrigeration systems to maintain cryogenic conditions are very large and have high energy consumption. In contrast, InGaAs/InP avalanche photodiodes (APD) based SPADs are compact, energy saving and low cost, and they also provide high performance in the near-infrared spectrum. Therefore, InGaAs/InP-based SPADs are widely used in many applications, especially in the QKD systems.^[12–14]

Unfortunately, InGaAs/InP-based SPADs also suffer from significant dark counts when operated in the geiger-mode. To reduce the dark counts, the gated mode operation is widely employed.^[16] However, in the gated mode, the weak avalanche signals are usually buried in the gating noise due to the charge–discharge response of APD capacitance to the gating signal. To discriminate the avalanche signals, the gating noise should be removed when possible. Recently, some novel gating techniques have been reported to suppress the gating noise while increasing the gating signal repetition rate over 1 GHz.^[17–19] One approach is sinusoidal gating. Due to the frequency response of the sinusoidal gating signal to the APD capacitance is distributed at the frequency of the gating signal and its harmonic frequencies; therefore, the fundamental component and the higher harmonics can be easily removed by narrow band elimination filters (BEFs) and low pass filters (LPFs), respectively. On the other hand, the energy of the avalanche signal contains many frequency components and almost all of them can pass through the BEF.^[17] In order to improve the performance, several sinusoidal gating techniques have been demonstrated. In Ref. [20], two balanced APDs are used to make the gating frequency tunable. By using the sinusoidal harmonic subtraction method, single-photon detection efficiency up to 50% at 1310 nm has been achieved.^[21] In the typical sinusoidal gating scheme, the BEF causes some distortion to the avalanche signals and results in a relatively large timing jitter for single-photon detection,^[17,22] limiting its applications in high speed QKD or ultra-sensitive laser ranging. To circumvent the problem on the BEF, reference [22] uses a low pass filtering (LPF) technique to minimize the distortion to the avalanche signals and realize a 1-GHz sinusoidal gating detector with a timing jitter as low as 60 ps. In Ref. [23], the timing response of a sinusoidally gated InGaAs/InP APD both in synchronous mode and free-running mode has been investigated at a fixed V_ex. However, the timing response of a single-photon detector is a strong function of detector bias conditions.^[24,25] Moreover, for sinusoidal gating, when the excess bias voltage (V_ex) is increased by increasing the direct-current (DC) bias voltage with fixed sine wave voltage, the applied gate-on time (T_g) is also increased. This may increase the timing jitter, especially in the high speed sinusoidal gating scheme, where the optical response of the avalanche photodiode is comparable with the T_g.^[16]

In this paper, we concentrate on the comprehensive characterization of the bias-dependent timing jitter of a 1-GHz sinusoidally gated InGaAs/InP APD. In our measurements, the APD was cooled to −30 degrees Celsius and the threshold voltage for the avalanche discrimination was set to −33 mV. Under middle V_ex conditions, an increase in the V_ex reduces the jitter; however, at low and high V_ex, we show that increasing the V_ex also has the effect of increasing the jitter. The smallest jitter of 93 ps is obtained at 2.8-V V_ex. In addition, the photon detection efficiency and the dark count rate of the detector are 21.4% and ∼2.08×10⁻⁵ per gate, respectively. The timing jitter measurement of the same APD but using pulse gating shows that this effect is likely related to the increment of the T_g when the V_ex is increased. Finally, we calculate the noise equivalent power (NEP) and the afterpulse probability (P_ap) of the detector, and find that both of them rise quickly at V_ex that exceed 2.8 V. We may conclude that the detector should be operated at V_ex of 2.8 V to exploit the fast time response (93 ps), low NEP (∼2.06×10⁻¹⁶ W/Hz^1/2) and low P_ap (7.11%).

Figure 1(a) shows the experimental setup for studying the bias-dependent timing jitter of a sinusoidally gated InGaAs/InP avalanche photodiode. The Fiber–Pigtailed InGaAs/InP APD (PGA-400, Princeton Lightwave Inc.) was cooled to −30 degrees Celsius. The sine wave signal at a frequency of 1 GHz was produced by a standard signal generator (MG645B) and amplified by a high power amplifier (H-Amp, Mini-circuits, ZHL-42W). Through a coupler, 90% of the signal was passed through a band pass filter (BPF) to provide the gating signal with a peak-to-peak amplitude of 6V_p–p, which was combined with the DC reverse bias voltage (V_DC) and supplied to the APD by using the gated passive quenching circuit (GPQC).^[17] Here, the BPF was used to eliminate the amplified sideband noise and harmonic noise. The other 10% was used to trigger the pulse laser. The trigger rate for the laser was set to 20 MHz by a prescaler whose divide ratio was 50. The pulsed diode laser (PDL 800-B, PicoQuant) emitted 30-ps laser pulses at 1550 nm wavelength. They were attenuated to 0.1 average photons per pulse by an optical attenuator (ATT, FVA-3150 EXFO) and coupled into the APD by single-mode fibers. In order to obtain the maximum photon detection efficiency (PDE), a delay module was used to tune the phase between the photon signal arrival and the gating signal. The output signals from the APD were processed by a band elimination filter (BEF), a low pass filter (LPF) and another two low noise amplifiers (LN-Amp, Mini-circuits, ZFL-1000LN+) to extract the avalanche signals. The BEF suppressed the capacitance response of the APD to the gating signal at the fundamental frequency of 1-GHz. Then the signals were amplified by a LN-Amp with a gain of 23 dB and subsequently led to a low pass filter (LPF) with a cutoff frequency of 1.5 GHz, which was used to reject the higher harmonics generated by a nonlinear capacitance response of the APD. Consequently, the noise level after the LPF was close to the thermal noise limit and the avalanche signals were distilled well. Before entering the time-correlated single-photon counting module, the avalanche signals were further amplified by another LN-Amp. Figure 1(b) shows a typical avalanche signal amplified by the second LN-Amp.

Fig. 1.

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Fig. 1. (a) Schematic diagram of the experimental setup for studying the bias-dependent timing jitter of a sinusoidally gated InGaAs/InP avalanche photodiode. H-Amp: high power amplifier; BPF: band pass filter; GPQC: gated passive quenching circuit; BEF: band elimination filter; LN-Amp: low noise amplifier; LPF: low pass filter; ATT: optical attenuator; TCSPC: time-correlated single-photon counting module. (b) Oscilloscope trace of the extracted avalanche signal after the second LN-Amp.

Photon arrivals are discriminated by sensing the leading edge of the avalanche current with a suitable threshold. Due to finite carrier propagation velocities and spatially different fields within the volume of the APD, the time from photon absorption to discrimination of avalanche current is not a fixed delay. This causes the timing jitter of the detector.^[25] To characterize bias-dependent timing jitter of the 1-GHz sinusoidally gated InGaAs/InP APD detector we used a TCSPC technique, whereby a histogram representing the probability distribution of time delays from the arrival of photons to the detection of the corresponding avalanche signals was accumulated. The timing jitter is usually defined as the full width of the maximum (FWHM) of the histogram. As shown in Fig. 1(a), a standard TCSPC module (SPC 130, Becker & Hickl GmbH) was used. The “Start” port of the TCSPC module was synchronized with the laser triggering signal, while the “Stop” port was triggered by the amplified avalanche signals. All the measurements reported in this paper were taken when the TCSPC module was configured with a time resolution of 8 ps (FWHM).

Since timing jitter is a strong function of detector bias voltage conditions, detector temperature, as well as the spatial position of the photon absorption in the detector, as has been observed in a silicon Geiger mode single-photon detector.^[24] Therefore, we fixed the temperature of the detector to −30 degrees Celsius and investigated the timing response only by changing the applied DC bias voltage. On the other hand, the timing jitter improves by reducing the threshold voltage of the timing discriminator of the TCSPC module.^[26,27] In our measurements, the threshold voltage was set to −33 mV. Because the avalanche signals were inverted before leading to the timing discriminator. Figure 2(a) presents the timing jitter as a function of the excess bias voltage (V_ex). As shown in the inset of Fig. 2(a), the V_ex is the voltage that exceeds the avalanche breakdown voltage (V_B) of the APD and adjusted by changing the V_DC from 0.2 V to 4.2 V in 0.2-V step. From Fig. 2(a) we can see that the timing jitter of the detector firstly increases at low V_ex (0.2 V–0.8 V). Then the timing jitter decreases with further increasing V_ex (1 V–2.8 V). Finally, the timing jitter increases again at high V_ex (3 V–4.2 V). The best jitter of 93 ps was achieved with a detection efficiency of 21.4% at the V_ex of 2.8 V. Figure 2(b) shows a typical normalized timing jitter histogram recorded by the TCSPC module at an excess bias of 2.8 V, corresponding to a PDE of 21.4%. From the histogram a timing jitter of 93 ps (FWHM) can be determined.

Fig. 2.

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	Fig. 2. (a) Bias-dependent timing jitter of the 1-GHz sinusoidally gated InGaAs/InP APD single-photon detector. (b) Normalized instrumental response of the system with 93 ps (FWHM) at the Vex of 2.8 V, and the PDE is 21.4%.

It has been reported that the timing jitter decreases with increasing avalanche mean propagation speed.^[24] The mean propagation speed of the avalanche is given by

To verify our explanation for the timing jitter performance in the 1-GHz sinusoidal gating scheme, we performed the similar timing jitter measurements on the same InGaAs/InP APD except that the 1-GHz sinusoidal gating was replaced by the 20-MHz pulse gating. The pulse gating with an amplitude of 3 V was generated by a function generator (AFG3022C) and the T_g was set to 16 ns, 20 ns, and 24 ns, respectively. In order to extract the weak avalanche signals buried in the gating spike noise, we used the self-differencing technique which is based on subtracting the output signal of the APD from a replica delayed by exactly one gate period.^[18] In our experiment, the APD output was divided into two equal components with a 50/50 power spliter (Mini-circuits, ZAPD-2-252-S+), which were then subtracted by a power combiner (Mini-circuits, ZFSCJ-2-1-S+). The coaxial cables connecting the spliter and the combiner have different lengths to induce a delay of one gate period (50 ns). Thus, the avalanche signals can be obtained at the output of the power combiner. The avalanche signals were then amplified and sent to the TCSPC module. Compared to the sinusoidal gating, the T_g in the pulse gating is invariable when the V_ex is increased, as shown in the inset of Fig. 3. The dependence of the timing jitter of the pulse gated detector on the V_ex is shown in Fig. 3. As has been demonstrated in previous research, the jitter reduces with increasing V_ex.^[21,23,24] Moreover, at low V_ex, the jitter reduces quickly, while at high V_ex the decrement reduces, maybe due to a saturation effect in V_p. On the other hand, for the same V_ex, the longer the gate-on time, the larger the timing jitter. In addition, compared to the timing jitter in the 1-GHz sinusoidal gating detector, the jitter in the pulse gating scheme significantly increases. These results manifestly demonstrate that a wider gate-on time is likely to result in a larger timing jitter.

Fig. 3.

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	Fig. 3. Bias-dependent timing jitter of the 20-MHz pulse gated single-photon detector with the same InGaAs/InP APD when the gate-on time is 16 ns, 20 ns, and 24 ns, respectively.

To evaluate the whole performance of the 1-GHz sinusoidal gating detector, it is necessary to introduce the noise equivalent power (NEP). The NEP is a useful figure of merit for photon-counting detectors because it incorporates both detection efficiency and dark count probability. The equation used to calculate the NEP is given by^[28]

Fig. 4.

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	Fig. 4. (a) Photon detection efficiency and dark count rate as a function of excess bias voltage. (b) Noise equivalent power versus excess bias voltage. The dashed horizontal lines denote the range of noise equivalent power at low Vex. The inset graph shows the Pap performance with the increased Vex.

In this paper, we report on the dependence of the timing jitter on the excess bias voltage (V_ex) of 1-GHz sinusoidally gated InGaAs/InP APD single-photon detector. It is found that the jitter increases at low and high V_ex, while it decreases at middle V_ex. By taking further timing jitter measurement of the same InGaAs/InP APD with pulsed gating, we conclude that this effect is likely related to the increase of both the V_ex amplitude and the width of the gate-on time (T_g).

According to our explanation, at low (0.2 V–0.8 V) and high (3 V–4.2 V) V_ex, the main contribution to the increase of the timing jitter is the increasing width of the T_g. While at middle V_ex (1 V–2.8 V), the increasing of the V_ex plays a dominant role in reducing the timing jitter by accelerating the avalanche buildup. The best timing jitter of 93 ps is achieved at the V_ex of 2.8 V. Under this condition, the dark count rate is ∼2.08×10⁻⁵ per gate and the photon detection efficiency is 21.4%. We also calculate the noise equivalent power (NEP) and the afterpulse probability (P_ap). The results indicate that the NEP is relatively constant at small V_ex that is less than 2.8 V, while it quickly rises when the V_ex is increased above 3 V. A NEP of ∼2.06×10⁻¹⁶ W/Hz^1/2 is achieved at 2.8-V V_ex. Coincidentally, the P_ap is also increased quickly when the V_ex is beyond 2.8 V. At 2.8-V V_ex, the P_ap is 7.11%. Therefore, it would be beneficial to operate this detector at an excess bias of 2.8 V to exploit the fast time response, low NEP and low P_ap. They are 93 ps, ∼2.06×10⁻¹⁶ W/Hz^1/2 and 7.11%, respectively. Besides, the photon detection efficiency is 21.4% with the dark count rate of ∼2.08×10⁻⁵ per gate.