## Abstract

We demonstrate 1 GHz count rate photon detection with photon number resolution by using a multi-pixel photon counter (MPPC) and performing baseline correction. A bare MPPC chip mounted on a high-frequency circuit board is employed to increase response speed. The photon number resolving capability is investigated at high repetition rates. This capability remains at a repetition rate of 1 GHz and at rates as high as an average of 2.6 photons detected per optical pulse. The photon detection efficiencies are 16% at λ = 450 nm and 4.5% at λ = 775 nm with a dark count rate of 270 kcps and an afterpulse probability of 0.007.

© 2012 OSA

## 1. Introduction

Multipixel silicon avalanche photodiodes, referred to as silicon photomultipliers (SiPMs) or multi-pixel photon counters (MPPCs), are photon detectors with high count rates, fast time response, large detection area, large detection dynamic range, and photon-number resolving capability. SiPMs were originally produced for use as high-sensitivity infrared photo detectors, and subsequently, have been further developed as an alternative to photomultiplier tubes to detect scintillation light for high-energy physics and for medical applications, such as positron emission tomography [1–5]. The applications of SiPMs have expanded rapidly to include fluorescence detection [6], Raman spectroscopy [7], and single-photon bio-imaging [8]. Recently, a photon count rate as high as 430 MHz has been demonstrated, opening up new applications, such as quantum cryptography, quantum random number generators, and photon counting reflectometry [9]. The photon number resolving capability of SiPMs at high count rates, however, has not been demonstrated [9,10]. SiPMs could be used for wider applications in, for example, quantum optics, if its photon number resolving capability at higher count rates is realized.

Self-differencing InGaAs avalanche photodiodes (SD InGaAs APDs) and parallel superconducting nanowire single-photon detectors (P-SNSPD) are the other photon number resolving detectors with high count rates [10, 11]. The SD InGaAs APD has a count rate of 497 MHz as a single photon detector [12], but has not achieved count rates of more than 100 MHz as a photon number resolving detector [10, 11]. The count rate of P-SNSPDs, which has the potential to be improved to 1 GHz [10], is 80 MHz at present [13].

The maximum count rate of SiPMs is determined by several factors, including number of pixels and timing characteristics, such as jitter, rise time, and dead time [14]. Small pixel-size detectors are effective for improving the characteristics mentioned above. SiPMs comprise several self-quenching Geiger-mode APD pixels in parallel [15–17]. Each APD pixel is inactive during the dead time after avalanche breakdown. When photons are incident on the SiPM within the dead time, the number of active pixels is reduced. This reduction causes lower photon detection efficiency (PDE) at higher count rates [18, 19]. The reduction of the PDE can be improved by increasing the number of pixels and decreasing the dead time. The smaller pixels have smaller capacitance, resulting in shorter dead time and shorter rise time, and the detector with smaller pixels has a larger number of pixels for the same effective area. SiPMs have dead space between pixels, where photons are not detected. The detector with smaller pixels has lower PDE due to larger dead space, but the improvements in PDE caused by the use of smaller pixels exceed the reduction of PDE at higher count rates. Total effective area also influences the timing characteristics. A larger total effective area increases rise time and dead time [14]. In light of the above issues, we adopted a SiPM design with a smaller pixel size and an effective area of 1 mm^{2} for GHz count rate operation.

Another problem to be resolved when operating SiPMs at high count rates is the long decay tail of the output signal [9]. The tail of the signal, which typically has decay rates from several nanoseconds to several tens of nanoseconds at room temperatures, would add up at high count rates. In such cases, the signal level gets higher with each detection and experiences large fluctuations corresponding to the variations of the detection timing and the number of detections. A high-pass filter is used to eliminate the long tail effect [9]. The fluctuation, however, remains considerable with the high-pass filter [9]. To alleviate these problems at GHz count rates, we employed baseline correction to calculate the pulse heights. In this paper, we report on methods for baseline correction and the photon-number resolving capability of the SiPM operated at high count rates.

## 2. Experimental setup

The experimental setup for the measurements of the photon number resolution at high repetition rates is shown in Fig. 1
. We have used a multi-pixel photon counter (MPPC, Hamamatsu S10362-1125U) for high count rate photon detection. The pixel size and the number of pixels of the MPPC are 25 μm × 25 μm and 1600, respectively, and the effective area is 1 mm^{2}. The self-inductance of a lead wire of the MPPC device package is estimated to be a few nH. An inductance of this size may increase the rise time of the MPPC output signal [14]. Therefore, we used a bare MPPC chip to remove the self-inductances of the lead wires of the device package. The bare MPPC chip and a preamplifier were mounted on a high-frequency printed circuit board. The preamplifier was composed of a common source circuit with a GaAs high electron mobility transistor (HEMT), positioned just behind the MPPC, and a shunt resistor of 50 ohms. A low pass filter of 1.8 GHz was used to reduce the electrical noise of the amplifiers. The signal from the MPPC was acquired by using a high-speed oscilloscope (Tektronix TDS7400).

High repetition rate pulse trains at a wavelength to which the MPPC is sensitive were obtained by upconversion of 1550 nm light to 775 nm light. First, 1550 nm continuous-wave light from a laser diode was modulated into a high repetition rate pulse train using an optical intensity modulator, and the pulses were fed into an optical amplifier followed by a second-harmonic generator (SHG). The width of the optical pulses was 0.1 ns. Then, the light from the SHG was passed through an optical band-pass filter and a fiber-coupled variable attenuator, and finally the beam injected from the attenuator was adapted to the size of the MPPC by a focusing lens. The number of photons detected per optical pulse was controlled through the optical amplifier setting. The printed circuit board with the MPPC was placed in an aluminum box to block ambient light.

All of the following measurements were performed at a bias voltage of 71.7 V, where afterpulse and cross-talk probabilities are sufficiently low and the photon detection efficiency is not too small. This bias voltage corresponds to an overvoltage of 1.9 V, which is the difference between the breakdown voltage and the bias voltage. The measured characteristics at this bias voltage are listed in Table 1 . Detailed descriptions of the methods used to obtain the parameters listed in the table and of the measurement setup are provided in Ref. 19. We use continuous-wave light from a 450-nm LED at a count rate of 10 Mcps for the measurements of the afterpulse probability and the photon detection efficiency at a wavelength of 450 nm, and we use a pulsed laser source at a repetition rate of 10 MHz at a wavelength of 407 nm for the measurement of the cross-talk probability. For the measurements of the photon detection efficiency at a wavelength of 775 nm, we used the same light source as for the high repetition rate measurements at a repetition rate of 10 MHz. To determine the cross-talk probability, it is assumed that a pulse generated by cross-talk does not generate another cross-talk pulse [19]. The dark count rate includes the afterpulses but not the cross-talk events.

## 3. Measurements and data analysis

Figure 2 shows the averaged signal pulse profile for 100 single-photon events recorded by using the setup in Fig. 1. The decay time and the 10-90% rise time of the pulse are 7.5 ns and 370 ps, respectively. The oscillations on the peak are clearly due to the preamplifier and the high frequency amplifier, because the profile of the oscillations differed when a different amplifier was employed. The other part of the tail is possibly distorted with respect to the waveform of the MPPC output due to the amplifiers.

A schematic of the response to optical pulses at a high repetition rate (0.67 GHz) is shown in Fig. 3
. The decay time of the tail of the signal pulse in Fig. 3 is set to be 7.5 ns. Since signal pulses add upon the tails of the previous signal pulses, baseline correction is necessary to determine the pulse heights of the individual signal pulses. We employed second-order finite differences for the baseline correction. Figure 3 describes the baseline correction by using second-order finite differences. When the decay time scale is sufficiently long compared to the time interval that is needed to obtain the pulse height, the tail is well-approximated by a straight line. The differentiation time Δ*t* used here is 0.5 ns. Then the time interval needed is 1 ns, which is sufficiently small compared to the decay time scale of 7.5 ns (see Fig. 3). In this case, the correction value for the pulse height estimation would be obtained from a voltage difference in the tail just before the rising edge of the signal pulse. Consequently, the pulse height at a time *t _{p}*,

*VH*, is expressed as the second-order finite difference, $\begin{array}{c}V{H}_{p}=V({t}_{p}+\Delta t)-V({t}_{p})+V({t}_{p}-\Delta t)-V({t}_{p})\\ =V({t}_{p}+\Delta t)-2V({t}_{p})+V({t}_{p}-\Delta t).\end{array}$ where

_{p}*V*(

*t*) is the signal voltage at a time

*t*and

*t*marks the onset of the pulse (see Fig. 3). To simulate real-time operation, output signals should be expressed as signals from a two-stage self-differencing circuit (see Discussion). In this case,

_{p}*VH*is a function of time

*t*,

Figure 4 shows the output signals calculated by the above equation from the data sets in which intensities of optical pulses are sufficiently high so that the probabilities of photon detection per optical pulse are above 0.9 at high repetition rates. A signal pulse height can be obtained from the peak value of a pulse in Fig. 4. The signal pulse height distributions at repetition rates from 0.1 GHz to 1 GHz are depicted in Fig. 5 . The pulse heights have offsets due to thebaseline correction. The offset values at each condition are different, and are within 20 mV for all the pulse height distributions below. The average number of photons detected per optical pulse for each distribution in Fig. 5 is approximately 2.6, taking the cross-talk probability into account. The photon number resolution deteriorates rapidly with increase in the repetition rate, and is lost at a repetition rate of 1 GHz. This is mainly because the error of the pulse height correction by second-order finite differences becomes larger due to the distortion of the pulse profile, timing jitter, and the fluctuation of the rise time of the pulse. Since the only controllable parameter is the differentiation time, the further correction for the signal issues ofjitter, noise, and other distortions cannot be carried out in this method beyond improvements of these signal issues themselves.

Additional data were obtained at a lower optical amplifier setting. The resulting pulse height distributions, with an average photon number of approximately 1, are shown in Fig. 6 . The photon number resolutions are found to be improved as a whole. The reason for the improvement will be discussed below.

Next, we analyze the data with another method to improve the photon number resolution. In Fig. 7a
, the corrected method for obtaining the pulse height is described. Here the height of the *i*th signal is to be determined. The slope of the baseline of the *i*th signal can be estimated from the slope of the tail of the *i*-1th signal by fitting a straight line to the tail. One problem in estimating the slope of the tail is timing jitter. Figure 8
plots the timing jitter for single-photon detection, including optical pulse width (0.1 ns) and electronic timing jitter. The signal timing is occasionally delayed by a considerable amount. If the interval between the *i*-1th and *i*th signals becomes significantly shorter due to timing jitter (illustrated by the dashed green line in Fig. 7a), the slope value in the interval to fit the straight line to the tail may be larger than the proper value because the fitting interval was set to be constant (see the solid green line in Fig. 7a). The reasons for using constant fitting-intervals will be described in the Discussion section. To mitigate this error, the slope of the tail of the *i*th signal can be used (the blue line in Fig. 7a), instead of the slope of the tail of the *i*-1th signal. The slope of the tail of the *i*th signal, however, would also be affected by a shorter interval between the *i*th and *i* + 1th signals (depicted by the dashed orange line in Fig. 7a).

This situation is the same for the presence of noise signals and the fluctuation of the rise time. Noise signals and longer rise times make the fitted tail slope values larger (see Fig. 7b, c). On the other hand, shorter rise times do not make the fitted tail slope values smaller. That is, all the effects mentioned above result in larger fitted tail slope values. Therefore, selecting the lower of the two fitted slope values between the *i*th and *i* + 1th slopes minimizes the contributions of noise and other fluctuations. The equation that we propose to determine the signal pulse height is

*t*is the peak time of the

_{i}*i*th pulse,

*a*is the slope value of the

_{i}*i*th fitted straight line. The factors

*k*

_{1}and

*k*

_{2}are introduced to Eq. (2) in order to correct the difference between the fitted tail slope value and the baseline slope value. In the following analysis, the factors were set soas to make the photon number resolution highest at each repetition rate while Δ

*t*was set to 0.5 ns at all repetition rates.

The pulse height distributions in Fig. 9 were calculated by Eq. (2) using the same data set as that used in Figs. 5 and 6. The photon number resolution is found to be improved with respect to the results of the original method, shown in Figs. 5 and 6. Figure 10 shows the deterioration of the resolution as a function of the number of detected photons at a repetition rate of 1 GHz. The resolution decreases rapidly with increasing photon number, and is lost when the average number of photons detected exceeds 3.

## 4. Discussion

The deterioration of the photon number resolving capability is caused by an increase in the variation of the pulse height. The increase in the variation of the pulse height occurs in the calculation of the pulse height for the following reasons. First, there is an error associated with the fitted tail slope values due to the electrical noise. Second, although the factors *k*_{1} and *k*_{2} are set to be constant in the calculation of the signal pulse height for each set of experimental parameters, the optimum factors may vary from shot to shot because of the distortion due to exponential tails. When the distortion exists, the optimum factors are functions of the signal pulse position on the tail of a previous signal pulse. Since the signal pulse position fluctuates due to the timing jitter, the optimum factors can vary with the position. At high repetition rates, a fitted tail slope value results from a superposition of tail slopes of the previous signal pulses. This means that the factors are a weighted average of each factor corresponding to the signal pulse position on the tail of a previous signal pulse. Since the weight for each factor is proportional to the slope value and the slope values as a whole increase with the average number of photons detected per optical pulse, the weight varies with the fluctuation of the number of photons detected which follows a Poisson distribution. Therefore, the variation of the factor will be increased at large detected photon counts. Furthermore, at repetition rates close to 1 GHz, the interval where the slope is fitted inevitably contains the large distortion following the rising edge of the signal. For these reasons, the variation of the pulse height rapidly increases with repetition rate close to 1 GHz.

The factors *k*_{1} and *k*_{2} also become functions of the fitting interval due to the distortion. When the fitting interval is below the time scale of the distortion, optimum factors greatly fluctuate with the fitting interval and the pulse position. Furthermore, a shorter fitting interval causes larger fluctuation of the fitted tail slope values because of the electrical noise. In fact, when the fitting interval is varied using the slope of one side of the signal pulse while keeping the factors constant, the photon number resolution deteriorates compared to that using Eq. (2). Although the factors can be varied as functions of the fitting interval, the pulse position, and the heights of the previous pulses, the amount of calculation required will considerably increase.

The second-order finite difference method has little ability to correct the deterioration of the photon number resolution caused by the signal issues, but has the potential to make real-time operation possible. This is because the second-order finite differences could be realized by using a two-stage self-differencing circuit as follows: An output signal from a self-differencing circuit, Δ*V*(*t*), is represented by a finite difference of an input signal, *V*(*t*), $\Delta V(t)=V(t)-V(t-\Delta t).$

An output from a two-stage self-differencing circuit, Δ^{2}*V*(*t*), is then expressed as a finite difference of Δ*V*(*t*), $\begin{array}{c}{\Delta}^{2}V(t)=\Delta V(t)-\Delta V(t-\Delta t)\\ =(V(t)-V(t-\Delta t))-(V(t-\Delta t)-V(t-\Delta t-\Delta t))\\ =V(t)-2V(t-\Delta t)+V(t-2\Delta t).\end{array}$

The right side of this equation is identical to that of Eq. (1), when *t* -Δ*t* is replaced by *t*.

## 5. Conclusion

We have demonstrated the operation of a multi-pixel photon counter at a 1 GHz count rate by reducing the rise time of the signal of the detector. A bare MPPC chip mounted on a high frequency printed circuit board is used to remove self-inductances of the lead wires of the device package, reducing the rise time. The pulse height distributions at high repetition rates were obtained by performing two types of baseline corrections to the signal from the MPPC. One is a second-order finite difference method. This method demonstrates the possibility of real-time operation of the photon number resolving detector at a repetition rate of 1 GHz because the second-order finite differences could theoretically be realized by using a two-stage self-differencing circuit. However, the photon number resolution in this method becomes poor at repetition rates close to 1 GHz due to the timing jitter, the fluctuation of the rise time, electrical noise, and the waveform distortion of the tail from the linear interpolation.

The resolution is improved by another method in which the baseline correction for the signal was performed by fitting a straight line to the slope of the tail near the rising edge of the pulse. The photon number resolving capability of the MPPC in this method is found to be maintained up to an average of 2.6 photons detected per optical pulse and at a repetition rate of 1 GHz. In this method, the main factor that limits the resolution is the waveform distortion of the tail from an exponential function due to the amplifiers.

## Acknowledgments

This work was supported by the National Institute of Information and Communication Technology (NICT) under the Ministry of Internal Affairs and Communications of Japan. We also would like to thank K. Sato (Hamamatsu photonics K.K.) for technical support.

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